Atmospheric monitoring is a vital part of environmental management. Monitoring temporal changes in atmospheric pollution on a local, regional and global scale is important in order to mitigate adverse effects on health and the environment. Currently there is general agreement that atmospheric pollution should be monitored, however, less emphasis is often placed on what should be achieved and the specific monitoring that should be included. Atmospheric pollution monitoring is often hampered by geographically restricted and site specific effects resulting in inefficient or ineffective information transfer to the local manager. The scientific community in the developed world often underestimate problems associated with the maintenance of comprehensive atmospheric measurement stations in Africa. A holistic approach is needed to optimise atmospheric monitoring according to specifications set out by system design; this includes site selection, site design, maintenance and quality control. The aim of this dissertation is to apply the Systems Engineering approach to a case study, the Welgegund atmospheric measurement station (WAMS), to offer a holistic view of interaction between different operational systems and the complexity behind their management in order to be informative to students and personnel from a non-engineering background. A knowledge gap exists that links practical industry related sciences such as engineering to more fundamental and theoretical sciences. In this dissertation the customer need was determined and an operational concept was developed for the WAMS system. The high level goals of the WAMS were derived and stated as applicable to other new as well as established measurement stations. Technical and fundamental requirements such as trained staff for appropriate logistical support and a broad spatial coverage of air quality monitoring were identified. The system boundaries and operational constraints were established for the WAMS, exposing weaknesses and proposing solutions to ensure long term sustainability. Weaknesses include irregular funding periods and retention of expertise (trained students leave academia for industry) whereas a possible solution included overlapping projects and contracts. Functional analysis highlighted the design and establishment process of the WAMS. Physical architectures and interfaces were explored and finally the success of the establishment of the WAMS was evaluated by a reliability block diagram. The reliability of the WAMS system was calculated to be 96.6 %. This agrees well with the percentage data coverage calculated for the gaseous (95.9 %), aerosol (93.4 %) and meteorological (94.6 %) systems (15 min averages). The reliability of the national grid to supply power to the WAMS was found to be the main restrictive component. It may be a challenge interacting and coordinating projects with different disciplines, branches or sectors outside of a speciality project. This study has bridged the gap between industry related sciences such as engineering to more fundamental and theoretical sciences. A framework has been provided that highlights the techniques of Systems Engineering and provides an understanding for the need and process of atmospheric monitoring. / MIng (Development and Management Engineering), North-West University, Potchefstroom Campus, 2015

BACKGROUND:General, breed- and diet-dependent associations between feed efficiency in beef cattle and single nucleotide polymorphisms (SNPs) or haplotypes were identified on a population of 1321 steers using a 50K SNP panel. Genomic associations with traditional two-step indicators of feed efficiency - residual feed intake (RFI), residual average daily gain (RADG), and residual intake gain (RIG) - were compared to associations with two complementary one-step indicators of feed efficiency: efficiency of intake (EI) and efficiency of gain (EG). Associations uncovered in a training data set were evaluated on independent validation data set. A multi-SNP model was developed to predict feed efficiency. Functional analysis of genes harboring SNPs significantly associated with feed efficiency and network visualization aided in the interpretation of the results.RESULTS:For the five feed efficiency indicators, the numbers of general, breed-dependent, and diet-dependent associations with SNPs (P-value<0.0001) were 31, 40, and 25, and with haplotypes were six, ten, and nine, respectively. Of these, 20 SNP and six haplotype associations overlapped between RFI and EI, and five SNP and one haplotype associations overlapped between RADG and EG. This result confirms the complementary value of the one and two-step indicators. The multi-SNP models included 89 SNPs and offered a precise prediction of the five feed efficiency indicators. The associations of 17 SNPs and 7 haplotypes with feed efficiency were confirmed on the validation data set. Nine clusters of Gene Ontology and KEGG pathway categories (mean P-value<0.001) including, 9nucleotide binding / ion transport, phosphorous metabolic process, and the MAPK signaling pathway were overrepresented among the genes harboring the SNPs associated with feed efficiency.CONCLUSIONS:The general SNP associations suggest that a single panel of genomic variants can be used regardless of breed and diet. The breed- and diet-dependent associations between SNPs and feed efficiency suggest that further refinement of variant panels require the consideration of the breed and management practices. The unique genomic variants associated with the one- and two-step indicators suggest that both types of indicators offer complementary description of feed efficiency that can be exploited for genome-enabled selection purposes.

