Os objetivos deste trabalho são: i) Fixado um inteiro positivo n, estudar dois métodos "construtivos" para aproximar-se uma função real contínua definida na esfera unitária S ^{r-1} de R^r, por polinômios esféricos de grau <=n; ii) Obter estimativas para as normas dos operadores de interpolação e hiperinterpolação, comparando-as com a norma da projeção ortogonal de C(S^{r-1}) sobre o espaço de polinômios onde as aproximações residem. / This work addresses two issues: i) To study two constructive methods to approximate a real continuous function on the unit sphere S^{r-1} of R^r by spherical polynomials of degree <=n (n fixed); ii) To estimate the norms of the interpolation and hyperinterpolation operators, comparing them with the norm of the orthogonal projection of C(S^{r-1}) over the polynomial space where the approximations live.

SiC is used as the main diffusion barrier in the fuel spheres of the pebble bed modular reactor (PBMR). The PBMR is a modern high temperature nuclear reactor. However, the release of silver from the fuel spheres has raised some doubts about the effectiveness of this barrier, which has led to many studies on the possible migration paths of silver. The reported results of these studies have shown largely differing results concerning the magnitude and temperature dependence of silver being transported through the fuel particle coatings. Results from earlier investigations could be interpreted as a diffusion process governed by an Arrhenius type temperature dependence. In this study, the silver diffusion in 6H-SiC was investigated using two methods. In the first method a thin silver layer was deposited on 6H-SiC by vapour deposition while in the second method silver was implanted in 6H-SiC at room temperature, 350°C and 600°C to a fluence of 2×1016 silver ions cm-2. Finally the effect of neutron irradiation on the diffusion of silver was investigated for the samples implanted at 350°C and 600°C. Silver depth profiles before and after annealing were determined by Rutherford backscattering (RBS). Both isothermal and isochronal annealing were used in this study. Diffusion coefficients as well as detection limits were extracted by comparing the silver depth profiles before and after annealing. The radiation damage after implantation and their recovery after isothermal and isochronal annealing were analysed by Rutherford backscattering spectroscopy combined with channelling. The results of in-diffusion of silver into 6H-SiC at temperatures below the melting point (960°C) using un-encapsulated 6H-SiC samples with 100 nm deposited silver indicated no in-diffusion of silver; however, disappearance of silver occurred at these temperatures. For the encapsulated samples, no in-diffusion of silver was observed at 800°C, 900°C and 1000°C but silver disappeared from the samples’ surface and was found on the walls of the quartz glass ampoule. This disappearance of silver was established to be due to the wetting problem that existed between silver and SiC. The room temperature implantation resulted in a completely amorphous surface layer of approximately 270 nm thick. Epitaxial re-growth from the bulk was already taking place during annealing at 700°C and the crystalline structure seemed to be fully recovered at 1600°C, for samples that were sequentially isochronally annealed from 700°C in steps of 100°C up to 1600°C. However, no silver signal was detected at this temperature, which left certain doubts regarding the crystalline structure of the samples at this temperature. This was speculated to be due to thermal etching of the top original amorphous layer while the deeper amorphous layer was epitaxial re-growth from the bulk. The decomposition of SiC, giving rise to a carbon peak in the RBS spectra due to evaporation of Si, was clearly observed on the same samples at 1600°C. Isothermal annealing at 1300°C for 10 h cycles up to 80h caused epixatial re-growth from the bulk during the first annealing cycle (10h). No further epitaxial re-growth from the bulk was observed up to 80h. This was believed to be due to the amorphous layer re-crystallising into crystals that were randomly oriented to the 6H-SiC substrate. No diffusion of silver was observed at temperatures below 1300°C but silver seemed to form precipitates at these temperatures. Diffusion of silver towards the surface accompanied by silver loss from the surface began at 1300°C and was very high at 1400°C, with silver profiles becoming asymmetric and closer to the surface. The loss of silver was already taking place at 1100°C. This loss was found to be due to the following: diffusion of silver towards the surface; the mass flow of silver via holes that were observed to be becoming larger with higher annealing temperatures on SiC surfaces and thermal etching of SiC. Isothermal annealing at 1300°C for 10h up to 80h caused diffusion of silver during the first annealing cycle, while no further diffusion was observed for any further annealing at the same temperature up to 80 h. The diffusion coefficient was not calculated due to the lack of information on the structural evolution of SiC during the first annealing cycle. Isothermal annealing at 1300°C and 1350°C for 30 minute cycles up to 120 minutes caused high diffusion during the first cycle and reduced diffusion during the second cycle, while no diffusion was observed for any further annealing longer than the second cycle. The higher diffusion during the first 30 minutes was due to ion induced amorphization. The diffusion of silver in amorphised SiC was measured at different temperatures in the range 1300°C to 1385°C and yielded to Do ~ 1.4 × 10-12 m2s-1 and Ea ~ 3.3 × 10-19 J. These values were found to be approximately the same as the values of silver diffusion in polycrystalline CVD-grown SiC found by our group which were due to grain boundary diffusion: Do ~ 4×10-12 m2 s-1 and Ea ~ 4×10-19 J. Implantation of silver at 600°C retained crystallinity although distortions occurred in the implanted region while implantation at 350°C also retained crystallinity but more distortions occurred as compared to silver implanted at 600°C. This was caused by the fact that at 600°C, the displaced atoms were more mobile because of their higher thermal energy than at 350°C. The higher thermal energy increased the probability of the displaced atoms combining with their original lattice sites. Annealing of these samples at 1300°C, 1350°C and 1500°C caused the annihilation of some defects but certain others were retained. No diffusion of silver was observed during annealing of the samples (implanted at 350°C and at 600°C) at 1300°C, 1350°C and 1500°C but silver moved towards the surface at 1500°C. The upper limit of the diffusion coefficient of D < 10-21 m2s-1 was obtained at 1300°C. The movement of silver towards the surface was found to be due to thermal etching at 1500°C. Neutron irradiation of these samples caused no silver diffusion but silver -110mAg, due to -109Ag capturing a neutron during neutron irradiation, was detected in the samples. / Thesis (PhD)--University of Pretoria, 2010. / Physics / unrestricted

