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A Petrov-Galerkin Quintic B-Spline Model for Nonlinear Wave Dynamics in the Time-Fractional Benney-Lin Equation

This paper presents an accurate and stable numerical framework for solving the time-fractional Benney-Lin equation by combining a Petrov-Galerkin finite element method with quintic B-spline basis functions for spatial discretization and the Grünwald-Letnikov definition for temporal fractional derivatives, effectively capturing nonlinear wave dynamics and memory effects through comprehensive error analysis and numerical experiments.

Moutaz Ramadan, Hayah Samy2026-07-13

🔢 mathematics

Controlling the Condition Number of Multiquadric RBF Matrices via Poisson Disk Sampling

This paper demonstrates that imposing Poisson disk sampling constraints on interpolation centers allows for the minimization of the condition number of Multiquadric Radial Basis Function matrices to a constant value independent of the number of points, thereby ensuring numerical stability through an adaptive relationship between the minimum inter-point distance, the shape parameter, and the total number of points.

João Rogério da Silva2026-07-13

🔢 mathematics

Lyapunov Integrability Test (LIT): a numerical framework for exploring integrability in continuous dynamical systems

The paper introduces the Lyapunov Integrability Test (LIT), a novel and efficient numerical framework that utilizes global Lyapunov exponent analysis to identify candidate integrable regimes in nonlinear dynamical systems, a method validated across diverse benchmark examples ranging from fluid flows to mechanical systems.

Wojciech Szumiński2026-07-13

🔢 mathematics

Bipolar Linguistic Z-Number Framework for FMEA Integrating BWM, CRITIC, and MABAC

This paper introduces a Bipolar Linguistic Z-Number (BLZ-Number) framework that unifies positive/negative assessments with linguistic reliability to enhance Failure Mode and Effects Analysis (FMEA) through a novel integration of BLZ-BWM, BLZ-CRITIC, and MABAC methods for more expressive and reliable risk evaluation.

Rıdvan Şahin, Elif Başkan, Ahmet Emir Köse2026-07-13

🔢 mathematics

Extended and Entanglement-assisted Quantum Quasi-twisted Codes

This paper introduces a novel approach utilizing one-generator quasi-twisted codes of index 3 and their extended versions to construct binary stabilizer quantum codes and maximal-entanglement entanglement-assisted quantum codes with improved and optimal parameters.

Akram Saleh, Mohammad Reza Soleymani2026-07-10

🔢 mathematics

Limit theorems for supercritical Mandelbrot's cascade in a random environment

This paper establishes a Fourier analytic framework for supercritical Mandelbrot cascades in a random environment to prove the existence of harmonic moments, demonstrate the exponential decay of characteristic functions, and derive refined limit theorems including improved central limit theorems, Edgeworth expansions, and a renewal theorem for $\log Y_n$ .

Yingqiu Li, Yanan Sun, Xin Zhang, Hailong Yang2026-07-10

🔢 mathematics

Variance component estimation in linear ill-posed models via null-space projections

This paper proposes a regularization-free variance component estimation framework for linear ill-posed models that utilizes null-space projections to eliminate unknown parameters and estimate variances directly from unbiased misclosures, thereby overcoming the bias, instability, and computational inefficiency inherent in conventional regularization-dependent approaches.

Kunpu Ji, Yunzhong Shen, Wu Chen, Xiaolong Mi, Bofeng Li, Qiujie Chen2026-07-10

🔢 mathematics

Auditing Generative AI Error Patterns in Applied Differential Calculus: Evidence from ChatGPT and Gemini

This descriptive-evaluative study audits ChatGPT and Gemini's performance in applied differential calculus, revealing that while both models can execute isolated procedures, they frequently fail in translating narrative conditions to functions, handling boundary constraints, and maintaining arithmetic consistency, thereby suggesting their solutions should be used as critique artifacts rather than unquestioned answers in education.

Polemer M. Cuarto2026-07-10

🔢 mathematics

Complexity Reveals the Microscopic Origins of Macroscopic Dynamics

This paper demonstrates that spectral localization in complex networks fundamentally shifts the understanding of macroscopic dynamics from global eigenmodes to the local behavior of dominant nodes, thereby enabling a node-resolved framework that identifies microscopic drivers and predicts transitions in heterogeneous systems where classical stability theories fail.

Malbor Asllani, Haoyang Qian, Gabriel Hood, Beata Casiday2026-07-10

🔢 mathematics

Multiscale analysis and homogenization of nonlocal thin films

This paper introduces a nonlocal variational model for thin films and establishes the $\Gamma$ -convergence of convolution-type functionals to a local integral functional on a lower-dimensional domain, characterizing the limit energy density through an asymptotic formula that reveals a scale separation effect under periodic homogenization.

Nadia Ansini, Antonio Tribuzio2026-07-09

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