In a previous paper [1] an Euler angle parameterization for SU (N) was given. Here we present a generalized Euler angle parameterization for U (N). The formula for the calculation of the volume for U (N), CP N as well as other SU (N) and U (N) cosets, normalized to this parameterization, will also be given. In addition, the mixed and pure state product measures for N-dimensional density matrice...

The scaling limit of the two-dimensional self-avoiding walk (SAW) is believed to be given by the Schramm-Loewner evolution (SLE) with the parameter κ equal to 8/3. The scaling limit of the SAW has a natural parameterization and SLE has a standard parameterization using the half-plane capacity. These two parameterizations do not correspond with one another. To make the scaling limit of the SAW a...

In isogeometric analysis framework, computational domain is exactly described using the same representation as that employed in the CAD process. For a CAD object, we can construct various computational domain with same shape but with different parameterization. One basic requirement is that the resulting parameterization should have no self-intersections. In this paper, a linear and easy-to-che...

In isogeometric analysis (IGA for short) framework, computational domain is exactly described using the same representation as that employed in the CAD process. For a CAD object, we can construct various computational domain with same shape but with different parameterization. One basic requirement is that the resulting parameterization should have no self-intersections. In this paper, a linear...

Existing Sundqvist-type parameterizations, which only consider dependence of the autoconversion rate on cloud liquid water content, are generalized to explicitly account for the droplet concentration and relative dispersion of the cloud droplet size distribution as well. The generalized Sundqvist-type parameterization includes the more commonly used Kessler-type parameterization as a special ca...

We present a novel algorithm for generating a planar parameterization of the region surrounding a curve embedded in a 3D surface, which we call a stroke parameterization. The technique, which extends the well-known Discrete Exponential Map [SGW06], uses the same basic geometric transformations and hence is both efficient and easy-to-implement. We also handle self-intersecting curves, for which ...

A new method of successive construction of a solution is developed for problems of strongly nonequilibrium Boltzmann kinetics beyond normal solutions. Firstly, the method provides dynamic equations for any manifold of distributions where one looks for an approximate solution. Secondly, it gives a successive procedure of obtaining corrections to these approximations. The method requires neither ...

Manifold parameterization considers the problem of parameterizing a given triangular mesh onto another mesh surface, which could be particularly plane or sphere surfaces. In this paper we propose a unified framework for manifold parameterization between arbitrary meshes with identical genus. Our approach does this task by directly mapping the connectivity of the source mesh onto the target mesh...

We study the problem of optimally sampling parametric surfaces by means of reparameterization. A criterion is first formulated for measuring the parameterization quality of a given surface. According to this criterion, the optimal parameterization is identified for the surface by exploring admissible reparameterizations. Then the optimal sampling of the surface is obtained by uniformly sampling...