141 papers
This paper establishes a mathematical framework for determining the recoverability of AI explanations by formulating them as inverse problems, deriving a complete trichotomy of identifiability and stability conditions for linear and nonlinear systems, and providing explicit bounds that distinguish intrinsic underdetermination from algorithmic variability.
This study introduces a robust and accurate backward one-step block hybrid numerical method, derived via multistep collocation with Chebyshev polynomials, to effectively solve stiff-oscillatory second-order initial value problems.
This paper introduces a regularized three-dimensional Caputo fractional replicator system with emotional factors that resolves the inherent singularity at the origin, establishes global Lipschitz continuity, and analytically characterizes the complete dynamical transition from stability to chaos through Hopf bifurcation and chaos certification, all validated against unregularized models and empirical behavioral data.
This paper presents a layered Lean 4 library for finite-dimensional quantum foundations that formalizes key representation theorems and complexity results while introducing a typed premise-audit framework to verify the coherence and validity of conditional mathematical theorems, such as the independence of subspace weights from orthogonal decompositions.
This paper presents a certified, seed-free interval algorithm that rigorously computes the Euclidean distance from a point to an ellipse by isolating roots of a quartic equation across dual parameterizations, ensuring guaranteed enclosure bounds without relying on heuristic seeds even in ill-conditioned cases.
This paper investigates and supports the hypothesis that Gian Lorenzo Bernini designed the three ovals of St. Peter's Square by modifying the radii of two primary "generating circles," a method that aligns with the square's actual dimensions and historical use of the *ovato tondo*.
This paper corrects a previously published error regarding the oscillatory behavior of second-order non-canonical neutral differential equations and establishes new, improved sufficient conditions for oscillation under sublinear assumptions using Riccati-type transformations and comparison principles, supported by illustrative examples.
This bibliometric study of 203 Scopus articles from 2011 to 2025 reveals a significant upward trend in research on dynamic software in mathematics education, highlighting GeoGebra as a dominant theme while identifying key gaps in computational thinking integration, adaptive learning, and primary school contexts.
This paper introduces a unified framework for induced structures within unary-binary operads to formally capture binary quadratic relations, demonstrating its utility by characterizing Novikov and multi-Novikov algebras as induced structures of differential and multi-differential commutative algebras.
This paper argues that anti-exceptionalism about logic faces an unresolved regress problem in cases of fundamental disagreement, where the abductive criteria used to choose between logical theories are themselves theory-laden and logically contested, thereby mirroring the intractable structure of the epistemological problem of the criterion.