[pt] Foi investigada a determinação de Ni e Pb por GFAAS em n-hexano, n-heptano, n-octano, n-decano, n-hexadecano e misturas de n-octano + acetona (99+1, v/v), n-octano + bromofórmio (99+1, v/v) e n-octano + disulfeto de carbono (99+1, v/v). Com relação à estabilidade foram preparadas soluções com concentração (ao nível de ng.mL-1) por dissolução direta de padrões orgânicos nos diferentes líquidos orgânicos, apresentando perdas significativas de Ni e Pb depois de alguns minutos. Não foi observado padrão algum relacionado com o comprimento da cadeia carbônica, apesar das perdas menores quando substâncias contendo O, S e Br estiveram presentes. Foi observada uma excelente estabilidade nos diferentes meios orgânicos estudados com a formação de microemulsões. As microemulsões foram preparadas pela mistura de 6,5 mL de propan- 1-ol com 3,3 mL de líquido orgânico e 0,1 mL de HNO3 50% v/v. Foram adicionados Ni e Pb na forma aquosa ou orgânica. Foram aplicadas modificação química convencional e permanente no presente estudo. As etapas de secagem e rampa apresentaram influência na sensibilidade e tiveram que ser otimizadas. Curvas analíticas aquosas apresentaram maiores sensibilidades que aquelas em meio orgânico. Entretanto, foi observada a mesma sensibilidade para os diferentes meios estabilizados com microemulsão. Assim, curvas analíticas em microemulsão, preparadas com um solvente orgânico puderam ser utilizadas. Foram analisadas amostras de gasolina e diesel comercial, depois de sua estabilização na forma de microemulsão e por um procedimento comparativo, observando-se boa concordância entre ambos os procedimentos. Os limites de detecção da determinação de amostras de gasolina e diesel comercial foram derivados de 10 medidas do branco, sendo estes de 4,5 e 3,6 µg.L-1 para Ni e Pb respectivamente. / [en] The behaviour of Ni and Pb in different organic liquids relatively to their determination by GFAAS was investigated. The following organic liquids were studied: n- hexane, n-heptane, n-octane, isooctane, toluene, n-decane, hexadecane and mixtures of n-octane + acetone (99+1, v/v), n-octane + bromoform (99+1, v/v), and n-octane + carbon disulfide (99+1, v/v). Concerning stability, ng ml-1 solutions prepared by direct dissolution of organic standards in the different organic liquids showed significant Ni and Pb losses after only few minutes. No clear loss pattern related to chain length or form could be observed, although the losses were systematically slower when the O, S and Br compounds were present. Excellent long term sample stabilization was observed for the different organic media investigated if microemulsions are used. Microemulsions were prepared by mixing 6.5 ml of propan-1-ol with 3.3 ml of the organic liquid and 0.1 ml of 50% v/v HNO3. Ni and Pb could be added in the aqueous or aqueous forms. Conventional aqueous modification was allowed as well as Ir as permanent modifier. The dry and ramp steps showed to influence sensitivity, and must be carefully optimized. The same sensitivity was observed for the different microemulsion stabilized organic media. Thus, calibration with microemulsions prepared with a single organic solvent was possible. Commercial gasoline and diesel samples were analyzed after microemulsion stabilization and by a comparative procedure. Good concordance between both procedures was observed. Detection limits (k=3) in the original gasoline or diesel samples, derived from ten blank measurements were 4.5 and 3.6 µgl-1 for Ni and Pb, respectively, well above the values found in the analyzed samples.

Doctor of Philosophy / Curriculum and Instruction Programs / Jennifer M. Bay-Williams / This study examined end-of-the-year seventh grade students’ rational number knowledge using comparison tasks and rational number subconstruct tasks. Comparison tasks included: comparing two decimals, comparing two fractions and comparing a fraction and a decimal. The subconstructs of rational number addressed in this research include: part-whole, measure, quotient, operator, and ratio. Between eighty-six and one-hundred-one students were assessed using a written instrument divided into three sections. Nine students were interviewed following the written instrument to probe for further understanding. Students were classified by error patterns using decimal comparison tasks. Students were initially to be classified into four groups according to the error pattern: whole number rule (WNR), zero rule (ZR), fraction rule (FR) or apparent expert (AE). However, two new patterns emerged: ignore zero rule (IZR) and money rule (MR). Students’ knowledge of the subconstructs of rational numbers was analyzed for the students as a whole, but also analyzed by classification to look for patterns within small groups of students and by individual students to create a thick, rich description of what students know about rational numbers. Students classified as WNR struggled across almost all of the tasks. ZR students performed in many ways similar to WNR but in other ways performed better. FR and MR students had more success across all tasks compared to WNR and ZR. On average apparent experts performed significantly better than those students classified by errors. However, further analysis revealed hidden misconceptions and deficiencies for a number of apparent experts. Results point to the need to make teachers more aware of the misconceptions and deficiencies because in many ways errors reflect the school experiences of students.

