Neste trabalho tratamos o assunto de existência e unicidade de estados de equilíbrio para uma classe importante de fluxos e aplicações com singularidades. Mostramos a existência de estados de equilíbrio para potenciais contínuos no contexto de fluxos singular-hiperbólicos, em particular fluxos de Lorenz. Demonstramos um critério para unicidade de estados de equilíbrio para aplicações unidimensionais do tipo Lorenz. Utilizando o critério, provamos que potenciais Hölder por partes com único estado de equilíbrio formam um conjunto aberto na topologia \'C POT.0\' e que a unicidade ainda é garantida para potenciais próximos a uma constante \'K IND. 0\' \' pertence a\' R / In this work we deal with the existence and uniqueness of equilibrium states for an important class of flows and transformations with singularities. In the context of singular-hyperbolic flows, we show the existence of equilibrium states for continuous potentials. In particular, this shows the existence of equilibrium states for Lorenz-like flows. We prove a criterium for the uniqueness of the equilibrium states of one-dimensional Lorenz-like applications. Using such criterium, we prove that piecewise Hölder continuous potentials with unique equilibrium states form an open in the \'C POT. 0\' topology and that the uniqueness is still guaranteed to a potential close to a constant \'K IND.0\' \'it belongs\' R

Depuis le début des années 2000, le secteur social et médico-social connait des évolutions et des mutations importantes. D’un côté, le nombre de personnes prises en charge est en perpétuelle augmentation. D’un autre côté, les finances et les budgets mis à disposition des établissements ne cessent de se réduire, ce qui oblige les décideurs à s’adapter et à trouver de nouvelles solutions pour faire plus avec moins de moyens. Dans cette thèse, nous étudions un problème pratique auquel sont souvent confrontés les directeurs des établissements qui est l’élaboration de plans d’actions optimaux. Un plan d’actions est un ensemble d’actions qui sont mises en place afin d’améliorer à la fois les performances de l’établissement et la qualité de prise en charge de ses résidents.Élaborer un plan d’actions optimal consiste à identifier et choisir les meilleures actions qui améliorent tous les objectifs du plan tout en respectant quelques contraintes. Après la présentation du contexte pratique et théorique, nous fournissons une modélisation formelle du problème sous forme d’un problème de sac-à-dos multi-objectif.Puis nous présentons quelques méthodes de résolution à base d’indicateurs de qualité et de la dominance de Lorenz. Nous montrons que la méthode IBMOLS combinée avec l’indicateur de qualité R2 permet d’obtenir des solutions efficaces et d’intégrer facilement les préférences du décideur. Nous montrons également que dans un contexte où les préférences du décideur sont inconnues ou les objectifs ont tous la même importance, la dominance de Lorenz est un outil très efficace qui permet, d’un côté, d’intégrer l’équité dans le processus de recherche et, d’un autre côté, de réduire le nombre de solutions non dominées ainsi que le temps d’exécution. / Since the early 2000s, the social and medico-social sector is experiencing significant evolutions and mutations. On the one hand, the number of persons taken over is constantly increasing. On the other hand, the finances and budgets available to the structures are constantly decreasing. This forces decision-makers to adapt and find new solutions to do more with fewer resources. In this thesis, we study a practical problem that is often faced by the decision-makers, which is the elaboration of optimal action plans. An action plan is a set of actions that are realized to improve both the performance of the structure and the quality of service offred to its residents. Elaborating an optimal action plan consists of identifying and selecting the best actions that improve all the objectives of the plan while respecting some constraints. After presenting the practical and theoretical context, we provide a formal modeling of the problem as a multi-objective knapsack problem. Then, we present a number of solution methods based on quality indicators and Lorenz dominance. We show that combining IBMOLS method with R2 indicator allows obtaining efficient solutions and easily integrating the decision-maker preferences. We also show that in a context where decision-maker preferences are not known or all the objectives are considered equals, Lorenz dominance is a very efficient tool to incorporate equity into the search process and reduce the number of non-dominated solutions as well as the algorithm runtime.

