The object of this paper is to indicate the immediate usefulness of Caratheodory's theory of the conformal mapping of variable regions in the study of boundary behavior of a fixed but arbitrary conformal map. We study especially the mapping of an infinite strip and its behavior at infinity. Studies of an infinite strip by other methods have previously been made, especially by Ahlfors, Ferrand, ...

The human brain cortex is a highly convoluted sheet. Mapping of the cortical surface into a canonical coordinate space is an important tool for the study of the structure and function of the brain. Here, we present a technique based on least-square conformal mapping with spring energy for the mapping of the cortical surface. This method aims to reduce the metric and area distortion while mainta...

Floryan, J.M. and C. Zemach, Schwarz-Christoffel methods for conformal mapping of regions with a periodic boundary, Journal of Computational and Applied Mathematics 46 (1993) 77-102. Numerical conformal mapping methods for regions with a periodic boundary have been developed. These methods are based on the generalized Schwarz-Christoffel equation and can deal with boundary curves of arbitrary f...

Geometrically, the theorem states that if a variety U/k becomes birationally equivalent to an Abelian variety over the algebraic closure of k, then it is birationally equivalent to an Abelian variety over k. (If k is a field with a discrete valuation, and ir is a prime element, then the curve defined by the equation X" + 7rY" + 7r2Zn = 0, with n = 3, shows that the conclusion of the theorem doe...

In the past ten years, there has been a growing interest in the theory of quantum computation and quantum information.ð1Þ Due to the quantum parallelism, quantum computers have the potential to outperform the classical computers. The quantum computers are based on two-level quantum systems, which are called qubits.ð2Þ In this paper, we will investigate a representation of a single qubit operati...

1 Microstructural evolution is typically beyond the reach of mathematical analysis, but in two dimensions certain problems become tractable by complex analysis. Via the analogy between the geometry of the plane and the algebra of complex numbers, moving free boundary problems may be elegantly formulated in terms of conformal maps. For over half a century, conformal mapping has been applied to c...