🔢 Category

math

273 papers

🔢 mathematics

Structural Construction of the Uniqueness Statement for the Riemann Hypothesis A Chain Map between the Additive and Multiplicative Sides, a Well-Defined Obstruction Functional, and a Spectral Uniqueness Theorem

This paper presents a structural framework that isolates the Riemann Hypothesis as a single, computable existence problem regarding the positivity of the Li criterion and the vanishing of the de Bruijn–Newman constant, by demonstrating that while the additive and multiplicative presentations of the zeta function lack structural isomorphism, their numerical agreement and spectral uniqueness are anchored by a fixed critical line of Re s = 1/2 derived from independent arithmetic and analytic symmetries.

Yang Liu¹2026-10-09
🔢 mathematics

A scalar mean-square stability and variance test for a discrete feedback loop with random gain and delay

This paper derives a lossless, scalar inequality that exactly characterizes the mean-square stability and variance amplification of a discrete feedback loop with random gain and delay, reducing a computationally expensive n2n^2-dimensional spectral radius test to a simple calculation based on the mean loop's impulse response and the statistics of the uncertainty.

Petr A. Piatkov2026-10-08
🔢 mathematics

Scott sobriety via observative nets and countable test families

This paper provides a direct convergence proof for Scott spaces on directed-complete posets with binary joins, demonstrating that the existence of a countable family of directed tests for Scott openness ensures every observative net strongly converges to the supremum of its range, thereby characterizing Scott sobriety without relying on product identities, joint continuity, or countability of the poset itself.

Xiaoquan Xu2026-10-08
🔢 mathematics

Tracing Creativity in Mathematical Modelling: An Event-Level Learning Analytics Study of Modelling Processes

This study introduces a trace-to-context learning analytics workflow to capture event-level creativity in mathematical modelling, revealing that while high- and low-creativity students share a common transition backbone, the former exhibit enriched pathways involving interpretation and communication, with creative moves being highly sensitive to specific modelling stages.

wangda zhu, jiaxin yang, xi wu, hao guo2026-10-07
🔢 mathematics

Resource Percolation and Consensus Formation in Multiplex Research Networks

This paper proposes a mathematical framework using multiplex network analysis, Laplacian consensus dynamics, and percolation theory to demonstrate that effective resource mobilization and innovation in research organizations depend on bridging the "percolation gap" between a resilient but exclusive "Rich-Club" core and the peripheral actors to ensure signals permeate the entire ecosystem.

Evans Takyi Ankomah-Asare, Jacob T. Akunor, Korku Dzidzornu2026-10-06
🔢 mathematics

Exact Polynomial Annihilation in Weakly Singular Abel-Volterra Equations via Algebraically-Mapped Fractional Chebyshev-Lobatto Collocation

This paper introduces an Algebraically-Mapped Fractional Chebyshev-Lobatto (AMF-CL) spectral collocation scheme that utilizes a non-linear geometric diffeomorphism to absorb weakly singular Abel-type kernels into a smooth domain, thereby achieving exact polynomial annihilation and restoring infinite exponential convergence for Volterra integro-differential equations that traditionally suffer from algebraic order reduction.

Oboni Victor Atabo2026-10-06
🔢 mathematics

Certified Recovery of Nonlocal Proximity Components from Finite Curve Samples

This paper presents a certified algorithm that guarantees the recovery of the nonlocal proximity component structure of a unit-speed C² curve in R³ from finite samples by constructing a cubic Hermite interpolant, establishing deformation retraction between exact and interpolated sublevel sets under explicit sampling and error conditions, and providing a validated interval-arithmetic certificate for the required geometric regularity.

Yiting Wang2026-10-06