This work is about convergence to equilibrium problems for equations coming from kinetic theory. The bulk of the work is about Hypocoercivity. Hypocoercivity is the phenomenon when a semigroup shows exponentially relaxation towards equilibrium without the corresponding coercivity (dissipativity) inequality on the Dirichlet form in the natural space, i.e. a lack of contractivity. In this work we look at showing hypocoercivity in weak measure distances, and using probabilistic techniques. First we review the history of convergence to equilibrium for kinetic equations, particularly for spatially inhomogeneous kinetic theory (Boltzmann and Fokker-Planck equations) which motivates hypocoercivity. We also review the existing work on showing hypocoercivity using probabilistic techniques. We then present three different ways of showing hypocoercivity using stochastic tools. First we study the kinetic Fokker-Planck equation on the torus. We give two different coupling strategies to show convergence in Wasserstein distance, $W_2$. The first relies on explicitly solving the stochastic differential equation. In the second we couple the driving Brownian motions of two solutions with different initial data, in a well chosen way, to show convergence. Next we look at a classical tool to show convergence to equilibrium for Markov processes, Harris's theorem. We use this to show quantitative convergence to equilibrium for three Markov jump processes coming from kinetic theory: the linear relaxation/BGK equation, the linear Boltzmann equation, and a jump process which is similar to the kinetic Fokker-Planck equation. We show convergence to equilibrium for these equations in total variation or weighted total variation norms. Lastly, we revisit a version of Harris's theorem in Wasserstein distance due to Hairer and Mattingly and use this to show quantitative hypocoercivity for the kinetic Fokker-Planck equation with a confining potential via Malliavin calculus. We also look at showing hypocoercivity in relative entropy. In his seminal work work on hypocoercivity Villani obtained results on hypocoercivity in relative entropy for the kinetic Fokker-Planck equation. We review this and subsequent work on hypocoercivity in relative entropy which is restricted to diffusions. We show entropic hypocoercivity for the linear relaxation Boltzmann equation on the torus which is a non-local collision equation. Here we can work around issues arising from the fact that the equation is not in the H\"{o}rmander sum of squares form used by Villani, by carefully modulating the entropy with hydrodynamical quantities. We also briefly review the work of others to show a similar result for a close to quadratic confining potential and then show hypocoercivity for the linear Boltzmann equation with close to quadratic confining potential using similar techniques. We also look at convergence to equilibrium for Kac's model coupled to a non-equilibrium thermostat. Here the equation is directly coercive rather than hypocoercive. We show existence and uniqueness of a steady state for this model. We then show that the solution will converge exponentially fast towards this steady state both in the GTW metric (a weak measure distance based on Fourier transforms) and in $W_2$. We study how these metrics behave with the dimension of the state space in order to get rates of convergence for the first marginal which are uniform in the number of particles.

Industrial policy in the form of direct and indirect government subsidy provision to firms in specific sectors of the economy is a common sight in many countries. Some of the most often quoted examples are East Asian economies such as japan and Taiwan. While industrial policy is touted as a possible engine to generate economic growth, empirical validations on the benefits from subsidy provisions have been mixed. It is often argued that a policy of non-intervention by the government may appear to be the optimal policy to pursue. However, this contrasts with the historical observations of regular government subsidy provisions to firms in many countries. This thesis constructs a two-sector non-monetary macroeconomic model with monopolistic competition to examine welfare and other related effects of a subsidy provision in the form of lump sum transfers or as some proportion of a variable cost component while firms in the perfectly competitive sector do not. This analysis is first carried out in an economy where labour supply is assumed to be exogenous and perfectly inelastic. This serves to provide a simple and clear exposition on the effects of a subsidy provision and to serve as a benchmark analysis to build upon. This is subsequently extended by allowing for labour supply to be endogenously determined to examine labour market effects of subsidy policies. The implications of subsidy provisions in the presence of international trade are studied by constructing a small open economy model where the effects of any policy implementation do not affect world prices or income. The principle findings we obtain are that when monopolistically competitive firms receive a cost-reducing subsidy, welfare improvements are always possible regardless of which cost variable the government subsidises. Furthermore, there is always a positive optimal subsidy which raises social welfare. When the supply of labour is endogenous, the corresponding tax imposed on income will always induce an increase in labour supply. Trade is shown not to affect the principle findings: there remains an optimal level of subsidy which is Pareto-improving. A further implication in the open economy context is that the subsidy acts as a form of import-substitution and export-promotion instrument which potentially alters the domestic economy's trade patterns.

