Supervised Learning of Lyapunov Functions Using Laplace Averages of Approximate Koopman Eigenfunctions

Koopman principle eigenfunctions and linearization of diffeomorphisms

This paper considers a nonlinear dynamical system on a complex, finite dimensional Banach space which has an asymptotically stable, hyperbolic fixed point. We investigate the connection between the so-called principle eigenfunctions of the Koopman operator and the existence of a topological conjugacy between the nonlinear dynamics and its linearization in the neighborhood of the fixed point. Th...

Heat Kernel Smoothing Using Laplace-Beltrami Eigenfunctions

We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green's function of an isotropic diffusion equation on a manifold is constructed as a linear combination of the Laplace-Beltraimi operator. The Green's function is then used in constructing heat kernel smoothing. Unlike many previous approaches, diffusion is analytically represented as a series expansi...

the relationship between using language learning strategies, learners’ optimism, educational status, duration of learning and demotivation

with the growth of more humanistic approaches towards teaching foreign languages, more emphasis has been put on learners’ feelings, emotions and individual differences. one of the issues in teaching and learning english as a foreign language is demotivation. the purpose of this study was to investigate the relationship between the components of language learning strategies, optimism, duration o...

Eigenfunctions of the Laplace operator

The study of the Laplace operator and its corresponding eigenvalue problem is crucial to understand the foundations of 3D shape analysis. For that reason the most important mathematical properties of the Laplace operator in Euclidean spaces, its eigenvalues and eigenfunctions are summarized and explained in this report. The basic definitions and concepts of infinite dimensional function spaces,...

Zeros of real analytic ergodic Laplace eigenfunctions