273 papers
This paper proposes a step-size-based spectral three-term conjugate gradient method that satisfies modified conjugacy and sufficient descent conditions, proving its global convergence and demonstrating superior computational efficiency and practical effectiveness in robotic motion control and image denoising applications.
This paper establishes sufficient conditions for the polyconvexity of incompressible, inversion-symmetric Valanis–Landel type energies by deriving an explicit polyconvex extension and demonstrating that while certain exponential Hencky-type energies are rank-one convex, the standard quadratic Hencky energy is not.
This paper presents an -Coefficient/Index Annihilation Theorem that derives the population statistics of a multi-factor function on a finite abelian group directly from its Fourier transform by showing that its -th moment consists of terms where the Fourier coefficient indices sum to zero, thereby serving as a powerful analytical tool for revealing variable relationships and constraining search algorithms.
This paper employs second-order averaging theory and Neimark-Sacker bifurcation analysis to demonstrate that while a Hopf-Langford system can exhibit periodic solutions near a zero-Hopf equilibrium, any resulting invariant torus is structurally unstable due to a strictly positive first Lyapunov coefficient, thereby precluding the existence of asymptotically stable tori in this family.
This qualitative study of 15 preschool teachers reveals that while they value pedagogical appropriateness, their ability to coordinate these demands with explicit mathematical structures in problem-posing tasks varies significantly, performing best in structured formats and struggling to create coherent mathematical problems in open-ended contexts.
This paper introduces a robust computational framework utilizing novel topological and geometric descriptors—specifically Begin-End Point Embedding, Density of Directions, and Euler characteristic-based summaries—to analyze and compare the structural organization of both continuous and discrete dynamical systems, demonstrating superior stability and interpretability across diverse benchmarks from low-dimensional models to high-dimensional turbulent flows.
This paper establishes the global well-posedness and energy stability of a nonlinear Euler–Bernoulli beam on a fractional viscoelastic foundation, while developing an unconditionally stable finite-element scheme with optimal error estimates and a reduced-order model that quantifies the interplay between geometric nonlinearity and hereditary damping.
This paper establishes a contraction certificate for approximate Koopman immersions with nonzero generator residuals by proving that the true nonlinear flow contracts if the weighted logarithmic norm of the latent matrix, restricted to the physical tangent space and augmented by the minimal-norm extension of the residual derivative, is negative, thereby enabling robust control design even when the full latent dynamics appear unstable.
This paper proves that in a Markovian poker tournament model where particles merge or redistribute mass, the empirical distribution of normalized masses converges to an exponential law as the population shrinks, provided the initial distribution has finite second moment and relative entropy, by combining nonlinear kinetic equation analysis with finite-population approximation techniques.
This paper demonstrates that a rotationally damped shear beam controlled by a finite family of piezoelectric patches and a uniform rotation channel is not null controllable in the natural energy space at any positive time, due to asymptotic obstructions arising from simultaneous Diophantine approximation of patch lengths that cause observability constants to grow polynomially with the number of modes.