A semigroup is simply a set with an associative binary operation; computational semigroup theory is the branch of mathematics concerned with developing techniques for computing with semigroups, as well as investigating semigroups with the help of computers. This thesis explores both sides of computational semigroup theory, across several topics, especially in the finite case. The central focus of this thesis is computing and describing maximal subsemigroups of finite semigroups. A maximal subsemigroup of a semigroup is a proper subsemigroup that is contained in no other proper subsemigroup. We present novel and useful algorithms for computing the maximal subsemigroups of an arbitrary finite semigroup, building on the paper of Graham, Graham, and Rhodes from 1968. In certain cases, the algorithms reduce to computing maximal subgroups of finite groups, and analysing graphs that capture information about the regular I-classes of a semigroup. We use the framework underpinning these algorithms to describe the maximal subsemigroups of many families of finite transformation and diagram monoids. This reproduces and greatly extends a large amount of existing work in the literature, and allows us to easily see the common features between these maximal subsemigroups. This thesis is also concerned with direct products of semigroups, and with a special class of semigroups known as Rees 0-matrix semigroups. We extend known results concerning the generating sets of direct products of semigroups; in doing so, we propose techniques for computing relatively small generating sets for certain kinds of direct products. Additionally, we characterise several features of Rees 0-matrix semigroups in terms of their underlying semigroups and matrices, such as their Green's relations and generating sets, and whether they are inverse. In doing so, we suggest new methods for computing Rees 0-matrix semigroups.

We investigate various relationships between categories of functors. The major examples are given by extending some duality to a larger structure, such as an adjunction or a recollement of abelian categories. We prove a theorem which provides a method of constructing recollements which uses 0-th derived functors. We will show that the hypotheses of this theorem are very commonly satisfied by giving many examples. In our most important example we show that the well-known Auslander-Gruson-Jensen equivalence extends to a recollement. We show that two recollements, both arising from different characterisations of purity, are strongly related to each other via a commutative diagram. This provides a structural explanation for the equivalence between two functorial characterisations of purity for modules. We show that the Auslander-Reiten formulas are a consequence of this commutative diagram. We define and characterise the contravariant functors which arise from a pp-pair. When working over an artin algebra, this provides a contravariant analogue of the well-known relationship between pp-pairs and covariant functors. We show that some of these results can be generalised to studying contravariant functors on locally finitely presented categories whose category of finitely presented objects is a dualising variety.

