273 papers
This paper establishes that a specific algebraic identity () serves as a necessary and sufficient condition for a coupled oscillator system to possess a unique positive real eigenvalue, effectively discretizing its parameter space onto a hyperboloid and providing an algebraic explanation for the fundamental frequency locking observed in standard A4 tuning forks.
This paper proposes a "complex-frame polyline" representation that augments standard geometric data with topological phase information to enable a bidirectional diagnostic framework capable of verifying both the reconstructibility of original curve families and the preservation of global topological properties like winding and linking.
This paper introduces the short-time quadratic-phase Fourier transform (ST-QPFT) and its multi-resolution variant to overcome the global limitations of the quadratic-phase Hilbert transform by localizing the kernel, while establishing their fundamental mathematical properties, clarifying their relationship to classical transforms via a chirp-reduction lemma, and validating the theory through numerical simulations.
This paper presents a constrained multi-agent optimal control framework for football tactical decision-making that establishes theoretical optimality conditions, implements a numerical solver, and validates the approach through reproducible synthetic experiments demonstrating significant improvements in strategic performance over baseline strategies.
This paper proposes a multi-agent dynamic system model of human "social flocking" behavior that integrates opinion states, cognitive velocity, and learning efficiency with social classification and norm mechanisms to analyze stability conditions and simulate collective dynamics such as cohesion and fragmentation.
This paper establishes the existence of solutions for a coupled system of nonlinear -fractional differential inclusions involving nested -Laplacian operators and nonlocal boundary conditions, while demonstrating the practical relevance of the proposed Caputo -fractional damping model through an aerospace vibration application.
This paper establishes the uniform inf–sup stability of quartic and quintic Scott–Vogelius finite elements on three-dimensional Freudenthal meshes by introducing a protected raw edge-star lifting lemma and an exact rational local linear map that resolves the gap in Zhang's previous work for degrees and $5$.
This paper presents a unified Lyapunov-Schmidt reduction framework to analyze the bifurcation and stability of reaction-diffusion-advection systems with nonlocal delay and nonlinear boundary conditions, deriving explicit criteria for steady-state and Hopf bifurcations that reveal how advection, competition, and boundary self-regulation jointly determine system dynamics.
This study demonstrates that undergraduate nutrition students construct meaningful mathematical understanding in STEM contexts not merely by achieving procedural accuracy, but by coordinating quantities, representations, and disciplinary assumptions through authentic problem-solving, a process best captured by analyzing collaborative reasoning and individual artifacts rather than aggregate grades alone.
This paper presents a scale-covariant, pre-solve screening algorithm for scalar finite-difference discretizations on positive nonuniform meshes that combines a deterministic, certified acceptance test with a risk-calibrated empirical rejection rule to validate stability and provide error certificates without requiring a reference solution.