We report passive mode locking of a soliton erbium-doped double-clad fiber laser operating at the 322nd harmonic of the fundamental cavity frequency. Repetition rates up to 3 GHz have been obtained with pulses of 1 ps duration and 18 pJ of energy. The supermode suppression at the 322nd harmonic is better than 25 dB. In addition, the transition dynamics from a bunched state of pulses to stable h...

Let M be a complete simply connected manifold which is in addition Gromov hyperbolic, coercive and roughly starlike. For a given harmonic function on M , a local Fatou Theorem and a pointwise criteria of nontangential convergence coming from the density of energy are shown: at almost all points of the boundary, the harmonic function converges non-tangentially if and only if the supremum of the ...

This article is concerned with conformal harmonic maps f : Σ → M from a closed connected surface Σ into a compact Riemannian manifoldM of dimension at least four, studied via a perturbative approach based upon the α-energy of Sacks and Uhlenbeck. It gives an estimate on the rate of growth of energy density in the bubbles of minimax α-energy critical points as α→ 1, when the bubbles are at a dis...

This paper presents a significant modification of our previously proposed speech recognizer’s front-end based on perceptual harmonic cepstral coefficients. The spectrum is split into two frequency bands, which correspond to the harmonic and non-harmonic components. A weighting function, which depends both on the voiced/unvoiced/ transitional classification and on the prominence of harmonic stru...

Harmonic maps between Riemannian manifolds are maps which extremize a certain natural energy functional; they appear in particle physics as nonlinear sigma models. Their infinitesimal deformations are called Jacobi fields. It is important to know whether the Jacobi fields along the harmonic maps between given Riemannian manifolds are integrable, i.e., arise from genuine variations through harmo...

Lattice networks of oscillators have been considered for a long time as good models for studying macroscopic energy trasport and its diffusion, i.e. for obtaining, on a macroscopic space-time scale, heat equation and Fourier law of conduction ([1]). It is well understood that the diffusive behavior of the energy is due to the non-linearity of the interactions, and that purely deterministic harm...

We sketch the proof that unitons (harmonic spheres in U(N)) correspond to holomorphicùniton bundles', and that these admit monad representations analogous to Donaldson's representation of instanton bundles. We also give a closed-form expression for the unitons involving only matrix operations , a nite-gap result (two-unitons have energy 4), computations of fundamental groups of energy 4 compone...

We explore frame-level audio feature learning for chord recognition using artificial neural networks. We present the argument that chroma vectors potentially hold enough information to model harmonic content of audio for chord recognition, but that standard chroma extractors compute too noisy features. This leads us to propose a learned chroma feature extractor based on artificial neural networ...

1-dimensional hamiltonian with ionization energy (ξ) is shown to be exactly the same with the total energy from the standard harmonic oscillator hamiltonian, with the harmonic oscillator potential, mωx/2. Commutation relations for the ladder operators, energy at the n state and the expectation value for the potential are analyzed and shown to be consistent with the principle of ξ. We also deriv...

The atomic force microscope ~AFM! is a powerful tool for investigating surfaces at atomic scales. Harmonic balance and power balance techniques are introduced to analyze the tapping-mode dynamics of the atomic force microscope. The harmonic balance perspective explains observations hitherto unexplained in the AFM literature. A nonconservative model for the cantilever–sample interaction is devel...