The kinetic schemes, also known as Boltzmann schemes are based on the moment-method-strategy, where an upwind scheme is first developed at the Boltzmann level and after taking suitable moments we arrive at an upwind scheme for the governing Euler or Navier-Stokes equations. The Kinetic Flux Vector Splitting (KFVS)scheme, which belongs to the family of kinetic schemes is being extensively used to compute inviscid as well as viscous flows around many complex configurations of practical interest over the past two decades. To resolve many flow features accurately, like suction peak, minimising the loss in stagnation pressure, shocks, slipstreams, triple points, vortex sheets, shock-shock interaction, mixing layers, flow separation in viscous flows require an accurate and low dissipative numerical scheme. The first order KFVS method even though is very robust suffers from the problem of having much more numerical diffusion than required, resulting in very badly smearing of the above features. However, numerical dissipation can be reduced considerably by using higher order kinetic schemes. But they require more points in the stencil and hence consume more computational time and memory. The second order schemes require flux or slope limiters in the neighbourhood of discontinuities to avoid spurious and physically meaningless wiggles or oscillations in pressure, temperature or density. The limiters generally restrict the residue fall in second order schemes while in first order schemes residue falls up to machine zero. Further, pressure and density contours or streamlines are much smoother for first order accurate schemes than second order accurate schemes. A question naturally arises about the possibility of constructing first order upwind schemes which retain almost all advantages mentioned above while at the same time crisply capture the flow features. In the present work, an attempt has been made to address the above issues by developing yet another kinetic scheme, known as the low dissipative modified KFVS (m-KFVS) method based on modified CIR (MCIR) splitting with molecular velocity dependent dissipation control function. Different choices for the dissipation control function are presented. A detailed mathematical analysis and the underlying physical arguments behind these choices are presented. The expressions for the m-KFVS fluxes are derived. For one of the choices, the expressions for the split fluxes are similar to the usual first order KFVS method. The mathematical properties of 1D m-KFVS fluxes and the eigenvalues of the corresponding flux Jacobians are studied numerically. The analysis of numerical dissipation is carried out both at Boltzmann and Euler levels. The expression for stability criterion is derived. In order to be consistent with the interior scheme, modified solid wall and outer boundary conditions are derived by extending the MCIR idea to boundaries. The cell-centred finite volume method based on m-KFVS is applied to several standard test cases for 1D, 2D and 3D inviscid flows. In the case of subsonic flows, the m-KFVS method produces much less numerical entropy compared to first order KFVS method and the results are comparable to second order accurate q-KFVS method. In transonic and supersonic flows, m-KFVS generates much less numerical dissipation compared to first order KFVS and even less compared to q-KFVS method. Further, the m-KFVS method captures the discontinuities more sharply with contours being smooth and near second order accuracy has been achieved in smooth regions, by still using first order stencil. Therefore, the numerical dissipation generated by m-KFVS is considerably reduced by suitably choosing the dissipation control variables. The Euler code based on m-KFVS method almost takes the same amount of computational time as that of KFVS method. Although, the formal accuracy is of order one, the m-KFVS method resolves the flow features much more accurately compared to first order KFVS method but the numerical dissipation generated by m-KFVS method may not be minimal. Hence, the dissipation control vector is in general not optimal. If we can find the optimal dissipation control vector then we will be able to achieve the minimal dissipation. In the present work, the above objective is attained by posing the minimisation of numerical dissipation in m-KFVS method as an optimal control problem. Here, the control variables are the dissipation control vector. The discrete form of the cost function, which is to be minimised is considered as the sum of the squares of change in entropy at all cells in the computational domain. The number of control variables is equal to the total number of cells or finite volumes in the computational domain, as each cell has only one dissipation control variable. In the present work, the minimum value of cost function is obtained by using gradient based optimisation method. The sensitivity gradients of the cost function with respect to the control variables are obtained using discrete adjoint approach. The discrete adjoint equations for the optimisation problem of minimising the numerical dissipation in m-KFVS method applied to 2D and 3D Euler equations are derived. The method of steepest descent is used to update the control variables. The automatic differentiation tool Tapenade has been used to ease the development of adjoint codes. The m-KFVS code combined with discrete adjoint code is applied to several standard test cases for inviscid flows. The test cases considered are, low Mach number flows past NACA 0012 airfoil and two element Williams airfoil, transonic and supersonic flows past NACA 0012 airfoil and finally, transonic flow past Onera M6 wing. Numerical results have shown that the m-KFVS-adjoint method produces even less numerical dissipation compared to m-KFVS method and hence results in more accurate solution. The m-KFVS-adjoint code takes more computational time compared to m-KFVS code. The present work demonstrates that it is possible to achieve near second order accuracy by formally first order accurate m-KFVS scheme while retaining advantages of first order accurate methods.

Young adult literature (YA) has been stereotypical in many of its portrayals of LGBTQ teens from the 1960s to the early 2000s, but three contemporary YA series--Cassandra Clare's The Mortal Instruments, Sarah Rees Brennan's Demons trilogy, and Holly Black's Modern Faerie Tales--indicate a change toward more nuanced characterizations. Using four categories--scriptedness, context, importance, and sexuality--to determine whether these representations of LGBTQ youth challenge or reiterate older tropes, my analysis indicates that YA has moved toward more complex representations of queerness, yet some normative discursive structures are still at work, such as poisonings or curses, supernatural parallels to coming out, and heteronormative humour. Although representations of queerness have diversified, then, the implicit ideologies in each author's portrayal of queerness demands closer attention.

This report has investigated the ethical issues associated with mining or processing of materials that make them considered as controversial. For each material, the main areas of use and the top producing countries are analysed, followed by social and/or environmental issues as well as potential problems in the future. In total, 13 materials are discussed, of which most are minerals. The overall issues, that are recurring throughout the report and are important to be aware of are: child labor, low safety standards, mining activity resulting in deforestation or harming biodiversity, mining processes that affect communities (e.g. because of large water consumption) and the risks associated with widespread illegal mining. The report also provides research about organisations and initiatives that aim to affect the problems, and gives a brief view over tools that can be used to increase awareness of these issues.

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UBC's Drs. Walter Hardy, Doug Bonn and Ruixing Liang were awarded the 2006 Brockhouse Canada Prize for Interdisciplinary Research in Science and Engineering. A partnership between Dr. Helen Burt's reseach laboratory and Angiotech Pharmaceuticals has earned the 2006 NSERC Synergy Award for Innovation.