The main purpose of this paper is the study of the analytic continuation of solutions of elliptic differential equations in two independent variables across an analytic boundary on which they satisfy further analytic equations connecting the point of the boundary, the value of the solution and those of its first order partial derivatives. In its simplest form the problem is that of the continua...

Spherical harmonic expansions (SHEs) play an important role in most of the physical sciences, especially geodesy. Despite many decades investigation, large order behavior SHE coefficients, and precise domain convergence for these expansions, have remained open questions. These questions are settled present paper generic planets, whose shape (topography) may include local peaks, but just one glo...

This letter addresses the problem of domain adaptation for task music source separation. Using datasets from two different domains, we compare performance a deep learning-based harmonic-percussive separation model under training scenarios, including supervised joint using data both domains and pre-training in one with fine-tuning another. We propose an adversarial unsupervised approach suitable...

We demonstrate a new method of detecting the presence of ferroelectric domains based on non-phase-matched second-harmonic generation. If a domain boundary is tilted relative to the input and output faces of the crystal, the far-field second-harmonic light consists of multiple beams, in contrast to the single beam generated in a single-domain crystal. The angular separation of the beams provides...

The Teichmüller harmonic map flow, introduced in [9], evolves both a map from a closed Riemann surface to an arbitrary compact Riemannian manifold, and a constant curvature metric on the domain, in order to reduce its harmonic map energy as quickly as possible. In this paper, we develop the geometric analysis of holomorphic quadratic differentials in order to explain what happens in the case th...