<p>In this work we examine a state constrained resource allocation model a with finite time horizon. Therefore, we use the necessary conditions of the Pontrjagin's Maximum Principle to find candidates for the solution and verify them later on using the sufficient conditions given by the duality concept of Klötzler. Moreover, we proof that the solution of the corresponding infinite horizon model does not fulfill the overtaking criterion of Weizsäcker.</p>

This thesis is a collection of four papers that explore the economics of forest carbon sequestration and optimal harvest decision, considering carbon storage in three major carbon pools: biomass, dead organic matter and wood product. The first three papers use a dynamic programming approach to determine the optimal harvest decision for a forest stand in the boreal forest of western Canada that provides both timber harvest volume and carbon sequestration services. The last paper uses an analytical model to confirm the findings in the first three papers that show that the optimal rotation age is dependent on the carbon stocks in the dead organic matter and wood product pools. In the first paper, the state of the forest at any point in time is described by stand age and the amount of carbon in the dead organic matter pool. The results of the study indicate that while optimal harvest age is relatively insensitive to carbon stocks in dead organic matter, initial carbon stock levels significantly affect economic returns to carbon management. In the second paper, the system is described by three state variables: stand age and the amount of carbon in the dead organic matter and wood product pools. The results of the study suggest that optimal behaviour of a landowner does not change much between cases where the market considers and ignores carbon storage in the wood product pool or between cases where the market considers and ignores fossil fuel carbon emissions. The third paper demonstrates that alternative baselines have little or no effect on the optimal decision, but can have a large effect on financial return to landowner. In the third paper, the forest stand is described by four state variables: the age of the stand, the initial stand age, carbon stocks in the DOM pool and the initial carbon stocks in the DOM pool. In the last paper, an analytical model is used to demonstrate that the optimal harvest decision is dependent on the initial DOM and wood product stocks. This finding is consistent with the results in the previous papers. / Forest Biology and Management

Studying dynamical mechanisms of perturbation growth in tropical cyclones is important from a perspective of designing ensemble prediction system and adaptive observations for tropical cyclones. In this thesis, the role of perturbations in ensemble forecasting and adaptive observations for tropical cyclones is investigated, especially focusing on tropical cyclone tracks. For this purpose, ensemble initial perturbations from operational numerical weather prediction centers are first diagnosed, followed by a study in which the structure and location of singular vectors computed for tropical cyclone-like vortices in a nondivergent barotropic framework are investigated. The three most significant findings of this study are that 1) perturbations grow in the vicinity of tropical cyclones through both baroclinic and barotropic energy conversion as seen in mid-latitude dynamics, that 2) those energy conversions lead to the modification in tracks of tropical cyclones, and that 3) the structure and the location of growing perturbations are sensitive to initial temperature and wind profiles of the tropical cyclone vortex. The above results (1) and (2) determine a mechanism how the ensemble spread of tropical cyclone tracks evolves with time in ensemble prediction systems at operational numerical weather prediction centers. In addition, those results identify the reason why the ensemble spread differs from one ensemble prediction system to another. The result (3) gives an insight into understanding what sensitivity analysis guidance targeted for tropical cyclones represents and helps to optimize observation network for tropical cyclones.

In this work we examine a state constrained resource allocation model a with finite time horizon. Therefore, we use the necessary conditions of the Pontrjagin's Maximum Principle to find candidates for the solution and verify them later on using the sufficient conditions given by the duality concept of Klötzler. Moreover, we proof that the solution of the corresponding infinite horizon model does not fulfill the overtaking criterion of Weizsäcker.

This work provides first and second-order expressions to approximate neighboring solutions to the m-point boundary value problem. Multi-point problems arise in optimal control because of interior constraints or switching dynamics. Many problems have this form, and so this work fills a void in the study of extremal fields and neighboring optimal control of constrained systems. Only first and second-order terms are written down, but the approach is systematic and higher order expressions can be found similarly. The constraints and their parameters define an extremal field because any solution to the problem must satisfy the constraints. The approach is to build a Taylor series using constraint differentials, state differentials, and state variations. The differential is key to these developments, and it is a unifying element in the optimization of points, optimal control, and neighboring optimal control. The method is demonstrated on several types of problems including lunar descent, which has nonlinear dynamics, bounded thrust, and free final time. The control structure is bang-off-bang, and the method successfully approximates the unknown initial conditions, switch times, and final time. Compared to indirect shooting, computation time decreases by about three orders of magnitude.

This dissertation proposes a new, synthesized perspective for explaining the “Nonmetropolitan Turnaround” in the 1970s and 1990s. By studying the definition of urbanization carefully, using the human ecological perspective, many processes happening during the “Nonmetropolitan Turnaround” in the 1970s and 1990s, such as suburbanization, deconcentration, and counterurbanization, can be understood as different forms of the urbanization processes. When the majority of the population was rural, the dominant pattern of urbanization was rural-urban migration. When the majority of the population became urban, the dominant urbanization pattern reversed to urbanrural migration because urban centers had reached beyond their optimal density and processes operated to reduce their density. This paper hypothesizes that the two “turnarounds” were simply the result of different aspects of urbanization complicated by metropolitan status reclassifications. The perspectives of suburbanization, counterurbanization and deconcentration are integrated into the urbanization perspective. Using migration flow data compiled by the Census Bureau from 1975 to 1980 and from 1995 to 2000, the summary analyses confirmed that the net migration due to the three forms of urbanization largely accounted for all of the net migrant flows. This dissertation further tested the validity of optimal density theory with net migration data and confirmed the utility of this perspective in predicting the direction of net migration.

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This thesis investigates the optimal use of intervention strategies to mitigate the spread of infectious diseases. Three main problems are addressed: (i) The optimal use vaccination and isolation resources under the assumption that these resources are limited. Specifically we address the problem of minimizing the outbreak size and we determine the optimal vaccination-only, isolation-only and mixed vaccination-isolation strategies. (ii) The optimal use of a single antiviral drug to minimize the total outbreak size, under the assumption that treatment causes de novo resistance. (iii) The optimal use of two antiviral drugs to minimize the total infectious burden. Specifically we address the situation where there are two different strains and each strain is effectively treated by only one drug. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2011-01-25 19:59:17.263

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