Orientador: Marcelo Messias / Banca: Claudio Aguinaldo Buzzi / Banca: Claudio Gomes Pessoa / Banca: Luis Fernando de Osório Mello / Banca: Fábio Scalco Dias / Resumo: Neste trabalho, apresentamos uma condição algébrica suficiente para determinar o comportamento não caótico de sistemas diferenciais polinomiais definidos em R^3. Usando essa condição, apresentamos um resultado parcial para uma conjectura sobre a não caoticidade de sistemas diferenciais polinomiais quadráticos definidos em R^3 com matriz jacobiana simétrica. Além disso, utilizando o mesmo resultado, estabelecemos condições para que certas classes de equações diferenciais ordinárias da forma x = f(x, ˙ x, ¨ x), conhecidas como jerk equations, e certas classes de sistemas do tipo Lorenz, não apresentem comportamento caótico. Por fim, investigamos o comportamento qualitativo de sistemas diferenciais polinomiais quadráticos definidos em R^3 que apresentam quádricas do tipo Gp = x2+y2−z2+p, com p ∈ [−1,1], como superfícies algébricas invariantes, incluindo o estudo do comportamento no infinito utilizando compactificação de Poincaré / Abstract: In this work, we present a sufficient algebraic condition to determine the nonchaotic behavior of polynomial differential systems defined in R^3. Using this condition, we present a partial positive answer for a conjecture concerning the nonchaotic behavior of quadratic differential systems in R^3 with a symmetric Jacobian matrix. Furthermore, using the same result, we establish conditions for certain classes of ordinary differential equations of the form x = f(x, ˙ x, ¨ x), called jerk equations, and certain classes of Lorenz-Like systems do not present chaotic behavior. Finally, we investigate the qualitative behavior of quadratic polynomial differential systems in R^3 which present the quadrics Gp = x2 + y2 − z2 + p, with p ∈ [−1,1] as invariant algebraic surfaces, including the study of their behavior at infinity, via Poincaré compactification / Doutor

The distribution question of the land is a distribution question of the social wealth at the same time,but because will produce the antithesis of the position to assign naturally, so a successful land reform is to need accepting by society and cooperating. Republic of Taiwan in 38 years onwards to promote land reform,by most scholars, is praised as a model of successful reform.The achievement is considered to be effective at easing or solving the land problem, and because of narrowing the wealth gap, reduce the contradiction of the society,thus stable at the time of Taiwan society,later, more to promote economic development miracle. Taiwan's land reform as a starting point,enhance the tenant farmer economic, social status,improving rural life,adequate stable social environment, in fact, the social level, is also a successful social reforms. Lorenz von Stein, is a national scholar, is also a pioneer in sociology, administrative science and history scholars,jurists, Its academic contribution to the integration of the four areas of the national science, economic theory, social theory, administrative theory and financial theory,advocated the philosophy of man and state the purpose of considering and development, countries with independent ability to promote "national organism," said,the individual must be set free only in groups,the purpose of groups in the protection of individual freedom,the problem for society, social order and social change, and other social issues and more insights. This article by Lorenz von Stein social theory perspective,to observe Taiwan's land reform process,and bring about social reform its evolution, and to explore the social changes in, the interaction between state and society, And the idea of control Society, it is not the social inequality, But society does not flow,and countries in social class inequalities caused by the flow of the class should not play a role.So that the task of the State to break the social classes in the defense and on special interests dominated,and integration of the interests of all social classes, to avoid special interests above the national class of cases. Therefore, Taiwan's current social problems,state if the integration by the interests of all social classes, uphold the principle of priority of public interest, although the social problems will continue to occur,but society still more to upgrade because of reform.

Harmonious Society's concept is the social life¡¦ picture that numerous bosom political ideal¡¦ philosopher have been expected together. passed over 2000 years, Human society¡¦ civilization had been many different social development stage and social types, whether the ideal harmonious social life can be clear? or still was not well-known state which likes a stone dropped into the sea? This paper attempted to base on stein¡¦ State Theory that can outline Harmonious Society' cognitive picture and possible way to realize. Stein¡¦ thought background establish in the theory framework of the historical observation, dialectical philosophy, spirit-material dualism and organism ontology philosophy mutually. This paper integrate namely human being, society and state three concepts into Social-Theory and State-Theory which has eternal essence, under the fore-mentioned to research how to construct Harmonious Society. Human being and society has separately conditions or agencies that make state become an organism which has mechanisms to overtake interests of personals and social groups. However, any sort of social-theory practice sides must get concrete practice ways and procedures by value theory(methodology) and real society¡¦ condition, harmonious society's construction way concerns with all real society has variation Because of time and space, hence it¡¦s an analysis of ¡utheory/ practice¡vrelation. But due to limited contexts and the length limits, this text only discuss how to construct Harmonious Society by approach to between¡umaterial/social structure¡vand¡uspirit/agency¡v, and it drew multi-dimensional conclusions of harmonious society's construction way. Finally, this article except continues Stein¡¦ thought to extend, hoped that can inherit and broaden theory's explanatory ability and analysis scope, by have more widespread being suitable. On the other hand, also carries on the empirical analysis by Taiwan 1949-2008 period's cases, analyzes its important national policy for several items of developing process, Does which have positive or negative of Taiwan¡¦ harmonious society's construction?

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A computational technique is introduced to reveal the complex intrinsic structure of homoclinic and heteroclinic bifurcations in a chaotic dynamical system. This technique is applied to several Lorenz-like systems with a saddle at the center, including the Lorenz system, the Shimizu-Morioka model, the homoclinic garden model, and the laser model. A multi-fractal, self-similar organization of heteroclinic and homoclinic bifurcations of saddle singularities is explored on a bi-parametric plane of those dynamical systems. Also a great detail is explored in the Shimizu-Morioka model as an example. The technique is also applied to a re exion symmetric dynamical system with a saddle-focus at the center (Chua's circuits). The layout of the homoclinic bifurcations near the primary one in such a system is studied theoretically, and a scalability ratio is proved. Another part of the dissertation explores the intrinsic mechanisms of escape in a reciprocally inhibitory FitzHugh-Nagumo type threecell network, using the phase-lag technique. The escape network can produce phase-locked states such as pace-makers, traveling-waves, and peristaltic patterns with recurrently phaselag varying.