Cheung, Man Wah. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 50-53). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Stochastic Stability --- p.2 / Chapter 1.2 --- Some Examples --- p.3 / Chapter 1.3 --- Our Main Focus --- p.5 / Chapter 1.4 --- Thesis Outline --- p.6 / Chapter 2 --- KMR's Approach and its Variations --- p.7 / Chapter 2.1 --- KMR's Approach --- p.7 / Chapter 2.2 --- Variations --- p.12 / Chapter 2.2.1 --- Bergin and Lipman (1996) --- p.12 / Chapter 2.2.2 --- Anderlini and Ianni (1996) --- p.12 / Chapter 2.2.3 --- Robson and Vega-Redondo (1996) --- p.13 / Chapter 2.2.4 --- Robles (1998) and Pak (2008) --- p.13 / Chapter 3 --- Mathematical Reviews on Nonstationary Markov Chain --- p.15 / Chapter 3.1 --- Ergodic Coefficient --- p.15 / Chapter 3.2 --- Weak Ergodicity --- p.16 / Chapter 3.3 --- Strong Ergodicity --- p.18 / Chapter 4 --- Existing Works on Time-Dependent Mutation Rates --- p.20 / Chapter 4.1 --- Model and Definitions --- p.20 / Chapter 4.2 --- Sufficient Condition for Weak Ergodicity --- p.23 / Chapter 4.3 --- Sufficient Condition for Strong Ergodicity --- p.24 / Chapter 5 --- Time-Dependent Mutations and Empirical Distribution --- p.26 / Chapter 5.1 --- Model --- p.28 / Chapter 5.2 --- Convergence of Empirical Distribution --- p.30 / Chapter 5.3 --- Proofs of Claims --- p.35 / Chapter 5.3.1 --- Proofs of Claims l(a)-(d) --- p.36 / Chapter 5.3.2 --- Proof of Claim 2 --- p.39 / Chapter 6 --- Open Problems --- p.42 / Chapter 6.1 --- Numerical Example and Simulations --- p.43 / Chapter 6.2 --- Numerical Results --- p.44 / Chapter 6.3 --- Other Discussions --- p.47 / Chapter 7 --- Conclusion --- p.48 / Bibliography --- p.50

