Min essä är en mind-map av konstverket, I see no God up here (2018)

Thesis (Masters Diploma (Electrical Engineering) -- Cape Technikon, Cape Town,1991 / The main reason for this project was "import replacement", as all our existing Point of Sale and Electronic Equipment had to be imported from Japan. After the Government I s steps to curb imports by placing extremely high levies on imported goods, it was decided to produce a completely local product. From past experience it was obvious that customer requirements varied greatly. This gave rise to the inception of a modular system, enabling the customer to "mix and match" modules to their requirements. The"concept is to use a HOST computer controlling a differential communications line with a maximum of 255 terminals which are all individually addressable. Each individual terminal would in turn control an internal differential communications line, called PNET, which is an acronym for "Peripheral Network". A decision was made to make all the peripherals intelligent, thereby alleviating the processor of all menial tasks. All peripherals local to the terminal would be connected to this network. The configuration can be seen graphically by refering to Figure 0-1. The communications protocol used is more sophisticated than that used for RS232 devices. The protocol has a POLL - ACKNOWLEDGE structure, where the HOST has complete control of the loop.

Binocular eye-gaze tracking can be used to estimate the point-of-gaze (POG) of a subject in real-world three-dimensional (3D) space using the vergence of the eyes. In this thesis, a novel non-contact, model-based technique for 3D POG estimation is presented. The non-contact system allows people to select real-world objects in 3D physical space using their eyes, without the need for head-mounted equipment. Using a model-based POG estimation algorithm allows for free head motion and a single stage of calibration. The users were free to naturally move and reorient their heads while operating the system, within an allowable headspace of 3.2 x 9.2 x 14 cm. A rela tively high precision, as measured by the standard deviation of the 3D POG estimates, was measured to be 0.26 cm and was achieved with the use of high speed sampling and digital filtering techniques. When observing points in a 3D volume, large head and eye rotations are far more common than when observing a 2D screen. A novel corneal reflection pattern matching algorithm is presented for increasing image feature tracking reliability in the presence of large eye rotations. It is shown that an average accuracy of 3.93 cm was achieved over seven different subjects and a workspace volume of 30 x 23 x 25 cm (width x height x depth). An example application is presented illustrating the use of the 3D POG as a human computer interface in a 3D game of Tic-Tac-Toe on a 3 x 3 x 3 volumetric display. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Let f be a point-to-set mapping from a topological X space X into the family 2(X) of nonempty closed subsets of X . K. Fan [13] proved that if X is a Hausdorff locally convex linear topological space and K is a nonempty compact convex subset of X , then an upper semicontinuous mapping (abbreviated by u.s.c.) f from K into k(K), the family of nonempty closed convex subsets of K, has a fixed point in K . Our main object in this work is to weaken "compactness" of K to "weak compactness" and prove a fixed point theorem for a mapping f on K into certain subfamily of 2(K). The definition of convex function has been extended to point-to-set mappings in Chapter I. Let I denote the identity mapping on a Banach space X. Assume that I-f is a convex mapping on a weakly compact closed convex subset K of X. Then any of the following conditions implies the existence of the fixed point of f on K: (1) f : K → 2(K) is u.s.c. and [formula omitted] d(x,f(x)) = 0. (2) f : K → 2(K) is u.s.c. and is asymptotically regular (see definition 1.3) at some point in K . (3) f : K → cc(K) is nonexpansive and the Banach space X has a strictly convex norm. Moreover, it has been shown that if f : K → cpt(K) (see definition 0.3) is nonexpansive and I-f is strictly convex (see definition 1.5) on K, then K has a fixed point on K . Finally, an effort has been made to investigate the properties of the set of fixed points of a point-to-set mappings. In Chapter II, we have confined ourselves to a reflexive Banach space X which has a weakly continuous duality map J (see definition 2.3) and X has a strictly convex norm. On such a special space we are able to prove that a nonexpansive mapping f : X → cc(X) such that f(x)ʗ K, for any x in a closed convex bounded subset K of X , has a fixed point. As an application of this result we prove a fixed point theorem for semicontractive mappings (see definition 2.7). F : X → cc(X) such that F(x)ʗK for any x ε K , where K and X are the same as above. . In the last Chapter, we have proved that if f is strictly nonexpansive on a.Banach space X into cpt(X) and if there is x(o) ε X such that [formula omitted] has a subsequence convergent to a set A ε cpt(X) under the Hausdorff metric D on cpt(X), then f has a fixed point in A . Furthermore we prove that a nonexpansive mapping f : K → cpt(K), where K is a weakly compact convex subset of a metrizable locally convex linear topological space X, has a fixed point in K, provided that a constant k > 0 exists such that the set E(x) = {y ε K ; d(x,y) ≥ kd(y,f(y))} is nonempty and convex and the mapping E : K → k(K), with E(x) defined above, is weakly locally closed (see definition 3.1). Finally the comparisons of the continuities of a point-to-set mapping have been made. / Science, Faculty of / Mathematics, Department of / Graduate