Adult female guinea pigs received subcutaneous implants of diethylstilbestrol-cholestrol pellets which produced splenomegaly and increased numbers of splenic Kurloff cells. Latex spheres subsequently injected intravenously were not phagocytized by Kurloff cells within the lungs and spleen as examined with the electron microscope. This is considered as evidence that Kurloff cells are probably not phagocytic. The origin of these cells is discussed.

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In real world applications such as the transporting of goods products, packing is a major issue. Goods products need to be packed such that the smallest space is wasted to achieve the maximum transportation efficiency. Packing becomes more challenging and complex when the product is circular/spherical. This thesis focuses on the best way to pack three-dimensional unit spheres into the smallest spherical and cubical space. Unit spheres are considered in lieu of non-identical spheres because the search mechanisms are more difficult in the latter set up and any improvements will be due to the search mechanism not to the ordering of the spheres. The two-unit sphere packing problems are solved by approximately using a variable neighborhood search (VNS) hybrid heuristic. A general search framework belonging to the Artificial Intelligence domain, the VNS offers a diversification of the search space by changing neighborhood structures and intensification by thoroughly investigating each neighborhood. It is exible, easy to implement, adaptable to both continuous and discrete optimization problems and has been use to solve a variety of problems including large-sized real-life problems. Its runtime is usually lower than other meta heuristic techniques. A tutorial on the VNS and its variants along with recent applications and areas of applicability of each variant. Subsequently, this thesis considers several variations of VNS heuristics for the two problems at hand, discusses their individual efficiencies and effectiveness, their convergence rates and studies their robustness. It highlights the importance of the hybridization which yields near global optima with high precision and accuracy, improving many best- known solutions indicate matching some, and improving the precision and accuracy of others. Keywords: variable neighborhood search, sphere packing, three-dimensional packing, meta heuristic, hybrid heuristics, multiple start heuristics.

