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A Novel Compartmental Model for the Mathematical Epidemiology of Addiction: Backward Bifurcation, Bistability, Persistence, and Treatment-Capacity Policy Implications

This paper develops a novel four-compartment epidemiological model for addiction dynamics that demonstrates how treatment-capacity saturation, rather than incidence saturation, uniquely drives backward bifurcation and bistability, creating a critical policy gap where the basic reproduction number fails to capture the risk of long-term persistence even below traditional thresholds.

Milad tahavor, Reza Memarbashi, Khashayar Ashkboos, Mohammad Mehdipour Zarrinkamar2026-08-25

🔢 mathematics

Synchronization of Sections With Homologous Initial Conditions on Connected Manifolds: A Lie Derivative Criterion

This paper establishes a coordinate-free Lie derivative criterion for the synchronization of fiber bundle sections with identical internal dynamics on connected manifolds, proving that vanishing Lie derivatives of section differences imply flow-equivariant diffeomorphism without requiring Laplacian diagonalization or a drive-response setup.

daqian chen2026-08-25

🔢 mathematics

On holomorphic retracts of polyballs with strictly convex factors and applications

This paper characterizes holomorphic retracts through the center of polyballs with strictly convex factors as either biholomorphic to linear retracts of individual factors or products thereof, a result that establishes the essential uniqueness of their product representations by proving they cannot be biholomorphically equivalent to other product domains with differing factor counts or dimensions.

Balakumar G. P., Jiju Mammen2026-08-24

🔢 mathematics

A Complementary Assignment Method for Delaying Group-Stage Rematches in the FIFA World Cup 2026 Knockout Bracket

This paper proposes a modified assignment method for the FIFA World Cup 2026 knockout bracket that treats the allocation of third-place qualifiers as a capacitated bipartite matching problem to ensure that no two teams from the same group meet before the semi-finals, thereby improving fairness and tournament appeal compared to the official schedule which fails this condition in 70 out of 495 scenarios.

Badr Boutaleb Joutei, Mourad Raif2026-08-24

🔢 mathematics

When Are AI Explanations Recoverable? Identifiability, Stability, and Transfer from an Inverse-Problem Perspective

This paper establishes a mathematical framework for determining the recoverability of AI explanations by formulating them as inverse problems, deriving a complete trichotomy of identifiability and stability conditions for linear and nonlinear systems, and providing explicit bounds that distinguish intrinsic underdetermination from algorithmic variability.

Chibuike Chiedozie Ibebuchi2026-08-24

🔢 mathematics

Backward One-Step Block Hybrid Numerical Method for Solving Second-Order Initial Value Problems

This study introduces a robust and accurate backward one-step block hybrid numerical method, derived via multistep collocation with Chebyshev polynomials, to effectively solve stiff-oscillatory second-order initial value problems.

OLUWADAMILOLA FAGBOHUN, Olabode B.T., Abidemi A., Momoh A. L.2026-08-24

🔢 mathematics

Regularization and Stability-Bifurcation-Chaos Trilogy for Caputo Fractional Replicator Dynamics with Global Lipschitz Guarantees

This paper introduces a regularized three-dimensional Caputo fractional replicator system with emotional factors that resolves the inherent singularity at the origin, establishes global Lipschitz continuity, and analytically characterizes the complete dynamical transition from stability to chaos through Hopf bifurcation and chaos certification, all validated against unregularized models and empirical behavioral data.

Tongxing Li, Yongfeng Zhang, Xiaodong Zhao, Jianzhong Zhang, Chengdai Huang2026-08-23

🔢 mathematics

A Layered Lean 4 Library for Finite-Dimensional Quantum Foundations with Typed Premise Auditing

This paper presents a layered Lean 4 library for finite-dimensional quantum foundations that formalizes key representation theorems and complexity results while introducing a typed premise-audit framework to verify the coherence and validity of conditional mathematical theorems, such as the independence of subspace weights from orthogonal decompositions.

Bertrand Dalimier2026-08-20

🔢 mathematics

A Certified Interval Method for the Distance from a Point to an Ellipse

This paper presents a certified, seed-free interval algorithm that rigorously computes the Euclidean distance from a point to an ellipse by isolating roots of a quartic equation across dual parameterizations, ensuring guaranteed enclosure bounds without relying on heuristic seeds even in ill-conditioned cases.

Peilin Luo2026-08-19

🔢 mathematics

On the Design of St. Peter’s Square in Rome

This paper investigates and supports the hypothesis that Gian Lorenzo Bernini designed the three ovals of St. Peter's Square by modifying the radii of two primary "generating circles," a method that aligns with the square's actual dimensions and historical use of the *ovato tondo*.

Jean-Marc GINOUX, Jean-Claude Golvin, Riccardo Meucci2026-08-18

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