No presente trabalho foram realizados estudos de equilíbrios químicos da fosfoetanolamina (FOS) ou 2-aminoetanol-dihidrogenofosfato, substância produzida no organismo humano, um precursor de fosfatidiletanolamina importante por regularizar o metabolismo de disfunção celular e metabólica. A constante de ionização de uma molécula é uma ferramenta interessante a fim de prever a sua absorção no organismo que geralmente, apenas ocorre com as moléculas na forma não ionizada. Na determinação usual de constantes de zwiterions como a FOS, não se considera o equilíbrio de formação de espécies não ionizadas como dímero (agregado). Neste trabalho comprovou-se o fenômeno de agregação da FOS por titulações potenciométricas e pelo método espectrofotométrico Azul de Molibdênio. Determinou-se a constante de agregação pelo método potenciométrico como sendo da ordem de 106. Realizou-se a determinação da primeira constante de ionização da FOS por titulações em meio ácido, na ausência do fenômeno de agregação, e verificou-se que é da ordem de 10-4. Pelo método espectrofotométrico Azul de Molibdênio determinou-se a porcentagem de fosfato iônico 1%, coerente com os resultados potenciométricos. A determinação da segunda constante de ionização da FOS foi realizada por titulações com monoetanolamina (MEA), uma base fraca. Verificou-se a possibilidade de utilização do sistema FOS/MEA como um tampão biológico, por meio do gráfico de máxima capacidade tamponante vs pH. A determinação de terceira constante de ionização da FOS foi realizada por meio de titulações com NaOH na ausência e na presença de formaldeído, bloqueando o grupo amino. A determinação simultânea das três constantes de ionização foi realizada por meio de uma titulação de retorno,com HCl e adição de NaOH. Com o tratamento matemático desta curva, determinou-se o número médio de protonação e verificaram-se as regiões de máxima capacidade tamponante. Obteve-se a curva de distribuição de espécies e o diagrama logarítmico para a FOS com os valores de constante de ionização determinados na ausência do fenômeno de agregação. Estudou-se a interação de íons cálcio e magnésio com a FOS, verificou-se que os complexos são do tipo ML e M2L. É importante salientar ainda, que não há relato na literatura desses estudos . / Studies on the chemical equilibrium of phosphoethanolamine (PEA) or 2-aminoethanol-dihydrogen phosphate, produced by the human body, as an important phosphatydilethanolamine precursor that regularizes the cell and metabolic disfuntion have been performed. The ionization constant is an interesting tool to foresee organic absortion which often occurs in non ionized form. In the usual determination of zwiterion, constants like PEA, the dimmer formation equilibrium is not always considered. In this work aggregation phenomena of PEA has been demonstrated by potentiometric titration and molybdenium blue spectrophotometric method. The aggregation constant was determinated by potentiometric method as 106. The first ionization constant determination of PEA was made by titration in acidic medium without aggregation phenomena and it was 10-4. The molybdenum blue spectrophotometric method was used to determine the free phosphate amount, 1%, was coherent with potentiometric results. The second ionization constant determination was made by titration with monoethanolamine (MEA), a weak base. There is the possibility of using the system PEA/MEA as a biological buffer, according to the maximum buffer capacity graphic versus pH. The third ionization constant determination was made by titration with NaOH, with and without formaldehyde, blocking the amino group. The simultaneous determination of the three constants of ionization was made by back titration, with HCl after the addition of NaOH. The average number of bound protons was done with mathematical treatment of back titration curve and then, the maximum buffer capacity regions were observed. The species distribution curve and logarithmic diagram were obtained using the ionization constant values determined in the aggregation phenomena absence. The interaction between calcium, magnesium and PEA was studied and the ML and M2L species were observed, not described in literature yet.

Fobia específica de altura ou acrofobia é um transtorno de ansiedade caracterizado pelo medo intenso e desproporcional de locais altos, levando à esquiva de situações e capaz de gerar sofrimento. Os diversos tipos de fobias parecem estar ligados a diferentes mecanismos de aquisição de medos. Mais do que experiências de aprendizado ou condicionamento, existem evidências de que anormalidades no controle da postura possam estar envolvidas na gênese do medo de altura. Deficiências na função vestibular podem levar um indivíduo a depender mais de sua visão ou de sua propriocepção para manter o controle postural. Lugares altos são um tipo de situação limite onde a falta de tais referências poderiam, em tese, desencadear reações de defesa e sintomas ansiosos. Além disso, o aumento de demanda por recursos cognitivos para a compensação do equilíbrio poderia deixar indivíduos acrofóbicos mais susceptíveis a interações entre o controle postural e atividades que demandem atenção. Esta dissertação testou a hipótese de que indivíduos com fobia específica de altura apresentam pior controle postural e maior interferência entre o controle do equilíbrio e o desempenho em tarefas que demandem atenção. Foram comparados 31 acrofóbicos (23 mulheres, 36,4±12 anos) e 34 controles não-fóbicos (22 mulheres, 32,4±12 anos). O desempenho da estabilidade postural em plataforma de posturografia dinâmica e o desempenho atencional foram simultaneamente avaliados através de teste em computador envolvendo o rastreio visual de um alvo em movimento imprevisível. Foram avaliadas as seguintes variáveis: ÁREA (área delimitada da excursão do centro de pressão em cm²); CPx e CPy (deslocamento total do centro de pressão na base de suporte em cm, na direção látero-lateral (eixo x) e ântero-posterior (eixo y)); VMx e VMy (velocidade média com a qual ocorre o deslocamento do centro de pressão em cm/s) e RMSx e RMSy (quadrado da média da raiz do deslocamento do centro de pressão, em cm, a partir da coordenada central (0,0) da base de apoio). O teste de atenção foi avaliado pela porcentagem de tempo em que o sujeito conseguia seguir anualmente o movimento do alvo. Indivíduos com acrofobia apresentaram uma pior estabilidade postural e um pior desempenho no teste atencional, além de uma maior interferência entre as tarefas. Estes resultados são compatíveis com a hipótese de que anormalidades do controle postural possam exercer um papel importante na gênese e na perpetuação dos sintomas de medo de altura. / INTRODUCTION: Fear of heights or acrophobia, is one of the most frequent subtypes of specific phobia frequently associated to depression and other anxiety disorders. Previous evidence suggests a correlation between acrophobia and abnormalities in balance control, particularly involving the use of visual information to keep postural stability. This study investigates the hypotheses that (1) abnormalities in balance control are more frequent in individuals with acrophobia even when not exposed to heights; (2) acrophobic symptoms are associated to abnormalities in visual perception of movement; and (3) individuals with acrophobia are more sensitive to balance-cognition interactions. METHOD: Thirty-one individuals with specific phobia of heights (23 women, 36.4±12 years) and thirty one non-phobic controls (22 women, 32.4±12 years) were compared using dynamic posturography and a manual tracking task. RESULTS: Acrophobics had poorer performance in both tasks, especially when carried out simultaneously. Previously described interference between posture control and cognitive activity seems to play a major role in these individuals. DISCUSSION: The presence of physiologic abnormalities is compatible with the hypothesis of a non-associative acquisition of fear of heights, i.e., not associated to previous traumatic events or other learning experiences. Clinically, this preliminary study corroborates the hypothesis that vestibular physical therapy can be particularly useful in treating individuals with fear of heights.

