42 papers
This paper presents an efficient computational method combining boundary matrices, normal forms, and closed-form formulas to calculate low-degree integral magnitude homology for finite graphs, demonstrating its superior ability to distinguish nonisomorphic graph pairs compared to ordinary invariants through extensive analysis of standard families and small connected graphs.
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.
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.
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.
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.
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.
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 .
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.
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.
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.