math papers | Gist.Science

Boundary-Consistent L1–Legendre Spectral Approximation of Nonlinear Caputo Reaction–Diffusion Problems with Integral Constraints

This paper develops and verifies a boundary-consistent L1–Legendre spectral method for nonlinear Caputo reaction–diffusion equations with integral constraints, demonstrating that directly assembling the strong-form operator is essential to avoid error plateaus and achieve machine-precision convergence where conventional derivative stiffness formulations fail.

Álvaro H. Salas2026-09-23

🔢 mathematics

Information Fields and the Navier–Stokes Equations: A Rigorous Audit of a Three-Layer Framework

This paper rigorously audits a proposed three-layer framework for the Navier–Stokes equations, proving that its core two-potential reconstruction fails due to a non-absorbable defect term, a helicity obstruction, and a gradient-closure gap, while confirming that only the stochastic Lagrangian representation provides an exact encoding in all dimensions.

daqian chen2026-09-23

🔢 mathematics

A Discrete Combinatorial Yamabe Flow Operator for Grayscale Image Structure Analysis: Curvature, Flow, and Conformal Enhancement

This paper introduces and theoretically analyzes a discrete combinatorial Yamabe flow operator for grayscale images that evolves piecewise-linear graph surfaces via conformal rescaling to concentrate curvature at genuine 2D singularities, demonstrating its utility for corner detection, structure-preserving smoothing, and sharpening while transparently acknowledging its performance limitations relative to state-of-the-art denoisers and the restricted scope of its evaluation due to computational constraints.

Md Hasibuzzaman, Gene Eu Jan, Chan-Yun Yang2026-09-22

🔢 mathematics

Texture Analysis for Heterogeneous Scientific Images: From Classical Descriptors to Learning-Based, Operator-Based, and Topological Methods

This survey reviews and categorizes a wide range of classical, learning-based, operator-based, and topological texture analysis methods by their underlying assumptions and information preservation capabilities, using digital rock physics to demonstrate how these choices critically impact the characterization of heterogeneous media properties like permeability and connectivity.

Naser Al-Khalayleh, Mohamed Jouini, Mokhtar Kirane, Laurent Najman, Fateh bouchaala2026-09-22

🔢 mathematics

Hybrid Neural and Numerical Inverse Identification of Fractional Memory and Regulatory Parameters in a Caputo Glucose Insulin Beta Cell Model

This paper presents a hybrid neural–numerical framework that combines sensitivity-based identifiability screening with a parametric neural surrogate to efficiently and accurately identify fractional-order memory and regulatory parameters in a nonlinear glucose–insulin–beta-cell model, achieving performance comparable to direct numerical inversion while significantly reducing computational costs.

Alvaro H. Salas, Gilder Cieza Altamirano2026-09-22

🔢 mathematics

Exact Admissibility and Spectral Ordering of Unequal-Order Four-Field Polynomial Discretizations for Free-Free Timoshenko Beams

This paper establishes an exact necessary-and-sufficient admissibility criterion and spectral ordering properties for unequal-order four-field polynomial discretizations of free-free Timoshenko beams, revealing how cross-field enrichment compensates for degree mismatches and demonstrating that stable finite-spectrum extraction requires specific coordinate choices and algebraic condensation to avoid sensitivity to polynomial representations.

Ming-Hung Li, You-Pei Li2026-09-22

🔢 mathematics

q-Mittag–Leffler Resolvents for Nonlinear Caputo q-Fractional Equations: Well-Posedness, Stability, and the q → 1− Classical Limit

This paper establishes the well-posedness and stability of nonlinear Caputo q-fractional equations by utilizing q-Mittag–Leffler resolvents and contraction arguments, while demonstrating their convergence to classical fractional dynamics as q approaches one.

Taylan Demi̇r, Mohammad Esmael Samei2026-09-22

🔢 mathematics

Nonlinear Nabla Caputo q-Fractional Difference Equations on Quantum Time Scales: Well-Posedness, Order Preservation, and the Classical q → 1− Limit

This paper establishes a well-posed nonlinear initial-value framework for Caputo-type q-fractional difference equations on quantum time scales, proving existence, uniqueness, and order preservation while demonstrating convergence to classical fractional dynamics as q approaches one.

Taylan Demi̇r, Mohammad Esmael Samei2026-09-22

🔢 mathematics

Fixed Point Results in Non-Linear (Θ, ℜm)-Rational type Contractive Mappings with Application in Fractional Differential Equations

This paper introduces non-linear (Θ, ℜm)-rational type contractive mappings on relation theoretic m-metric spaces to establish multi-valued fixed point results, which are then applied to prove the existence and uniqueness of solutions for Caputo fractional differential equations and approximated using shooting, homotopy perturbation, and matrix methods.

Muhammad Tariq, Mujahid Abbas, Saber Mansoor, Talat Nazir2026-09-21

🔢 mathematics

An Equidistant Truncated Euler--Maruyama Method for Nonlinear Time-Changed Stochastic Differential Equations

This paper proposes an equidistant truncated Euler–Maruyama method for solving nonlinear time-changed stochastic differential equations with superlinear growth, establishing a strong convergence rate arbitrarily close to $\min\{\beta_1, \alpha\beta_2, \alpha/2\}$ under polynomial growth, monotonicity, and Hölder regularity conditions.

Ruchun Zuo, Qian Guo2026-09-21

← Previous Next →