Calcium phosphate spheres as biomaterials have been attracting attention in recent years. Calcium phosphate occurs naturally in bone, and a hollow structure could be advantageous for drug loading and release. The combination of a calcium phosphate chemistry and a spherical-hollow structure could be an optimal strategy for specific biomaterial applications, e.g., certain dental and drug-delivery applications. The focus of this thesis is on the synthesis, formation mechanism and applications of hollow, spherical calcium phosphate particles. First, the thesis describes two methods for the synthesis of calcium phosphate (CaP) spherical particles. The first method involves synthesis of hollow calcium phosphate spherical particles via a supersaturated buffer solution based on a previous study. It was utilised to prepare spheres for applications in drug delivery and dentistry. The second method was developed to explain the mechanism of formation of hollow calcium phosphate spheres. It aimed at revealing the particular function of magnesium in the formation of spherical particles. With the use of this modified method, it could be concluded that the only ions active in the formation of CaP spherical particles are calcium ions, phosphate ions and magnesium ions. Compared with the thermodynamics of micellisation, a new model, called three ions virtual micelle effect, was developed to explain the mechanism of the Mg function. Following this mechanism, a series of spherical particles of other compositions were explored. These spherical particles included strontium phosphate, barium phosphate, calcium fluoride, strontium fluoride and barium fluoride. In this thesis, CaP spheres were studied for the controlled delivery of active ingredients and as active agent for tooth remineralisation. The first investigated application was to control the release of vancomycin from Poly(methyl methacrylate) (PMMA) cement via strontium-doped CaP spheres (SCPS). The results showed that incorporation of CaP spheres into PMMA could enhance antibiotic release while maintaining the mechanical strength. The second application was to control hydrogen peroxide (HP) release from two bleaching gel, in which CP-loaded CaP spheres were the active ingredient. One gel with low HP concentration was developed as an at-home bleaching gel, and one with high HP concentration was developed as an in-office bleaching gel. The results showed that CaP spheres would give a controlled release of peroxide and thus have a potential to increase the efficacy of the bleaching. The third application was to investigate the potential for an anti-sensitivity effect of the spheres, as active agents in toothpaste. We studied the tooth tubules occlusion and the remineralisation effect of CaP spheres. After 7 days of application, the open dentin tubules and surface were fully covered by a newly formed apatite layer, demonstrating the remineralisation potential of the spheres.

Foi estudada a cristalização de suspensões aquosas de esferas de poliestireno (850&#197, 910&#197 e 1090&#197 de diâmetro) no limite de baixas concentrações -1011 a 1013 esferas / cm3. A dependência do parâmetro de rede com a concentração original (n) da suspensão aquosa apresenta uma transição de fase da fase bcc para fcc, conforme já foi observada por outros autores. Observamos também que durante a cristalização a concentração de esferas no cristal Ra sistematicamente maior do que na solução original, portanto a água estaria sendo expelida para a solução durante a cristalização. Baseado nestas observações nós propomos um modelo de cristalização onde os cristalites (concentração n1) estão em equilíbrio termodinâmico com uma solução com concentração n2 (n1&#62 n &#62 n2), dando para cada concentração inicial um diferente parâmetro de rede determinado por este equilíbrio. Nossos resultados mostraram que o coeficiente de expulsão da água durante a cristalização é dependente do raio da esfera. Para realizar as medidas de parâmetro de rede nós adaptamos para as nossas condições particulares o método de Debye-Scherrer usado em difração de raios-X por cristais. O equivalente à fonte de raios-X era um laser de Argônio com comprimentos de onda variáveis. Diversas experiências novas são sugeridas. / The crystallization of aqueous suspensions of polystyrene spheres 850&#197, 910&#197 and 1090&#197 of diameter) was studied in the limit of low concentration -1011 to 1013 spheres / cm3. The dependence of the lattice parameter with the original concentration (n) of the aqueous suspension shows a phase transition from bcc to fcc phase as it was already been observed by others authors. We also observed that during crystallization the concentration of spheres in the crystal was systematically higher than in the original solution, showing that water should be expelled toward the solution during crystallization where the crystallites (concentration n1) are in thermodynamic equilibrium with a solution with concentration n2 (n1&#62 n &#62 n2) giving for each initial concentration a different lattice parameter determined by this equilibrium. Our results showed that coefficient of water rejection during crystallization is dependent on the sphere radius. In order to make the measurements of the lattice parameter we adapted to our particular conditions the Debye-Scherrer method used in X-ray diffraction of crystals. The equivalent to the X-ray source was a tunable Argon laser. Several new experiments are suggested.

