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Now showing items 1-10 of 12

#### Interpolatory bivariate refinable functions and subdivision

(Stellenbosch : Stellenbosch University, 2008-03)

See full text for abstract.

#### Explicit class field theory for rational function fields

(Stellenbosch : Stellenbosch University, 2008-12)

Class field theory describes the abelian extensions of a given field K in terms of various
class groups of K, and can be viewed as one of the great successes of 20th century
number theory. However, the main results in ...

#### Vector refinable splines and subdivision

(Stellenbosch : Stellenbosch University, 2008-12)

In this thesis we study a standard example of refinable functions, that is, functions which can be reproduced by the integer shifts of their own dilations. Using the cardinal B-spline as an introductory example, we prove ...

#### Local class field theory via Lubin-Tate theory

(Stellenbosch : Stellenbosch University, 2008-12)

This is an exposition of the explicit approach to Local Class Field Theory
due to J. Tate and J. Lubin. We mainly follow the treatment given in [15]
and [25]. We start with an informal introduction to p-adic numbers. ...

#### On the computation of freely generated modular lattices

(Stellenbosch : Stellenbosch University, 2008-12)

Please refer to full text for abstract.

#### Interpolatory refinement pairs with properties of symmetry and polynomial filling

(Stellenbosch : University of Stellenbosch, 2008-03)

Subdivision techniques have, over the last two decades, developed into a powerful
tool in computer-aided geometric design (CAGD). In some applications it is
required that data be preserved exactly; hence the need for ...

#### Growth optimal portfolios and real world pricing

(Stellenbosch : Stellenbosch University, 2008-12)

In the Benchmark Approach to Finance, it has been shown that by taking the
Growth Optimal Portfolio as numéraire, a candidate for a pricing derivatives
formula under the real world probability can be given. This result ...

#### Fast generation of digitally reconstructed radiographs for use in 2D-3D image registration

(Stellenbosch : Stellenbosch University, 2008-12)

A novel implementation exploiting modern hardware is explored and found to be a significant improvement over current methods used. A 50 times performance increase in the computation time of DRRs is achieved over the ...

#### Computing the Greeks using the integration by parts formula for the Skorohod integral

(Stellenbosch : Stellenbosch University, 2008-03)

The computation of the greeks of an option is an important aspect of financial
mathematics. The information gained from knowing the value of a greek of
an option can help investors decide whether or not to hold on to or ...

#### The transfer of distributions by LULU smoothers

(Stellenbosch : Stellenbosch University, 2008-12)

LULU smoothers is a class of nonlinear smoothers and they are compositions
of the maximum and minimum operators. By analogy to the discrete Fourier
transform and the discrete wavelet transform, one can use LULU smoothers
to ...