Mixture experiments are widely applied. The Scheffé quadratic polynomial is the most popular mixture model in industry due to its simplicity, but it fails to accurately describe the behaviour of response variables that deviate greatly from linear blending. Higherorder Scheffé polynomials do possess the ability to predict such behaviour but become increasingly more complex to use and the number of estimable parameters grow exponentially [15]. A parameter-parsimonious mixture model, developed from the linear blending rule with weighted power means and Wohl's Q-fractions, is introduced. Bootstrap is employed to analyse the model statistically. The model is proved to be flexible enough to model non-linear deviations from linear blending without losing the simplicity of the linear blending rule. / Dissertation (MSc)--University of Pretoria, 2011. / Chemical Engineering / unrestricted

The PhD thesis considers four topics in dynamical systems and is based on one paper and three manuscripts. In Paper I we apply methods of interval analysis in order to compute the rigorous enclosure of rotation number. The described algorithm is supplemented with a method of proving the existence of periodic points which is used to check rationality of the rotation number. In Manuscript II we provide a numerical algorithm for computing critical points of the multiplier map for the quadratic family (i.e., points where the derivative of the multiplier with respect to the complex parameter vanishes). Manuscript III concerns continued fractions of quadratic irrationals. We show that the generating function corresponding to the sequence of denominators of the best rational approximants of a quadratic irrational is a rational function with integer coefficients. As a corollary we can compute the Lévy constant of any quadratic irrational explicitly in terms of its partial quotients. Finally, in Manuscript IV we develop a method for finding rigorous enclosures of all odd periodic solutions of the stationary Kuramoto-Sivashinsky equation. The problem is reduced to a bounded, finite-dimensional constraint satisfaction problem whose solution gives the desired information about the original problem. Developed approach allows us to exclude the regions in L2, where no solution can exist.

The sorption of humic acid (HA) and HA size fractions onto magnetite has been studied. There is considerable irreversibility in the interaction of the humic with the magnetite surface, but the presence of Eu3+ ions has no effect on the sorption of humic onto magnetite. The magnitude of the sorption to magnetite increases with HA fraction size for all ionic strengths between 0.01 and 3 mol dm-3. Increasing ionic strength also increases sorption. Asymmetric Flow Field Flow Fractionation analysis of HA sorption to magnetite after 1 day revealed preferential sorption of lower molecular weight material. Eu3+ sorption onto magnetite was studied as a function of Eu concentration, which showed an increase in relative sorption as Eu concentration decreased. The behaviour of Eu3+ in ternary (HA/Eu3+/magnetite) systems is heavily influenced by HA, and from the data there is direct evidence for ternary complex formation. Larger HA size fractions retain more Eu3+ in solution than the smaller fractions. The binding strengths of HA size fractions were determined through ion exchange resin experiments: generally the larger fractions (> 10 kDa) showed stronger binding than the smaller components, but the unfractionated sample showed the strongest binding.First order dissociation rate constants have been determined for the whole HA and HA size fractions. The dissociation rate constants are independent of HA fraction size, but the larger species bind more Eu non-exchangeably. Time series ultrafiltration of Eu3+/whole humic mixtures has shown a shift in the distribution of metal ions to larger size fractions after a few days. Two ternary system kinetic speciation models have been developed to predict the behaviour of HA and Eu3+ in ternary systems. The two differ in their description of the multi-component behaviour of the binary HA-mineral interaction. The first assumes a single HA species and two surface binding sites and was found to perform better overall than the second, which has a single surface sorption site and two HA species in solution. The exchangeable binding strengths for the different HA samples calculated from both models showed similarities to those measured experimentally.

