Following the ideas of Liniger and Willoughby (although acting along different lines), a new family of schemes, derived from the trapezoidal rule, is developed, which enables the fitting of the scheme to arbitrary sets of equations.

Suppose that π be a set of primes and F a local Fitting class. Let Kπ(F) be the set of finite π-soluble groups with a Hall πsubgroup belonging to F. In this paper, we show that the class Kπ(F) is a local Fitting class. Thus, an interesting Shemetkov question for Fitting classes will be answered positively. By using the result, the F-radical of a Hall π-subgroup of a finite π-soluble group is de...

Let φ : Rm → Rd be a map of free modules over a commutative ring R. Fitting’s Lemma shows that the “Fitting ideal,” the ideal of d × d minors of φ, annihilates the cokernel of φ and is a good approximation to the whole annihilator in a certain sense. In characteristic 0 we define a Fitting ideal in the more general case of a map of graded free modules over a Z/2graded skew-commutative algebra a...

Currently many eLearning platforms exist that are offered by other universities which are simply deploying eLearning technologies as media streams or online courses. The clear aim of this position paper is to find the essence where diverse universities will be able to compete on the education market in the digital future by reducing teaching costs, finding an innovative model fitting to specifi...

We address the problem of using hand-drawn sketch to edit facial identity, such as enlarging the shape or modifying the position of eyes or mouth, in the whole video. This task is formulated as a 3D face model reconstruction and deformation problem. We first introduce a two-stage realtime 3D face model fitting schema to recover facial identity and expressions from the video. We recognize the us...

Introduction Surface-based approaches have frequently been used to analyse social and economic data. Using approaches such as kernel regression it has been possible to fit continuous surfaces to spatially reference social and economic data, such as house prices. The technique has often proved a useful tool in identifying trends in the data for example one can identify areas of town in which hou...

A model to describe the damage state of materials is developed within the framework of Continuum Damage Mechanics. The damage variable is considered as a random variable. To predict the damage state in a body, knowledge of its intrinsic damage distribution is required. After dividing the body into a number of elementary cells, the intrinsic damage distribution can be determined utilizing statis...

Carnap (in, [ I ] , p. 566) has remarked that his measure function m* is jitting fof finite languages using a fixed number of one-place predicates, i.e., for any sentence i, m*(;) is the same In all such restricted finite languages in which i occurs. The main purpose of this brief note is to show by means of a counter-example that * does not have the intuitively desirable property of fittingne...

This paper summarizes recent research at Edinburgh University on applying domain knowledge of standard shapes and relationships to solve or improve reverse engineering problems. The problems considered are how to enforce known relationships when data fitting, how to extract features even in noisy data, how to get better shape parameter estimates and how to infer data about unseen features.