The thesis presents results from five related studies concerned with the development and application of analytical techniques for the measurement of inequality. Four of the research pieces are analytical works focusing on the methodology of inequality measurement, while the fifth is an empirical study of income mobility and inequality in Australia. The most significant work of the dissertation is concerned with the derivation of a new information-theoretic index for the measurement of inequality. The proposed index is based upon the same relationship between information theory and inequality measurement used for the construction of Generalized Entropy (GE) inequality measures and is equivalent to a technique established in the field of signal processing. The measure shares the axiomatic superiority of GE measures over other measurement techniques and exhibits an additional attractive decomposition property such that the contribution of any set of individuals towards inequality is directly observable. No existing axiomatically complete measure possesses this property and thus the new measure has a degree of dominance over other techniques such as the Gini coefficient and Theil’s entropy measures. An empirical illustration of the new index using U.S. unit record income data is provided to demonstrate the alternative decomposition technique. It is shown that persons self-described as ‘White’ or ‘Japanese’ in the U.S. census drive a greater proportion of total inequality than persons from other racial groups relative to their respective population sizes. Other theoretical work in the thesis focuses on the construction and interpretation of Lorenz curves. A new parametric functional form for estimating the Lorenz curve is presented and closed form expressions for the implicit probability density function, cumulative distribution function and Gini coefficient are derived. Furthermore the proposed Lorenz curve is shown to provide a better fit to a range of real world data than other single parameter specifications such as the Pareto formulation. In a separate chapter the issue of Lorenz curve determination is addressed by determining a convex spline to interpolate Lorenz curves from grouped data. The spline is shown to provide better estimates of the Gini coefficient than other interpolation techniques and always satisfies the regularity conditions required for a Lorenz curve. Additional work on Lorenz curves examines the link between these functions and GE inequality metrics. In the thesis it is shown that these indices may be derived as direct functions of the Lorenz curve and analytical expressions for various GE measures are given in terms of Lorenz curve parameters. These results provide a basis for studying the effect of Lorenz curve construction upon the calculation of entropy based inequality measurements. The thesis concludes with an empirical study into income inequality and mobility in Australia using the HILDA unit record and household data panel. The research shows that Australian income mobility is slightly lower than in other developed countries and that much of the observed mobility occurs at the lower end of the income distribution.

The thesis presents results from five related studies concerned with the development and application of analytical techniques for the measurement of inequality. Four of the research pieces are analytical works focusing on the methodology of inequality measurement, while the fifth is an empirical study of income mobility and inequality in Australia. The most significant work of the dissertation is concerned with the derivation of a new information-theoretic index for the measurement of inequality. The proposed index is based upon the same relationship between information theory and inequality measurement used for the construction of Generalized Entropy (GE) inequality measures and is equivalent to a technique established in the field of signal processing. The measure shares the axiomatic superiority of GE measures over other measurement techniques and exhibits an additional attractive decomposition property such that the contribution of any set of individuals towards inequality is directly observable. No existing axiomatically complete measure possesses this property and thus the new measure has a degree of dominance over other techniques such as the Gini coefficient and Theil’s entropy measures. An empirical illustration of the new index using U.S. unit record income data is provided to demonstrate the alternative decomposition technique. It is shown that persons self-described as ‘White’ or ‘Japanese’ in the U.S. census drive a greater proportion of total inequality than persons from other racial groups relative to their respective population sizes. Other theoretical work in the thesis focuses on the construction and interpretation of Lorenz curves. A new parametric functional form for estimating the Lorenz curve is presented and closed form expressions for the implicit probability density function, cumulative distribution function and Gini coefficient are derived. Furthermore the proposed Lorenz curve is shown to provide a better fit to a range of real world data than other single parameter specifications such as the Pareto formulation. In a separate chapter the issue of Lorenz curve determination is addressed by determining a convex spline to interpolate Lorenz curves from grouped data. The spline is shown to provide better estimates of the Gini coefficient than other interpolation techniques and always satisfies the regularity conditions required for a Lorenz curve. Additional work on Lorenz curves examines the link between these functions and GE inequality metrics. In the thesis it is shown that these indices may be derived as direct functions of the Lorenz curve and analytical expressions for various GE measures are given in terms of Lorenz curve parameters. These results provide a basis for studying the effect of Lorenz curve construction upon the calculation of entropy based inequality measurements. The thesis concludes with an empirical study into income inequality and mobility in Australia using the HILDA unit record and household data panel. The research shows that Australian income mobility is slightly lower than in other developed countries and that much of the observed mobility occurs at the lower end of the income distribution.

Zugl.: Erlangen, Nürnberg, Univ., Habil.-Schr., 2005