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Includes bibliography. / Successful multivariable control system design demands knowledge, skill and creativity of the designer. The goal of the research described in this dissertation was to investigate, implement, and evaluate methods by which artificial intelligence techniques, in a broad sense, may be used in a design system to assist the user. An intelligent, interactive, control system design tool has been developed to fulfil this aim. The design tool comprises two main components; an expert system on the upper level, and a powerful CACSD package on the lower level. The expert system has been constructed to assist and guide the designer in using the facilities provided by the underlying CACSD package. Unlike other expert systems, the user is also aided in formulating and refining a comprehensive and achievable design specification, and in dealing with conflicts which may arise within this specification. The assistance is aimed at both novice and experienced designers. The CACSD package includes a synthesis program which attempts to find a controller that satisfies the design specification. The synthesis program is based upon a recent factorization theory approach, where the linear multivariable control system design problem is translated into, and techniques efficiency solved as, a quadratic programming problem, which significantly improve the time and space of this method have been developed, making it practical to solve substantial multivariable design problems using only a microcomputer. The design system has been used by students at the University of Cape Town. Designs produced using the expert system tool are compared against those produced using classical design methods.

Tal i bråkform är en viktig del av den svenska läroplanen, ett räknesätt som många elever har svårt att förstå. Lärare behöver vara insatta i olika undervisningsmetoder för tal i bråk-form, för att skapa bra undervisningstillfällen för elever. Detta behövs speciellt för elever i matematiksvårigheter. Undervisning ska anpassas utifrån elevers behov, vilket sker bäst när lärare känner till undervisningsmetoder som är fördelaktiga för elevers inlärning. Denna litte-raturstudie presenterar därför 15 undervisningsmetoder som forskning konstaterar som fördel-aktiga för undervisning om tal i bråkform för elever i matematiksvårigheter. Undervisnings-metoderna skiljer sig åt och är fördelaktiga på olika sätt. Undervisningsmetoderna passar också olika bra beroende på elevers tidigare kunskaper. Samtliga undervisningsmetoder för-klaras för att ge en tydlig bild av hur de kan bidra till fördelaktiga inlärningstillfällen för ele-ver i matematiksvårigheter. / Fractions is an important part of the Swedish curriculum, which many students have diffi-culties understanding. Teachers need to be familiar with different teaching methods for frac-tions to create good teaching opportunities for students. Especially for students with mathe-matic difficulties. Teaching should be adapted based on students’ needs, which happens best when teachers know which teaching methods that are beneficial for students’ learning. This literature study therefore presents 15 teaching methods that research finds to be advantageous for teaching fractions to students in mathematical difficulties. The teaching methods differ and are advantageous in different ways. The teaching methods also suit the students differ-ently depending on the students’ previous knowledge. All 15 teaching methods are explained to give a clear picture of how they can contribute to advantageous learning opportunities for students with mathematical difficulties.

The concept of fractions is necessary and vital knowledge in mathematics and has an essential role in perceptions of other mathematical areas. But many claims that this concept is both hard to teach and difficult to understand and thus avoids teaching and using fractions. To find out how the pupils perceive and reason about fractions, didactic theory, George Pólya's, and Frank Lester's problem-solving strategies and the subject theory has been used as a theoretical framework. In the study, which is a case study, participated 24 pupils the ages were between 9 and 10 and performed three diagnoses with a specific focus at part of a whole and part of a number. The diagnostic results were analyzed quantitatively, and then semi-structured interviews were conducted with six pupils according to the selection has obtained from the percentage of the solution frequencies. The results from the diagnoses show that the pupils' solution frequency on the diagnoses was between 14% and 90%. The analyzes from the semi-structured interviews show that the pupils with a lower solution frequency had inadequate knowledge of the concept of fractions and insufficient knowledge of the subject theory and used problem-solving strategies to a very meager extent. The pupils with a higher solution frequency had good perceptions of fractions and had good knowledge of the theory of the subject, and use problem-solving strategies to a much greater extent.

This thesis aims to study a connection between indecomposable elements in the cubic fields and the Jacobi-Perron algorithm (JPA). JPA is a multidimensional generalization of the usual continued fractions algorithm. We work in the family of Ennola's cubic fields and we examine how the indecomposable elements are related to elements originating from this algorithm and whether some of these elements generate all indecomposable elements in the fields. We formulate conjectures on how to determine which elements will generate the indecomposable elements. We also prove some necessary conditions that have to hold for elements originating from this algorithm to generate indecomposable elements. 1