It is demonstrated that for certain markets where traders have constant elasticity of substitution utility (CES) functions, the existence of a price equilibrium can be determined in polynomial time. It is also shown that for a certain range of elasticity of substitution where the CES market does not satisfy gross subsitutability that price equilibira can be computed in polynomial time. It is also shown that for markets satisfying gross substitutability, equilibria can be computed in polynomial time even if the excess demand is a correspondence. On the experimental side, equilibrium computation algorithms from computer science without running time guarantees are shown to be competitive with software packages used in applied microeconomics. Simulations also lend support to the Nash equilibrium solution concept by showing that agents employing heuristics in a restricted form of Texas Holdem converge to an approximate equilibrium. Monte Carlo simulations also indicate the long run preponderance of skill over chance in Holdem tournaments.

Presently, the more or less global political consensus is that the primary task of government is to perpetually maximise a quantity called 'economic growth'. Given the decline of 'socialist' models of industrialisation, the economic consensus is that economic growth is best achieved through the deregulation of markets, industry and trade, as free markets are self-regulating institutions that automatically and efficiently optimise growth through their tendency to reach 'equilibrium.' Another word for this consensus might be 'neoliberalism'. This cosy situation, however, is increasingly under challenge from the recent transformation of global warming from a deniable proposition to a clear and present danger. As ecologists and earth scientists have long argued, global warming (an unforeseen side effect of what was called the 'energy crisis' in the 1970s) is just one of many aspects of a generalised global ecological crisis. The biosphere, environmentalists tell us, is radically 'out of balance'. Given this impasse, it appears that the science of social systems (economics) and the science of living systems (ecology) are incommensurable. This incommensurability is the starting point of the thesis, which seeks to provide a genealogy of the concepts of equilibrium and growth as they appear in the claims of both disciplines to represent 'hard' science. Drawing from debates in the philosophy of science, studies in the history of ideas, the anthropology of technology, and political economy, the thesis charts the mutual exchange of metaphors and analogies between the natural and the social sciences, and traces a surprisingly parallel trajectory in the separate histories of economics and ecology. Beginning with early historicist and organicist conceptual frameworks, both sciences embraced 'mechanism' in their bid to attain the mantle of Science. For both sciences, the attainment of this status was associated with the incorporation of the language of energetics and an insistent identification of 'equilibrium' with the central scientific object of inquiry, 'the market' and 'the ecosystem' respectively. What is ironic in these claims is that the acceptance of the machine metaphor effecti vely screened out the study of actual machinery from the pure states of nature called 'the market' or 'the economy.' This history is taken up to the climactic moment of the early 1970s, when, it is argued, the ontological foundations of ecology and economics collided. This is the moment from which the political discourses of neoliberal globalisation and global environmental crisis both date, and since then we see the rise of hybrid discourses that attempt to address and overcome the deep contradictions of disciplinary specialisation. The thesis concludes with a brief discussion of the implications of this conceptual legacy, and in analysing the interactions of the 'new ecology' and the 'new economy', offers suggestions as to why what appeared in 1971 as a fundamental and obvious contradiction between 'growth' and 'equilibrium', no longer attracts debate.