One of the methods used for the construction of the classical Alexander horned sphere leads naturally to generalization to horned spheres of higher order. Let M2, denote the Alexander horned sphere. This is a 2-horned sphere of order 2. Denote by M 3 and M4, two 2-horned spheres of orders 3 and 4, respectively, constructed by such a generalization. The fundamental groups of the complements of M2, M3, and M4 are derived, and representations of these groups onto the Alternating Group, A5, are found. The form of the presentations of these fundamental groups leads to a more general class of groups, denoted by Gk, k ≥ 2. A set of homomorphisms ϴkl : Gk, k ≥ l ≥ 2 is found, which has a clear geometric meaning as applied to the groups G2, G3, and G4. Two theorems relating to direct systems of non-abelian groups are proved and applied to the groups Gk. The implication of these theorems is that the groups Gk, k≥2 are all free groups of countably infinite rank and that the embeddings of M2, M3, and M4 in E3 cannot be distinguished by means of fundamental groups. *33 pages)

This research mainly includes two parts. First, monodispersed silica spheres with diameter about 58 and 73 nm were successfully synthesized. The tablet-like silica template could be made using a stainless steel mold by pressing the mold with a pressure ~ 10 MPa. The advantage of this molding process is it takes only a short time to accomplish the total fabrication. Second, infiltration of the carbon precursor was done using the monomers resorcinol (R) and furfural (F) in the interval of tablet-like silica template, and then polymerization and drying. It was subsequently carbonized in N2 atmosphere at 800 ¢J and then the silica template was removed by 20 wt % HF solution. The activated porous carbon material has larger specific surface area than the traditional powder carbon material. The chemical activation process by KOH plays a vital role in raising the specific surface area, since the KOH would etch the carbon pore surface to produce a large number of micropores (diameter < 2 nm), forming a macro-micro or meso-micro porous carbon materials. The F/R molar ratios for polymerization between 2.0 to 3.0 were applied and the carbon yields of these resins were higher than 51% in this range. An F/R ratio below 2.0 or 3.0 gave a lower carbon yield when carbonization at 800 ¢J. X-ray diffraction analyses on the macroporous carbon materials indicate a semi-crystalline structure which belong to the hexagonal crystal system with (002) d-spacing of = 0.373 nm, which is larger than the 0.339 nm of graphite. In Raman spectra analysis, the integral area of D-peak (ID) and G-peak (IG) is an index to define the degree of graphitization. The ratios ID/IG of lie between 1.7 - 1.8, which are larger than that of graphite (ID/IG = 0.1 - 0.3), so the FR series macroporous carbon is mostly amorphous and is far from highly crystallized structure. The un-activated macroporous carbon materials has open pore structure, the pore diameter is 56 nm which is classified to the macroporous scale. The nitrogen adsorption/desorption isotherm of the porous carbon materials belongs to the type IV, with H1 type hysteresis. The BET results show that the specific surface area increases with increasing KOH concentration; whereas the open pore structure remain the same. SEM observations reveal the pore structure doesn¡¦t collapse but the pore wall does become thinner. From this work, macroporous carbon materials with total pore volume as high as 2.23 cm3/g and the specific surface area as high as 658 m2/g have successfully been synthesized. Activation by KOH creates more micropores on its carbon walls, resulting in a macro-microporous carbon material having two scales of pores in the same time and with a high surface area of 1404 m2/g.

Inquiry into how social movements affect change has historically been grounded in either sociology or communication studies and has focused primarily on collective action in public spheres. However, important movement activity also takes place in the private sphere between individuals. Such interactions fall outside of traditional definitions of collective action and are often absent from contemporary social movement theory.One social movement that cannot be studied adequately using existing theory and methods is the American ethical vegetarian movement. To correct this oversight in social movement theory, this dissertation undertakes a rhetorical study of the ethical vegetarian movement, focusing not only on collective action but also on the role of personal interaction in identity formation, participant recruitment, and participant mobilization. A major finding of this study is that personal interaction is the primary reason why individuals choose to adopt and advocate a vegetarian or vegan lifestyle. In order to establish how movement rhetoric works, the dissertation includes rhetorical analyses of cookbooks, organization literature, media representation, interviews with movement advocates, and vegetarian conversion narratives, collected through a national survey. The author explores the use and consequences of unintentional, religious, and embodied rhetoric as means of confrontation and conversion in the ethical vegetarian movement.In this dissertation, Patricia Malesh argues for an interdisciplinary approach to the study of social movements that includes inquiry into personal interaction as movement activity. Such an inquiry clarifies the relationship between personal and collective identities and deconstructs the dichotomy between private and public spheres. She also establishes a rhetorical definition of individual movements, which exposes the interplay between movement goals and methods of persuasion and helps differentiate between similar movements (e.g., vegetarian and animal rights movements) and align those that are seemingly unrelated (e.g., vegetarian and feminist movements). The author concludes by discussing the future of the ethical vegetarian movement in the face of globalization and incorporation. She argues that rhetoricians--those who study the practice and implications of communication--should contribute more consistently to the study of how social identity is negotiated through language and action in social movements.