math papers | Gist.Science

Koopman Eigenfunctionals Associated with Floquet Multipliers of Attracting Periodic Orbits in Parabolic Semiflows

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.

Yuanchao Xu2026-09-10

🔢 mathematics

Sparse observations of semilinear parabolic equations: spatial maxima and threshold times

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 $N$ -center problem and validating the approach through one-dimensional and industrial geometry examples.

Uldis Strautins2026-09-09

🔢 mathematics

A Converse to the Bergman--Bieri--Groves Theorem

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 $(\mathbb{C}^*)^n$ by proving that those with finite rational logarithmic limit sets and finite logarithmic type are necessarily algebraic.

Mounir Nisse2026-09-09

🔢 mathematics

A Sharp Diameter–Area Rhombus Inclusion and Applications to Newtonian Capacity

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.

Juan Ignacio Guzmán2026-09-09

🔢 mathematics

Chaotic Dynamics of Clifford Attractors and its Application in Economics

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.

HIMANSHU BARANWAL, Shubham Maurya, Sishu Shankar Muni, A. K. B. Chand2026-09-09

🔢 mathematics

A Measurement Framework for Magnitude–Extent Indices

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.

Ren Zhang2026-09-09

🔢 mathematics

Pointwise Monotonicity of the Allen--Cahn Flow and Dynamical Limitations of Energy-Stable Schemes

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.

Pansheng Li, Dongling Wang2026-09-08

🔢 mathematics

Fluctuation-Free Quadrature and Thermodynamic Response Functions

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.

Ercan Gürvit2026-09-08

🔢 mathematics

Farey-Recursive Shortest Completions and Universal Spectra in Rational Balance Languages

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.

Alp Eren Bütün2026-09-08

🔢 mathematics

Graded L1-2-3 time stepping and adaptive tension splines for two-dimensional time-fractional reaction–diffusion equations

This paper proposes a high-order numerical method for two-dimensional time-fractional reaction–diffusion equations by introducing an adaptive tension spline spatial operator that selects optimal parameters based on local solution modes and a stable L1-2-3 time-stepping scheme on graded meshes, thereby achieving a temporal convergence order of approximately $4-\alpha$ while correcting misconceptions regarding fourth-order accuracy in existing non-polynomial spline literature.

Binod Kumar, Rishikesh Kumar, {Mani Bhushan Kumar, Deo Aryan2026-09-08