The research in this thesis was initially motivated by an outstanding problem posed by Argyros and Haydon. They used a generalised version of the Bourgain-Delbaen construction to construct a Banach space $XK$ for which the only bounded linear operators on $XK$ are compact perturbations of (scalar multiples of) the identity; we say that a space with this property has very few operators. The space $XK$ possesses a number of additional interesting properties, most notably, it has $ell_1$ dual. Since $ell_1$ possesses the Schur property, weakly compact and norm compact operators on $XK$ coincide. Combined with the other properties of the Argyros-Haydon space, it is tempting to conjecture that such a space must necessarily have very few operators. Curiously however, the proof that $XK$ has very few operators made no use of the Schur property of $ell_1$. We therefore arrive at the following question (originally posed in cite{AH}): must a HI, $mathcal{L}_{infty}$, $ell_1$ predual with few operators (every operator is a strictly singular perturbation of $lambda I$) necessarily have very few operators? We begin by giving a detailed exposition of the original Bourgain-Delbaen construction and the generalised construction due to Argyros and Haydon. We show how these two constructions are related, and as a corollary, are able to prove that there exists some $delta > 0$ and an uncountable set of isometries on the original Bourgain-Delbaen spaces which are pairwise distance $delta$ apart. We subsequently extend these ideas to obtain our main results. We construct new Banach spaces of Bourgain-Delbaen type, all of which have $ell_1$ dual. The first class of spaces are HI and possess few, but not very few operators. We thus have a negative solution to the Argyros-Haydon question. We remark that all these spaces have finite dimensional Calkin algebra, and we investigate the corollaries of this result. We also construct a space with $ell_1$ Calkin algebra and show that whilst this space is still of Bourgain-Delbaen type with $ell_1$ dual, it behaves somewhat differently to the first class of spaces. Finally, we briefly consider shift-invariant $ell_1$ preduals, and hint at how one might use the Bourgain-Delbaen construction to produce new, exotic examples.

Thesis (MComm)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: In this dissertation I investigate the class number one problem in function fields. More precisely I give a survey of the current state of research into extensions of a rational function field over a finite field with principal ring of integers. I focus particularly on the quadratic case and throughout draw analogies and motivations from the classical number field situation. It was the "Prince of Mathematicians" C.F. Gauss who first undertook an in depth study of quadratic extensions of the rational numbers and the corresponding rings of integers. More recently however work has been done in the situation of function fields in which the arithmetic is very similar. I begin with an introduction into the arithmetic in function fields over a finite field and prove the analogies of many of the classical results. I then proceed to demonstrate how the algebra and arithmetic in function fields can be interpreted geometrically in terms of curves and introduce the associated geometric language. After presenting some conjectures, I proceed to give a survey of known results in the situation of quadratic function fields. I present also a few results of my own in this section. Lastly I state some recent results regarding arbitrary extensions of a rational function field with principal ring of integers and give some heuristic results regarding class groups in function fields. / AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ek die klasgetal een probleem in funksieliggame. Meer spesifiek ondersoek ek die huidige staat van navorsing aangaande uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam sodat die ring van heelgetalle 'n hoofidealgebied is. Ek kyk in besonder na die kwadratiese geval, en deurgaans verwys ek na die analoog in die klassieke getalleliggaam situasie. Dit was die beroemde wiskundige C.F. Gauss wat eerste kwadratiese uitbreidings van die rasionale getalle en die ooreenstemende ring van heelgetalle in diepte ondersoek het. Onlangs het wiskundiges hierdie probleme ook ondersoek in die situasie van funksieliggame oor 'n eindige liggaam waar die algebraïese struktuur baie soortgelyk is. Ek begin met 'n inleiding tot die rekenkunde in funksieliggame oor 'n eindige liggaam en bewys die analogie van baie van die klassieke resultate. Dan verduidelik ek hoe die algebra in funksieliggame geometries beskou kan word in terme van kurwes en gee 'n kort inleiding tot die geometriese taal. Nadat ek 'n paar vermoedes bespreek, gee ek 'n oorsig van wat alreeds vir quadratiese funksieliggame bewys is. In hierdie afdeling word 'n paar resultate van my eie ook bewys. Dan vermeld ek 'n paar resultate aangaande algemene uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam waar die van ring heelgetalle 'n hoofidealgebied is. Laastens verwys ek na 'n paar heurisitiese resultate aangaande klasgroepe in funksieliggame.

