This thesis covers fundamental properties of metric spaces, as well as completeness, compactness, and separability of metric spaces.

The Mirrlees Review recommends that commodity taxation should in general be uniform, but with some goods consumed in conjunction with labour supply (such as child care) left untaxed. This paper examines the validity of this claim in an optimal income tax framework. Contrary to the recommendation of the Review, our theoretical results imply that even if all goods other than the good needed for working are separable from leisure, the optimal tax on these goods should not be uniform. Instead, goods with larger expenditure elasticities should be discouraged relatively more by the tax system. If the government fully subsidises the cost of the good needed for working, then commodity taxation is uniform under the standard separability assumption. Our results imply that the optimal commodity tax system is dependent on the expenditure side of the government. A calibration exercise presented in the paper suggests that these results can be quantitatively important.

There are various notions of positivity for matrices and linear matrix-valued maps that play important roles in quantum information theory. The cones of positive semidefinite matrices and completely positive linear maps, which represent quantum states and quantum channels respectively, are the most ubiquitous positive cones. There are also many natural cones that can been regarded as "more" or "less" positive than these standard examples. In particular, entanglement theory deals with the cones of separable operators and entanglement witnesses, which satisfy very strong and weak positivity properties respectively. Rather complementary to the various cones that arise in entanglement theory are norms. The trace norm (or operator norm, depending on context) for operators and the diamond norm (or completely bounded norm) for superoperators are the typical norms that are seen throughout quantum information theory. In this work our main goal is to develop a family of norms that play a role analogous to the cone of entanglement witnesses. We investigate the basic mathematical properties of these norms, including their relationships with other well-known norms, their isometry groups, and their dual norms. We also make the place of these norms in entanglement theory rigorous by showing that entanglement witnesses arise from minimal operator systems, and analogously our norms arise from minimal operator spaces. Finally, we connect the various cones and norms considered here to several seemingly unrelated problems from other areas. We characterize the problem of whether or not non-positive partial transpose bound entangled states exist in terms of one of our norms, and provide evidence in favour of their existence. We also characterize the minimum gate fidelity of a quantum channel, the maximum output purity and its completely bounded counterpart, and the geometric measure of entanglement in terms of these norms. / Natural Sciences and Engineering Research Council (Canada Graduate Scholarship), Brock Scholarship

Spectroradiometer data (350 – 2500 nm) were acquired in late summer 1999 over various forest sites in Appomattox Buckingham State Forest, Virginia, to assess the spectral differentiability among six major forestry tree species, loblolly pine (Pinus taeda), Virginia pine (Pinus virginiana), shortleaf pine (Pinus echinata), scarlet oak (Quercus coccinea), white oak (Quercus alba), and yellow poplar (Liriodendron tulipifera). Data were smoothed using both moving (9-point) and static (10 nm average) filters and curve shape was determined using first and second differences of resultant data sets. Stepwise discriminant analysis decreased the number of independent variables to those significant for spectral discrimination at -level of 0.0025. Canonical discriminant analysis and a normal discriminant analysis were performed on the data sets to test separability between and within taxonomic groups. The hardwood and pine groups were shown to be highly differentiable with a 100% cross-validation accuracy. The three pines were less differentiable, with cross-validation results varying from 61.64% to 84.25%, while spectral separability among the three hardwood species showed more promise, with classification accuracies ranging from 78.36% to 92.54%. The second difference of the 9-point weighted average filter was the most effective data set, with accuracies ranging from 84.25% to 100.00% for the separability tests. Overall, variables needed for spectral discrimination were well distributed across the 350 nm to 2500 nm spectral range, indicating the usefulness of the whole wavelength range for discriminating between taxonomic groups and among species. Derivative analysis was shown to be effective for between and within group spectral discrimination, given that the data were smoothed first. Given the caveat of the limited species diversity examined, results of this study indicate that leaf-on hyperspectral remotely sensed data will likely afford spectral discrimination between hardwoods and softwoods, while discrimination within taxonomic groups might be more problematic. / Master of Science

We define a strong form of subgroup separability, which we call RS separability, and we use this to combine LERF and Agol’s RFRS condition on groups into a property called LVRSS. We show that some infinite classes of groups that are known to be both subgroup separable and virtually RFRS are also LVRSS. We also provide evidence for the naturalness of RS separability and LVRSS by showing that they are preserved under various operations on groups. / text

Let G be a reductive algebraic group defined over an algebraically closed field of characteristic p. A subgroup H of G is called G-complete reducible whenever H is contained in a parabolic subgroup P of G, it is contained in some Levi subgroup of P. In this thesis, we present a pair of reductive subgroups H and M of G of type E_7 such that H<M and H is G-completely reducible but not M-completely reducible.

