After discussing some basic facts about generalized module maps, we use the representation theory of the algebra Ba(E) of adjointable operators on a Hilbert B–module E to show that the quotient of the group of generalized unitaries on E and its normal subgroup of unitaries on E is a subgroup of the group of automorphisms of the range ideal BE of E in B. We determine the kernel of the canonical ...

The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.

Introduction. If d is a positive square-free integer let Id be the ring of integers in Q(\Jd). Id is a Euclidean domain if d = 1, 2, 3, 7, 11. The groups PSL2(/d) = Fd over these Euclidean rings have recently been investigated. Methods for generating presentations as well as actual presentations were given in [2], [3] and [8], while these groups were shown to be describable in terms of generali...

Given a surface in 3-space or scattered points from a surface, we present algorithms for fitting the data by a surface which can be generated by a one–parameter subgroup of the group of similarities. These surfaces are general cones and cylinders, surfaces of revolution, helical surfaces and spiral surfaces.

We demonstrate a new generalized least-squares fitting method which can be used to estimate the slope of the best-fitting straight line that results when two separate data sets which are expected to be linearly correlated are subject to different uncertainties in their measurements. The algorithm determines not only the optimum slope, but also produces estimates of the intrinsic errors associat...

fitting of regression models to life data, where the life distribution location parameter is a linear function of covariates. The fitting yields maximum likelihood estimates of parameters of a regression model with a Weibull, exponential, extreme value, normal, lognormal, logistic, loglogistic, or generalized gamma distribution. The data can be complete, right censored, left censored, or interv...

There are several procedures for fitting generalized additive models, i.e. multivariate regression models for an exponential family response where the influence of each single covariates is assumed to have unknown, potentially non-linear shape. Simulated data is used to compare a smoothing parameter optimization approach for selection of smoothness and covariate, a stepwise approach, a mixed mo...

A tight-binding procedure is presented for fitting electronic band structures of crystals. It is based on a fully automated method of determining all possible independent matrix elements for arbitrary crystal structures. A fit, using this method, for the band structure of hexagonal close-packed Tc is more than an order of magnitude better than previous fits. A practical procedure for optimizing...

Generalized additive models are an effective regression tool, popular in the statistics literature, that provides an automatic extension of traditional linear models to nonlinear systems. We present a distributed algorithm for fitting generalized additive models, based on the alternating direction method of multipliers (ADMM). In our algorithm the component functions of the model are fit indepe...