Physical properties are fundamental to all chemical, biochemical and environmental industries. One of these properties is the normal boiling point of a compound. However, experimental values in literature are quite limited and measurements are expensive and time consuming. For this reason, group contribution estimation methods are generally used. Group contribution is the simplest form of estimation requiring only the molecular structure as input. Consequently, the aim of this project was the development of a reliable group contribution method for the estimation of normal boiling points of non-electrolytes applicable for a broad range of components. A literature review of the available methods for the prediction of the normal boiling points from molecular structure only, was initially undertaken. From the review, the Cordes and Rarey (2002) method suggested the best scientific approach to group contribution. This involved defining the structural first-order groups according to its neighbouring atoms. This definition also provided knowledge of the neighbourhood and the electronic structure of the group. The method also yielded the lowest average absolute deviation and probability of prediction failure. Consequently, the proposed group contribution method was then developed using the Cordes and Rarey method as a starting point. The data set included experimental data for approximately 3000 components, 2700 of which were stored in the Dortmund Data Bank (DDB) and about 300 stored in Beilstein. The mathematical formalism was modified to allow for separate examination and regression of individual contributions using a meta-language filter program developed specifically for this purpose. The results of this separate examination lead to the detection of unreliable data, the re-classification of structural groups, and introduction of new structural groups to extend the range of the method. The method was extended using steric parameters, additional corrections and group interaction parameters. Steric parameters contain information about the greater neighbourhood of a carbon. The additional corrections were introduced to account for certain electronic and structural effects that the first-order groups could not capture. Group interactions were introduced to allow for the estimation of complex multifunctional compounds, for which previous methods gave extraordinary large deviations from experimental findings. Several approaches to find an improved linearization function did not lead to an improvement of the Cordes and Rarey method. The results of the new method are extensively compared to the work of Cordes and Rarey and currently-used methods and are shown to be far more accurate and reliable. Overall, the proposed method yielded an average absolute deviation of 6.50K (1.52%) for a set of 2820 components. For the available methods, Joback and Reid produced an average absolute deviation of 21.37K (4.67%) for a set of 2514 components, 14.46K (3.53%) for 2578 components for Stein and Brown, 13.22K (3.15%) for 2267 components for Constantinou and Gani, 10.23 (2.33%) for 1675 components for Marrero and Pardillo and 8.18K (1.90%) for 2766 components for Cordes and Rarey. This implies that the proposed method yielded the lowest average deviation with the broadest range of applicability. Also, on an analysis of the probability of prediction failure, only 3% of the data was greater than 20K for the proposed method. This detailed comparison serves as a very valuable tool for the estimation of prediction reliability and probable error. Structural groups were defined in a standardized form and the fragmentation of the molecular structures was performed by an automatic procedure to eliminate any arbitrary assumptions. / Thesis (M.Sc.Eng.)-University of Natal, Durban, 2004.

A morphism $\sigma$ is \emph{(strongly) unambiguous} with respect to a word $\alpha$ if there is no other morphism $\tau$ that maps $\alpha$ to the same image as $\sigma$. Moreover, $\sigma$ is said to be \emph{weakly unambiguous} with respect to a word $\alpha$ if $\sigma$ is the only \emph{nonerasing} morphism that can map $\alpha$ to $\sigma(\alpha)$, i.\,e., there does not exist any other nonerasing morphism $\tau$ satisfying $\tau(\alpha) = \sigma(\alpha)$. In the first main part of the present thesis, we wish to characterise those words with respect to which there exists a weakly unambiguous \emph{length-increasing} morphism that maps a word to an image that is strictly longer than the word. Our main result is a compact characterisation that holds for all morphisms with ternary or larger target alphabets. We also comprehensively describe those words that have a weakly unambiguous length-increasing morphism with a unary target alphabet, but we have to leave the problem open for binary alphabets, where we can merely give some non-characteristic conditions. \par The second main part of the present thesis studies the question of whether, for any given word, there exists a strongly unambiguous \emph{1-uniform} morphism, i.\,e., a morphism that maps every letter in the word to an image of length $1$. This problem shows some connections to previous research on \emph{fixed points} of nontrivial morphisms, i.\,e., those words $\alpha$ for which there is a morphism $\phi$ satisfying $\phi(\alpha) = \alpha$ and, for a symbol $x$ in $\alpha$, $\phi(x) \neq x$. Therefore, we can expand our examination of the existence of unambiguous morphisms to a discussion of the question of whether we can reduce the number of different symbols in a word that is not a fixed point such that the resulting word is again not a fixed point. This problem is quite similar to the setting of Billaud's Conjecture, the correctness of which we prove for a special case.