This thesis is focused on separation water drops from jet of steam. Liested are some of basic principles of separation of moisture and particles, as well as equipment, which are using these principles. Furthemore, this thesis include the part devoted to water drop formation during condesation of vapor. Last part is focused on the design of cyclone separator.

A demanda atual pela utilização de materiais reciclados na construção deve-se ao aumento crescente do consumo de agregados, à exaustão de jazidas próximas aos grandes centros e à proibição de deposição de resíduos inertes em aterros sanitários. Paralelamente, com o crescimento evidente do setor da construção em muitos países, o gerenciamento dos resíduos de construção e demolição (RCD) tornou-se uma questão econômica e ambiental prioritária. Para a sustentabilidade do meio ambiente construído é imprescindível o desenvolvimento de novas aplicações para o agregado reciclado visando a ampliação das taxas de reciclagem. No entanto, a situação da fração areia de RCD é crítica, pois apesar de representar de 40 a 60% em massa do resíduo, é descartada como resíduo da própria reciclagem ou utilizada em aplicações de baixo valor agregado. Dentro deste contexto, o objetivo deste trabalho consiste em estudar alternativas para a produção de areia reciclada a partir do processamento integral de resíduos de construções e demolições da região metropolitana de São Paulo, em uma abordagem inédita mundialmente. O estudo realizado pode ser subdividido em quatro etapas principais: a) amostragem; b) produção de areia a partir dos resíduos amostrados; c) estudos de separabilidade da areia reciclada; d) caracterização tecnológica dos produtos gerados como ferramenta de controle de qualidade de eficiência dos processos. Os resultados demonstraram que o processamento integral de RCD por britagem terciária em impactador de eixo vertical é determinante na cominuição seletiva das fases porosas e na liberação entre a pasta de cimento e as fases minerais. O produto gerado apresentou menor conteúdo de pasta de cimento, partículas mais esféricas e reduzida porosidade. Adicionalmente demonstrou-se a separabilidade densitária e magnética entre as fases minerais dos agregados e a pasta de cimento. Dentre os procedimentos de caracterização destaca-se o desenvolvimento de uma metodologia para definição das associações das fases presentes, particularmente da individualização da pasta de cimento e carbonatos. / The current demand for recycling on construction is due to the increasing consumption of aggregates, the exhaustion of deposits close to large cities as well as the ban on inert materials dumping in landfills and the rising cost of its disposal. Moreover, with the remarkable increasing on construction activities in many countries, the management of Construction and Demolition Waste (CDW) became an economical and environmental priority issue. To the sustainability of the built environment, the development of new applications for recycled aggregates and the increase of recycling rates are vital. However, the situation of the sand fraction of CDW is critical; although it accounts for 40 to 60% by weight of the waste, it is disregarded as waste recycling material or used in applications with low added-value. In this context, the present research explores the potential of mineral processing technologies to produce recycled sand by total comminution of the CDW on sand fractions in an unprecedented approach worldwide. The improvement on recycled sand quality is crucial for the enlargement of recycling rates. The study may be described in four main steps: a) sampling of construction and demolition waste from Sao Paulo metropolitan area, Brazil; b) production of recycled sand from the sampled waste; c) separability studies of the recycled sand; d) technological characterization of the attained products to evaluate the processing efficiency. The results demonstrated that the processing of the whole waste by tertiary crushing is fundamental to the selective comminution of porous phases and to the separation of cement paste from mineral phases. The attained product exhibited reduced content of cement paste, particles with higher sphericity and lower porosity. Additionally, it was demonstrated that the separability of aggregates from cement paste is feasible by density and magnetic separation. Regarding the characterization procedures, the development of an innovative method for a precise evaluation of the content of cement paste and phases associations, must be highlighted, especially on the measurement of cement paste and carbonates separately.

<p>In case of the PDE's the concept of solving by separation of variables</p><p>has a well defined meaning. One seeks a solution in a form of a</p><p>product or sum and tries to build the general solution out of these</p><p>particular solutions. There are also known systems of second order</p><p>ODE's describing potential motions and certain rigid bodies that are</p><p>considered to be separable. However, in those cases, the concept of</p><p>separation of variables is more elusive; no general definition is</p><p>given.</p><p>In this thesis we study how these systems of equations separate and find that their separation usually can be reduced to sequential separation of single first order ODE´s. However, it appears that other mechanisms of separability are possible.</p>

In case of the PDE's the concept of solving by separation of variables has a well defined meaning. One seeks a solution in a form of a product or sum and tries to build the general solution out of these particular solutions. There are also known systems of second order ODE's describing potential motions and certain rigid bodies that are considered to be separable. However, in those cases, the concept of separation of variables is more elusive; no general definition is given. In this thesis we study how these systems of equations separate and find that their separation usually can be reduced to sequential separation of single first order ODE´s. However, it appears that other mechanisms of separability are possible.