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A q-Legendre Operational Matrix Framework for the Schwarzian KdV Equation under Möbius Periodic Boundary Conditions: Spectral Accuracy and a Boundary-Induced Finite-Time Blow-up Diagnosis

This study introduces a q-Legendre spectral framework for solving the Schwarzian KdV equation under Möbius periodic boundary conditions, demonstrating spectral accuracy while diagnosing a genuine, boundary-induced finite-time blow-up mechanism distinct from numerical aliasing errors, with stability characteristics varying non-monotonically across parameter sets representing different atomic lattice structures.

Cenk KESAN2026-08-07

🔢 mathematics

Fourier series for Henstock-Kurzweil integrable functions

This paper establishes the convergence and localization of Fourier series for functions that are Henstock-Kurzweil integrable but not Lebesgue integrable due to singular behavior at the origin, provided they satisfy specific Dini-type or bounded-variation conditions.

Manuel Bello-Hernandez, Pablo Saenz-Lopez-Guerra2026-08-06

🔢 mathematics

Multi-sites fisheries modeling with Itô stochastic differential equations and stochastic optimization problem

This paper proposes a numerically efficient Itô stochastic differential equation model for multi-site fisheries utilizing Fish Aggregating Devices (FADs) and solves a corresponding stochastic optimization problem to maximize fishing profits by optimally controlling fishing efforts.

Sidy Ly, Mouhamadou A.M.T. Balde, Babacar M. Ndiaye2026-08-06

🔢 mathematics

A Nash-Game Approach to Elliptic Cauchy Data Completion with Robust Error Bounds in Practical Noisy Regimes

This paper proposes a Nash game formulation with Tikhonov regularization to solve the ill-posed elliptic Cauchy problem, establishing explicit, non-asymptotic error bounds for the reconstruction in practical noisy regimes without requiring additional spectral source-type assumptions.

Elyes Ahmed, Saber Amdouni, Amel Ben Abda2026-08-06

🔢 mathematics

Variable Smoothing for Weakly Convex Problems with Non-Euclidean Directions

This paper introduces MELMO, a Moreau envelope smoothing algorithm utilizing linear minimization oracles that achieves explicit convergence trade-offs and establishes $O(k^{-1/3})$ rates for composite stationarity in weakly convex optimization problems with non-Euclidean structures.

Farid Najar2026-08-06

🔢 mathematics

Coupling of Local and Nonlocal Problems Using Local Boundary Conditions

This paper presents a novel 1D coupling method for local and nonlocal diffusion problems that exclusively utilizes local boundary conditions to achieve a seamless, natural integration with quantifiable $O(h)$ convergence, verified through finite element and Galerkin projection discretizations.

Burak Aksoylu, Fatih Celiker, Patrick Diehl2026-08-05

🔢 mathematics

Geometry, Conditioning, and Parity in One-Sided Directional Curvature Recovery, with a Controlled Comparison of Estimators

This paper establishes fundamental theoretical limits on Hessian recovery from one-sided directional curvature measurements—including identifiability, conditioning, and parity constraints—and provides a rigorously controlled comparison of eight estimators under oracle-optimal sampling conditions.

RamaKrishna Pasupuleti2026-08-05

🔢 mathematics

Group-theoretic and equivalence-symmetry analysis of a susceptible–infected–AIDS HIV model

This paper distinguishes between genuine Lie point symmetries and equivalence transformations in a three-compartment HIV model, demonstrating that while only time translation is a true symmetry, rescaling parameters alongside populations yields an equivalence group that reduces the system to a dimensionless form while preserving its key dynamical properties.

Samuel Okon Essang2026-08-03

🔢 mathematics

Machine Learning the Phase Structure and Algebraic Invariants of Clifford- and Grassmann-Valued Cellular Automata

This paper demonstrates that machine learning techniques, including unsupervised clustering, supervised classification, and symbolic regression, can effectively uncover the phase structures, algebraic invariants, and transferable dynamical fingerprints of Clifford- and Grassmann-valued cellular automata, revealing how metric signatures and normalization protocols influence the emergence of order, chaos, and algebraic diversity.

fuat kaan mirza2026-07-31

🔢 mathematics

Steady-state bifurcation and pattern formation in an immune chemotaxis system with volume-filling effects

This paper investigates the steady-state bifurcation and pattern formation in a three-component immune chemotaxis model with volume-filling effects by establishing the existence, direction, and stability of nonconstant solutions and demonstrating how cellular crowding influences spatial dynamics.

Xiaoyan Gao, Yafei Yang, Liangying Miao2026-07-31

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