Natural boundaries and spectral theory

Natural boundaries and spectral theory

We present and exploit an analogy between lack of absolutely continuous spectrum for Schrödinger operators and natural boundaries for power series. Among our new results are generalizations of Hecke’s example and natural boundary examples for random power series where independence is not assumed.

Natural Boundaries

In this paper we propose a method to use the concept of natural boundaries in the exploration decisions of an autonomous robot on a virtual disaster site. The algorithm we created is based upon various methods from image morphology. By estimating the size of exploration frontiers we show that it’s possible to have global exploration algorithm.

Choquet theory, boundaries and applications

Natural Boundaries of Dirichlet Series

We prove some conditions on the existence of natural boundaries of Dirichlet series. We show that generically the presumed boundary is the natural one. We also give an application of natural boundaries in determining asymptotic results.

Spectral Continuity Measures at Mandarin Syllable Boundaries

In Text-to-Speech (TTS) systems based on concatenative synthesis, the naturalness of synthetic speech is highly affected by the spectral continuities at the concatenation point. In this paper, we focused on 4 kinds of syllable boundaries in mandarin and used several spectral distance measures combined with time derivatives distance measures to predict their audible discontinuities. A perceptual...