Let X be a Banach space and denote by SS₁(X) the set of all S₁-strictly singular operators from X to X. We prove that there is a Banach space X such that SS₁(X) is not a closed ideal. More specifically, we construct space X and operators T₁ and T₂ in SS₁(X) such that T₁+T₂ is not in SS₁(X). We show one example where the space X is reflexive and other where it is c₀-saturated. We also develop some results about S_alpha-strictly singular operators for alpha less than omega_1. / text

This study assessed the convergent validity of the Functional Assessment Informant Record for Teachers (FAIR-T; Edwards, 2002) with analog functional analyses (FAs). Participants were five teachers and students located at a specialized school serving individuals with disabilities. Teachers had worked with the student for a minimum of 1 month, and students displayed a variety of behavioral topographies. The FAIR-T was conducted by the researcher using telephone or video conferencing technology, and analog functional analyses were conducted in a clinic setting by trained therapists within the course of the student’s typical treatment plan. Results of the FAIR-T were coded according to function, and the results of the analog FAs were graphed and analyzed visually. Results of the FAIR-T and FAs indicated limited convergence between the two assessment methods, though results were somewhat inconclusive. Results are discussed in relation to the utility of the FAIR-T, particularly in the school setting. Directions for future research are discussed in light of the need to delineate efficient means with which to conduct functional behavior assessments within the schools.

In this thesis, we investigate the pathwise regularity of partial sum process of general orthogonal series, and prove that the partial sum process is a geometric 2-rough process under the same condition as in Menshov-Rademacher Theorem. For Fourier series, the condition can be improved, and an equivalent condition on the limit function is identified.

The method of steepest descent is used to minimize typical functionals from elasticity.

This paper is a study of linear operators defined on normed linear spaces. A basic knowledge of set theory and vector spaces is assumed, and all spaces considered have real vector spaces. The first chapter is a general introduction that contains assumed definitions and theorems. Included in this chapter is material concerning linear functionals, continuity, and boundedness. The second chapter contains the proofs of three fundamental theorems of linear analysis: the Open Mapping Theorem, the Hahn-Banach Theorem, and the Uniform Boundedness Principle. The third chapter is concerned with applying some of the results established in earlier chapters. In particular, the concepts of compact operators and Schauder bases are introduced, and a proof that an operator is compact if and only if its adjoint is compact is included. This chapter concludes with a proof of an important application of the Open Mapping Theorem, namely, the Closed Graph Theorem.

The goal of this thesis is to give an exposition of the following recent result of Freeman, Lennard, Odell, Turett and Randrianantoanina. A Banach space has the Schur property if and only if every weakly compact set is contained in the closed convex hull of a weakly null sequence. This result complements an old result of Grothendieck (now called the Grothendieck Compactness Principle) stating that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. We include many of the relevant definitions and preliminary results which are required in the proofs of both of these theorems.