In this thesis, fixed point theory is used to construct a fractal type sets and to solve data classification problem. Fixed point method, which is a beautiful mixture of analysis, topology, and geometry has been revealed as a very powerful and important tool in the study of nonlinear phenomena. The existence of fixed points is therefore of paramount importance in several areas of mathematics and other sciences. In particular, fixed points techniques have been applied in such diverse fields as biology, chemistry, economics, engineering, game theory and physics. In Chapter 2 of this thesis it is demonstrated how to define and construct a fractal type sets with the help of iterations of a finite family of generalized F-contraction mappings, a class of mappings more general than contraction mappings, defined in the context of b-metric space. This leads to a variety of results for iterated function system satisfying a different set of contractive conditions. The results unify, generalize and extend various results in the existing literature. In Chapter 3, the theory of support vector machine for linear and nonlinear classification of data and the notion of generalized support vector machine is considered. In the thesis it is also shown that the problem of generalized support vector machine can be considered in the framework of generalized variation inequalities and results on the existence of solutions are established. / FUSION

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Recursive partitioning is embedded into the general and well-established class of parametric models that can be fitted using M-type estimators (including maximum likelihood). An algorithm for model-based recursive partitioning is suggested for which the basic steps are: (1) fit a parametric model to a data set, (2) test for parameter instability over a set of partitioning variables, (3) if there is some overall parameter instability, split the model with respect to the variable associated with the highest instability, (4) repeat the procedure in each of the daughter nodes. The algorithm yields a partitioned (or segmented) parametric model that can effectively be visualized and that subject-matter scientists are used to analyze and interpret. / Series: Research Report Series / Department of Statistics and Mathematics

Doctor of Philosophy / Department of Mathematics / Pietro Poggi-Corradini / We consider iteration of an analytic self-map f of the unit ball in the N-dimensional complex space C[superscript]N. Many facts were established about such maps and their dynamics in the 1-dimensional case (i.e. for self-maps of the unit disk), and we generalize some of them in higher dimensions. In one dimension, the classical Denjoy-Wolff theorem states the convergence of forward iterates to a unique attracting fixed point, while backward iterates have much more complicated nature. However, under additional conditions (when the hyperbolic distance between two consecutive points stays bounded), backward iteration sequence converges to a point on the boundary of the unit disk, which happens to be a fixed point with multiplier greater than or equal to 1. In this paper, we explore backward-iteration sequences in higher dimension. Our main result shows that in the case when f is hyperbolic or elliptic, such sequences with bounded hyperbolic step converge to a point on the boundary, other than the Denjoy-Wolff (attracting) point. These points are called boundary repelling fixed points (BRFPs) and possess several nice properties. In particular, in the case when such points are isolated from other BRFPs, they are completely characterized as limits of backward iteration sequences. Similarly to classical results, it is also possible to construct a (semi) conjugation to an automorphism of the unit ball. However, unlike in the 1-dimensional case, not all BRFPs are isolated, and we present several counterexamples to show that. We conclude with some results in the parabolic case.

A dissertation submitted to the Faculty of Engineenug, University of the Witwatersrand, in fulfilment. of the requirements for the degree of Master of Science in Engineering, / A multi variable control strategy for a grinding circuit at East Driefontein has been implemented by others and has enabled it to operate under stable conditions. The next development needed was to find conditions under which tne efficiency of the circuit was the greatest. Optimum set points exist for the multi variable controller to keep the circuit at its most efficient state. This project was done to determine these set points, and how it affected the operation of the circuit. The strategy involved the collection of process data, the development of mathematical models and the determination of these optimum set points by simulation, This option reduced interference with routine production operations, which is often a prohibiting factor during any development work on an existing process. The optimum set points were successfully determined, and were compared with previous findings and current plant practice. / AC2017

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