math papers | Gist.Science

A counterexample to the complex polynomial Koebe radius conjecture

This paper disproves the 2018 complex-coefficient polynomial Koebe radius conjecture by constructing a specific normalized cubic polynomial that is univalent on a neighborhood of the unit disk yet omits a point with a modulus strictly smaller than the conjectured radius, thereby establishing a strict separation between real and complex cubic Koebe radii and proving that degree three is the minimal degree for such a counterexample.

Aran S. Ziegler2026-10-26

🔢 mathematics

A novel parallel approach for solving some free boundary value problems

This paper presents a novel unified parallel framework for solving general obstacle and free boundary value problems by establishing theoretical convergence for both direct and indirect iterative methods, extending these approaches to higher dimensions via directional splitting and time-stepping, and validating their efficacy through applications in constrained quadratic programming and image deblurring.

Amboru Yalamanda, Peeyush Singh2026-10-23

🔢 mathematics

The Geometric Product of í µí² Vectors: a Grade-Spectrum Theorem, Exact Second Moments, and a Two-Scale Cut-off for Random Versors

This paper establishes a comprehensive geometric product theorem that expresses the squared coordinates and grade-wise energy distribution of Clifford algebra versors as determinants of their associated orthogonal maps, revealing deep connections to Krawtchouk transforms, spin-group reconstruction, and random walk mixing times on the orthogonal group.

Balasaheb B. Waphare2026-10-23

🔢 mathematics

Tandem Queues with Hybrid Abandonment in Heavy Traffic

This paper provides the first heavy-traffic characterization of a two-stage tandem queue with abandonment only in the first stage, proving that the second-stage queue length is asymptotically exponentially distributed and independent of the first stage by extending Markovian arrival process techniques to hybrid-abandonment systems.

Cameron Curtis, Izzy Grosof, Seyed Iravani2026-10-23

🔢 mathematics

Curse of Dimensionality: Bypassing via Chaotic Fractal Self-Similarity Invariant Mapping

This paper proposes a novel strategy to bypass the curse of dimensionality by utilizing Chaotic Fractal Self-Similarity Invariant Mapping based on the Kepler–Bouwkamp formula, demonstrating through theoretical proofs and numerical validation that computational complexity can remain independent of target dimension when structural self-similarity is preserved.

Zhang Karsa2026-10-23

🔢 mathematics

A Stimulated Arrival Multi-Server Markovian Queue With Differentiated Vacations

This paper presents a continuous-time Markovian model for a multi-server queueing system featuring state-dependent stimulated arrivals and a differentiated two-stage vacation policy, utilizing probability generating functions to derive long-run probabilities and performance measures for realistic service environments.

A. Kalaivani, B. Deepa, K. Vijaya2026-10-22

🔢 mathematics

Traveling waves in a cell-to-cell transmission model for the spread of viral infections

This paper establishes the existence and characterizes the profiles of traveling waves in a spatially discrete cell-to-cell viral infection model with distributed time delays, utilizing fixed-point arguments, phase-plane analysis of a reduced ODE system, and numerical simulations.

Yusuke Asai, Shingo Iwami, Yoshihisa Morita2026-10-22

🔢 mathematics

On reliable computing on the real numbers

This paper presents a computational framework based on Brouwer's intuitionistic view of the continuum, using asymptotic sequences of functions on unit interval partitions to approximate continuous functions and prove the Brouwer Continuity Theorem without relying on the Axiom of Continuity.

Stanislaw Ambroszkiewicz2026-10-22

🔢 mathematics

The initial condition as a decaying forcing: ageing and Lyapunov exponents of fractional maps

This paper demonstrates that fractional logistic and Hénon maps can be exactly reformulated as autonomous systems on memory modes to enable efficient computation of Lyapunov exponents, revealing that the initial condition acts as a decaying power-law forcing that induces a persistent, non-trivial memory of the starting state in chaotic regimes.

Stefano Fazzino2026-10-22

🔢 mathematics

A Two-Stage Finite Element Approach for High-precision Guaranteed Lower Eigenvalue Bounds

This paper proposes a new two-stage finite element algorithm that employs high-order elements on graded meshes to generate rigorous lower eigenvalue bounds as sharp as standard high-order upper bounds, effectively closing a long-standing gap in accuracy and significantly outperforming existing methods like Crouzeix--Raviart in terms of computational efficiency.

Xuefeng LIU, Michael Plum2026-10-21

← Previous Next →

math

A counterexample to the complex polynomial Koebe radius conjecture

A novel parallel approach for solving some free boundary value problems

The Geometric Product of í µí² Vectors: a Grade-Spectrum Theorem, Exact Second Moments, and a Two-Scale Cut-off for Random Versors

Tandem Queues with Hybrid Abandonment in Heavy Traffic

Curse of Dimensionality: Bypassing via Chaotic Fractal Self-Similarity Invariant Mapping

A Stimulated Arrival Multi-Server Markovian Queue With Differentiated Vacations

Traveling waves in a cell-to-cell transmission model for the spread of viral infections

On reliable computing on the real numbers

The initial condition as a decaying forcing: ageing and Lyapunov exponents of fractional maps

A Two-Stage Finite Element Approach for High-precision Guaranteed Lower Eigenvalue Bounds

The Geometric Product of í µí² Vectors: a Grade-Spectrum Theorem, Exact Second Moments, and a Two-Scale Cut-off for Random Versors