273 papers
This paper introduces Modular Phase Geometry as a finite arithmetic framework for semiprime residue states that combines exact character laws and product properties with virtual physics assays to demonstrate measurable structured signatures, while explicitly clarifying that the construction is not a factorization algorithm nor a claim of physical fundamentality.
This paper constructs scalar Koopman eigenfunctionals for exponentially attracting periodic orbits in semilinear parabolic semiflows by deriving them from dominant Floquet multipliers via a direct Laplace-limit argument on isochron sections, extending them to continuous time, and analyzing their behavior regarding phase-frequency shifts and the topological obstructions caused by negative multipliers.
This paper establishes optimal lower bounds for the first threshold time of semilinear parabolic equations by combining classical extremal extensions of sparse, bounded-error spatial observations with scalar comparison equations, while explicitly linking the required sensor density to the metric -center problem and validating the approach through one-dimensional and industrial geometry examples.
This paper establishes a converse to the Bergman--Bieri--Groves theorem in dimension one and provides a broader criterion for the algebraicity of closed analytic subvarieties in by proving that those with finite rational logarithmic limit sets and finite logarithmic type are necessarily algebraic.
This paper establishes a sharp geometric inclusion theorem showing that the Steiner symmetral of a planar convex body contains a canonical rhombus with specific diagonal dimensions, which is then utilized to derive a scale-invariant inequality for Newtonian capacity.
This paper provides a comprehensive dynamical analysis of the Clifford attractor using various bifurcation, stability, and chaos detection techniques to characterize its rich behaviors and demonstrates its novel applicability in addressing modern economic challenges.
This paper proposes a unified magnitude–extent measurement framework that quantifies phenomena by determining the maximal level of a quantity sustained over a specific domain extent, thereby integrating diverse indices across fields such as physical activity, bibliometrics, and environmental monitoring while clarifying the impact of scale and resolution on their interpretation.
This paper establishes that pointwise monotonicity, a local dynamical criterion distinct from energy stability, is preserved by the exact Allen-Cahn flow and fully implicit Euler method but often violated by widely used second-order energy-stable schemes, leading to artificial delays or incorrect pointwise increments even in the presence of active diffusion.
This paper establishes a thermodynamic interpretation of the fluctuation-free quadrature theorem, demonstrating how its hierarchical node expansion systematically recovers ensemble cumulants and response functions while enabling efficient high-dimensional integration and tracking phase transitions in solvable models.
This paper establishes a cross-parameter Ordered Farey Recursion that decomposes the shortest-completion profiles of rational balance languages via explicit index maps, revealing that their local dynamics correspond to classical Christoffel paths and their global structure yields universal completion spectra derived from unimodular coordinate transformations.