🔢 Category

math

273 papers

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Complex Probabilistic Neutrosophic Sets for Multi-Criteria Decision-Making: New Aggregation Operators and Comparative Analysis

This paper introduces the novel complex probabilistic neutrosophic (CPN) set to better capture expert opinion acceptance levels in uncertain real-life scenarios, proposes new weighted averaging and geometric aggregation operators, and validates a corresponding multi-criteria decision-making framework through a car selection case study and comparative analysis.

Faisal Al-Sharqi, Ashraf Al-Quran2026-10-21
🔢 mathematics

Proof Assistants at the interplay of mathematical cultures: a semiotic-cultural analysis of proof in higher education

This paper employs a semiotic-cultural framework to analyze how Proof Assistants, specifically Verbose Lean, function as epistemic revelators in undergraduate mathematics by reconfiguring proof practices and making implicit assumptions explicit through the necessary formalization of mathematical objects and inferential steps.

Carola Manolino, Cécile Ouvrier-Buffet2026-10-21
🔢 mathematics

Proximal Point Algorithms in Hadamard Spaces and Generalized Fermat-Torricelli Problem

This paper develops a double sum inexact cyclic proximal point algorithm for Hadamard spaces, establishing its linear and superlinear convergence under metric subregularity, proving finite termination via weak sharp minima, and applying these results to solve a new generalized Fermat–Torricelli problem with explicit resolvent formulas and numerical validation.

Kumaresh Kundu, Debashish Paul, Binayak S. Choudhury2026-10-21
🔢 mathematics

Laplace Transform Inversion Techniques for the Ruin Probability of the Compound Poisson Process Perturbed by Diffusion

This paper evaluates and compares the Talbot, Euler, and saddlepoint approximation techniques for numerically inverting the Laplace transform to estimate ruin probabilities in a compound Poisson process perturbed by diffusion, finding that while all three methods yield small relative errors for extremely small probabilities, the Talbot method achieves the highest accuracy.

Raphael Waller, Riccardo Gatto2026-10-21
🔢 mathematics

Lyapunov exponents of fractional-order systems: definition from the diffusive representation, ageing of memory and effect of memory truncation

This paper establishes a rigorous definition for Lyapunov exponents in fractional-order Caputo systems by utilizing diffusive representation to transform them into autonomous equations on a Hilbert space, thereby resolving issues related to non-invariance and memory ageing while demonstrating that positive exponents are robust against memory truncation whereas improper truncation methods can artificially suppress chaos and introduce spurious negative exponents.

Stefano Fazzino2026-10-21
🔢 mathematics

Convolution and Correlation Theorems Associated with the Linear Canonical Empirical Wavelet Transform and Their Applications

This paper establishes a rigorous convolution-correlation calculus for a fixed-partition linear canonical empirical wavelet transform, proving exact representation theorems, frame bounds, and stability results while demonstrating the invariance of synthesized identities under dual choices and validating these findings through reproducible computations.

Owais Ahmad, Aamir Ayoub Mir2026-10-20
🔢 mathematics

Double-Exponential Quadrature and the S Transformation for Three-Centre Two-Electron Coulomb and Hybrid Integrals

This paper investigates two double-exponential quadrature formulations for accurately and efficiently evaluating three-centre two-electron Coulomb and hybrid integrals over Slater-type functions, demonstrating that combining the S transformation with Fourier-type DE quadrature is particularly effective for handling the strongly oscillatory kernels involved.

Hassan Safouhi2026-10-20