In this diploma thesis, selected techniques for construction of optimal portfo- lios are presented. Risk measures and other criteria (Markowitz approach, Value at risk, Conditional value at risk, Mean absolute deviation, Spectral risk measure and Kelly criterion) are defined in the first part. We derived analytical solution for some cases of optimization problems, in some other cases there exists numeri- cal solution only however. Advantages and disadvantages, theoretical properties and practical aspects of software implementation in Wolfram Mathematica are also mentioned. Simulation methods suitable for portfolio optimization are brie- fly presented with their motivation in the second part. Multivariate distributions: normal, t-distribution and skewed t-distribution are presented in the third part with connection to optimization of portfolio with assumption of multivariate dis- tribution of financial losses. Optimization methods are illustrated on real data in the fourth part of this thesis. Analytical methods are compared with numerical ones. 1

Governments all over the world are faced with numerous challenges while running their countries on a daily basis. The predominant challenges which arise are those which involve statistical methodologies. Official statistics to South Africa’s infrastructure are very important and because of this it is important that an effort is made to reduce the challenges that occur during the development of official statistics. For official statistics to be developed successfully quality standards need to be built into an organisational framework and form a system of architecture (Statistics New Zealand 2009:1). Therefore, this study seeks to develop a statistical methodology that is appropriate and scientifically correct using an automated statistical system for audits in government regulatory authorities. The study makes use of Mathematica to provide guidelines on how to develop and use an automated statistical audit system. A comprehensive literature study was conducted using existing secondary sources. A quantitative research paradigm was adopted for this study, to empirically assess the demographic characteristics of tenants of Social Housing Estates and their perceptions towards the rental units they inhabit. More specifically a descriptive study was undertaken. Furthermore, a sample size was selected by means of convenience sampling for a case study on SHRA to assess the respondent’s biographical information. From this sample, a pilot study was conducted investigating the general perceptions of the respondents regarding the physical conditions and quality of their units. The technical development of an automated statistical audit system was discussed. This process involved the development and use of a questionnaire design tool, statistical analysis and reporting and how Mathematica software served as a platform for developing the system. The findings of this study provide insights on how government regulatory authorities can best utilise automated statistical audits for regulation purposes and achieved this by developing an automated statistical audit system for government regulatory authorities. It is hoped that the findings of this study will provide government regulatory authorities with practical suggestions or solutions regarding the generating of official statistics for regulatory purposes, and that the suggestions for future research will inspire future researchers to further investigate automated statistical audit systems, statistical analysis, automated questionnaire development, and government regulatory authorities individually.

The major objectives of this thesis involve the development of both dynamic and interactive applications aimed at complementing traditional engineering and science coursework, laboratory exercises, research, and providing users with easy access by publishing the applications on Wolframs Demonstration website. A number of applications have been carefully designed to meet cognitive demands as well as provide easy-to-use interactivity. Recent technology introduced by Wolfram Mathematica called CDF (Computable Document Format) provides a resource that gives ideas a communication pipeline in which technical content can be presented in an interactive format. This new and exciting technology has the potential to help students enhance depth and quality of understanding as well as provide teachers and researchers with methods to convey concepts at all levels. Our approach in helping students and researchers with teaching and understanding traditionally difficult concepts in science and engineering relies on the ability to use dynamic, interactive learning modules anywhere at any time. The strategy for developing these applications resulted in some excellent outcomes. A variety of different subjects were explored, which included; numerical integration, Green's functions and Duhamel's methods, chaotic maps, one-dimensional diffusion using numerical methods, and two-dimensional wave mechanics using analytical methods. The wide range of topics and fields of study give CDF technology a powerful edge in connecting with all types of learners through interactive learning. / Master of Science