Elastic deformation has wide applications in medical simulations, therefore when it comes to designing physical behavior of objects for realistic training applications, determining material parameters so that objects behave in a desired way becomes a crucial. In this work we consider the problem of elasticity parameter estimation for deformable bodies, which is important for accurate medical simulations. Our work has two major steps: the first step is the data acquisition and preparation, and the second step is the parameter estimation. The experimental setup for data acquisition consists of depth and force sensors. Surface deformations are acquired as a series of images along with the corresponding applied forces. The contact point of the force sensor on the surface is found visually and the corresponding applied forces are acquired directly from the force sensor. A complete mesh deformation which is obtained from a surface tracking method is employed along with force measurements in the elasticity parameter estimation method. Our approach to estimate the physical material properties is based on an inverse linear finite element method. We have experimented with two approaches to optimize the elasticity parameters: a linear iterative method and a force-displacement error minimization method. The two methods were tested on the simulation data, and the second method was tested on three deformable objects. The results are presented for the data captured by two different depth sensors. The result is a set of two parameters, the Young's modulus and the Poisson's ratio, which represents the stiffness of the object under test.

Optical techniques have been used to study the behaviour of ethylene and hydrogen near their liquid-vapour critical points. From measurements of the coexistence curve of ethylene over the reduced temperature range 1.5 x 10⁻⁶ < t < 4.5 x 10⁻², where t — (Tc — T)/Tc and Tc is the critical temperature, we find the critical exponent β = 0.327±.002 and the corrections-to-scaling exponent ∆ = 0.46±.02. Similar measurements for hydrogen over the range 3.2 x 10⁻⁵ < t < 7.0 x 10⁻² give β = 0.326 ± .002 and ∆ = 0.46 ± .02. Measurements of the compressibility of hydrogen give the critical exponent [Formula Omitted] = 1.19 ± .05 and the critical amplitude ratio [Formula Omitted] = 5.2 ± .4. With the exception of ∆, which is slightly lower than its predicted value of 0.5, the results for these universal quantities are in agreement with theoretical predictions. The leading coexistence curve amplitude for hydrogen, B₀ = 1.19±.03, is lower than the corresponding values for ethylene, B₀ = 1.56 ± .03, and for other room-temperature fluids. This decrease is in qualitative agreement with the predictions of a theory of quantum effects on critical behaviour. Measurements of the coexistence curve diameter for both fluids show an anomaly near the critical point having a form consistent with the predicted t¹⁻α temperature dependence. These results are in agreement with a recent theory of the effects of many-body forces on the diameter; the hydrogen data indicate that these forces are attractive in that fluid. This suggests that quantum mechanical exchange interactions are important near the critical point of hydrogen. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis is concerned with an investigation of the generalizations of continuous real functions of a real variable. In particular, the relationship between uniform continuity and ordinary continuity is concerned. The concept of uniform continuity was first introduced by Heine about 1900.

The purpose of this thesis is to investigate the relation Z for point sets in a topological space. There were two original goals which caused the study.

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