273 papers
This paper presents a topology-aware compatible discretization for incompressible viscous flows on closed surfaces that dynamically evolves harmonic modes to ensure exact discrete co-closedness, energy stability, and rigorous convergence on nontrivial topologies.
This paper proposes a unified measure-theoretic framework that characterizes the evolution of mixed atomic and continuous workload distributions in scalar Markov processes through coupled equations, successfully recovering classical results and extending the analysis to complex systems involving dead bands, regime switching, and hysteresis control.
This quasi-experimental study demonstrates that teaching axial and central symmetry through mathematical thought experiments significantly improves fifth-grade students' academic achievement and APOS-based learning levels compared to conventional instruction.
This study, utilizing the Anthropological Theory of the Didactic to analyze sixth-grade classroom data, argues that understanding fractions as quantities of units and recognizing arithmetic operations as manifestations of a common organization are essential for developing a coherent and unified understanding of fraction arithmetic.
This paper establishes a sharp, margin-adaptive stability theory for the inverse problem of recovering individual boundary regulators from two-sided reflected delay dynamics, proving optimal Lipschitz recovery, pathwise synchronization to a random equilibrium, and uniform Wong–Zakai convergence under strict delay dissipativity.
This paper presents a Chebyshev-based method for approximating matrix functions, particularly for exponential integrators, by constructing Faber expansions on an ellipse enclosing the matrix's field-of-values, deriving error bounds, proposing a novel algorithm to determine the ellipse from Ritz values, and providing an efficient residual-based error estimator.
This paper develops a Caputo–Fabrizio fractional mathematical model to analyze the dynamics of *Dactylopius opuntiae* infestation on prickly pear in Morocco, establishing solution existence, deriving stability conditions via the effective reproduction number, and employing numerical algorithms and optimal control theory to evaluate quarantine and treatment strategies for effective pest management.
This paper employs asymptotic analysis to derive two distinct variational models describing the dynamics of an elastic body containing a heavy, curvilinear thin filament, with the specific limit behavior determined by the scaling ratio between the inclusion's and the matrix's elastic moduli as the inclusion's width vanishes.
This paper introduces a flexible parametric 8-point approximating subdivision scheme derived from the difference between 6-point Lagrange and B-spline refinements, featuring three shape parameters that enable C6 to C8 continuity, Gibbs-free conditions, and enhanced geometric control for computer-aided curve design.
This paper establishes a theoretical quadratic bound on the spectral drift of Loop subdivision and provides extensive numerical evidence confirming that the low-frequency eigenpairs of the discrete Laplace operator remain stable under refinement, with drift decaying at a rate proportional to the square of the mesh size.