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We have created a three-dimensional, implicit finite difference model that can accurately calculate temperatures within the bulk of a sample during a friction stir fabrication process. The model was written in Wolfram Mathematica® 7 for Students, and allows for time-efficient calculation of thermal profiles. The non-dimensionality of the model allows for accurate refinement of the temporospatial mesh, and provides portability across material types. The model provides insight as to the mechanism of heat generation by qualifying the fraction of mechanical energy converted to thermal energy for different material types and sample geometries. Finally, our model gives an understanding of the effects of the heat transfer at the boundaries of the workpiece and suggests a backside heat loss localized at the center of the tool due to a decrease in thermal contact resistance. We have explored the effects of processing parameters on the performance of the friction stir fabrication process. The process has four stages; tool insertion, warm-up, bead formation, and steady-state translation. The tool insertion phase is characterized by a rapid increase in system horsepower requirements. During the warm-up phase, the mechanical energy of the rotating tip is converted to thermal energy. Once enough thermal energy has been transferred to the workpiece, the volume between the tip and the workpiece is filled by feedstock material. Finally, the tool is translated under relatively steady-state conditions. The success or failure of the process is dependent on adequate material delivery to the system. The horsepower requirements of the process depend on the material type and the rate of material delivery. We have explored the effect of processing parameters on the microstructure of the processed samples. Optical microscopy shows that the stratification of layers within the weld and the depth of the weld are both dependent on the processing parameters. EBSD analysis coupled with Vicker's microhardness measurements of the processed pieces show that the grain size within the weld nugget is constant over the range of processing parameters available to the system. Data also show that pressure and heat inherent in friction stir processing of strain-hardened Al5083 counteract strengthening of the temper of the alloy. / Ph. D.

GP has traditionally been implemented in LISP but there is a slow migration towards faster languages like C++. Any implementation language is dictated not only by the speed of the platform but also by the desirability of such an implementation. With a large number of scientists migrating to scientifically-biased programming languages like Mathematica, such provides an ideal testbed for GP.In this study it was attempted to implement GP on a Mathematica platform, exploiting the advantages of Mathematica's unique capabilities. Wherever possible, optimizations have been applied to drive the GP algorithm towards realistic goals. At an early stage it was noted that the standard GP algorithm could be significantly speeded up by parallelisation and the distribution of processing. This was incorporated into the algorithm, using known techniques and Mathematica-specific knowledge.

Functionality for efficient computation of properties of system lifetimes was developed, based on the Mathematica framework. The model of these systems consists of a system structure and the components independent lifetime distributions. The components are assumed to be non-repairable. In this work a very general implementation was created, allowing a large number of lifetime distributions from Mathematica for all the component distributions. All system structures with a monotone increasing structure function can be used. Special effort has been made to compute fast results when using the exponential distribution for component distributions. Standby systems have also been modeled in similar generality. Both warm and cold standby components are supported. During development, a large collection of examples were also used to test functionality and efficiency. A number of these examples are presented. The implementation was evaluated on large real world system examples, and was found to be efficient. New results are presented for standby systems, especially for the case of mixed warm and cold standby components.

Information and communication technologies (further referred to as "ICT") are increasingly influencing whole structure of the society. The integration of ICT into education together with the transition of the traditional teaching into a modern learning environment is therefore understood as one of the key factors of further development. This work examines some of the possibilities of applying electronical support for teaching chemistry at high schools. It focuses mainly on the visualisation of the subject matter, suitable positive motivation and incitement of the students. This paper describes in detail the presentation of subjects in chemistry using software applets of Wolfram Mathematica. One of the goals of this paper is to introduce the software and to present its potential application in teaching chemistry. Furthermore it shall encourage the use of particular demonstrations applets of the software Wolfram Mahematica. To achieve this goals, the author of this paper describes in detail the source codes of seven demonstrations applets called "Formulas and Structures for Some Simple Molecules", "Build Your Own Atoms", "Visualizing Atomic Orbitals", "Alkanes", "Oxidation States of Carbon", "Valence Shell Electron Pair Repulsion (VSEPR) Theory" and "Ideal Gas Law", which are available for free on...