In a previous paper [1] an Euler angle parameterization for SU(4) was given. Here we present the derivation of a generalized Euler angle parameterization for SU(N). The formula for the calculation of the Haar measure for SU(N) as well as its relation to Marinov’s volume formula for SU(N) [2,3] will also be derived. As an example of this parameterization’s usefulness, the density matrix paramete...

Problem of parameterization of multi-output autoregressive regressive Gaussian model (ARX) is studied in the context of prior design of adaptive controllers. The substantial role of prior distribution of unknown parameters on the parameterization is demonstrated. Among several parameterizations a nontraditional one is advocated which • makes it possible to model the system output entry-wise, th...

This paper presents a geometric method for parameterization, matching, and analysis of surface shapes. Surfaces are parameterized and represented by intrinsic coordinate maps derived from the conformal structure of the shape. This parameterization is invariant to rigid transformations of the shape, as well as angle-preserving parameterizations of the surface. Shape matching between coordinate m...

Dip moveout (DMO) and azimuth moveout (AMO) are considered in a general framework that allows for lateral variations in the velocity model, including those which generate caustics in the wavefield. DMO and AMO are constructed through the composition of operators, using the scattering angle and azimuth parameterization. In this parameterization, impulse responses are computed in a gaussian gas l...

The second order properties of a process are usually characterized by the autocovariance function. In the stationary case, the parameterization by the partial autocorrelation function is relatively recent. We extend this parameterization to the nonstationary case. The advantage of this function is that it is subject to very simple constraints in comparison with the autocovariance function which...

The K-profile parameterization of upperocean mixing is tested and extended using observations and large eddy simulations of upper-ocean response to a westerly windburst. A nonlocal momentum flux term is added, and the amplitude of the nonlocal scalar flux is recalibrated. Parameterizations of Stokes drift effects are added following recent work by McWilliams and Sullivan (2001). These changes a...

Cubicoids (degree 3 surfaces) always have a parameterization in tenos of rational functions, (a polynomial divided by another). On the other hand cubics (degree 3 plane curves) do not always have a rational parameterization. However they always have a parameterization of the type which allows a single square root of rational functions. [n this paper we describe algorithms to obtain rational and...

This paper describes a method for semi-regular remeshing of arbitrary shapes. The proposed approach is based on building a parameterization map which is smooth with respect to a differential structure built on the base domain. A global parametric energy functional is introduced and optimized in order to establish a globally smooth parameterization. The proposed approach avoids using meta-mesh c...

The second order properties of a process are usually characterized by the autocovariance function. In the stationary case, the parameterization by the partial autocorrelation function is relatively recent. We extend this parameterization to the nonstationary case. The advantage of this function is that it is subject to very simple constraints in comparison with the autocovariance function which...

In Parts II and III we have discussed extensively the dehnition and evaluation of queueing network models. Here, in Part IV, we discuss the parameterization of these models. Parameterization is the heart of the modelling process, for the results of a study can be no more accurate than the parameter values provided to the queueing network evaluation algorithms. Our presentation is divided into t...