The Classical Model describing the effects of temperature on enzyme activity consists of two processes: the catalytic reaction defined by ΔG cat and irreversible inactivation defined by ΔG inact, this model however, does not account for the observed temperature- dependant behaviour of enzymes. The recent development of the Equilibrium Model is governed not only by ΔG cat and ΔG inact but also by two new intrinsic parameters ΔHeq and Teq, which describe the enthalpy and the temperature of the midpoint, respectively, of a active and reversibly inactive enzyme transition. Teq is central to the physiological adaptation of an enzyme to its environmental temperature and links the molecular, physiological and environmental aspects of life to temperature in a way that has not been previously possible. The Equilibrium Model is therefore a more complete and accurate description of the effects of temperature on enzymes, it has provided new tools for describing and investigating enzyme thermal adaptation and possibly new biotechnological tools. The effects of the incorporating in the new Model of the parameters Teq and ΔH eq yield major differences from the Classical Model, with simulated data calculated according to the Equilibrium Model fitting well to experimental data and showing an initial rate temperature optimum that is independent of assay duration. Simulated data simulated according to the Classical Model can not be fitted to experimental data. All enzymes so far studied (gt30) display behaviour predicted by the Equilibrium Model. The research described here has set out to: experimentally test observations made by Eisenthal et al., on the basis of enzyme reactor data simulated according to the Equilibrium Model; to test the Equilibrium Model using an unusual (rapidly renaturable) enzyme, RNAase; and to test the proposed molecular basis of the Equilibrium Model by examining the effect of a change at the enzymes active site. The experimental results gathered here on the effect of time and temperature on enzyme reactor output confirm the predictions made by Eisenthal et al. (2006) and indicate that the Equilibrium Model can be a useful aid in predicting reactor performance. The Equilibrium Model depends upon the acquisition of data on the variation of the Vmax of an enzyme with time and temperature, and the non-ideal behaviour of RNase A made it impossible to collect such data for this enzyme, as a result the Equilibrium Model could not be applied. The disulfide bond within the active site cleft of A.k 1 protease was cleaved as a probe of the mechanism of the Equilibrium Model, which is proposed to arise from molecular changes at the enzymes active site. Support for the proposed mechanism was gained through the comparison of experimentally determined temperature dependence of the native and reduced forms of the enzyme and application of this data to the Equilibrium Model.

No description available.

This study investigates general equilibrium effects of an alternative social security policy in Indonesia. The study aims to analyse some financial issues of the proposed policy using a dynamic CGE model. The focus is investigating possible tax scenarios to finance the proposed policy and their impacts on the economy. The simulation results suggest that the consumption tax base should be used as the main financing method. This is because based on various simulations the selected consumption taxes have less negative impacts on the economy than the selected income taxes. Those selected consumption taxes more equitably distribute tax burden and improve income inequality in the long run. However, the increasing price because of this policy selection should also be considered seriously. The simulations also include the study of the demographic transition in Indonesia. A view that is common in the literature is that the rapid increase of labor force in the next three decades could raise the proportion of skilled workers in the labor force and enhance the economic growth. Instead the simulations suggest contrary results. When we repeat the tax/transfer simulations with the demographic transition, real GDP per capita and consumption per capita fall further below the baseline projections. Further simulations are conducted to investigate possible policy actions to mitigate the effects of this demographic transition. This study also covers possible allocation decision trade-offs surrounding the proposed social security policy. That is, the trade-offs between universal social pension insurance and universal social health insurance, and between universal tax-financed social security programs and other important development programs. Given the limitation of our study, that all stakeholders have agreed to develop a universal tax-financed social security program, we conclude that universal tax-financed social health insurance should be given more priority than universal tax-financed social pension insurance. The study concludes with some remarks regarding important areas for future research.