Esta tese trata, de forma ampla, da relação ciência e sociedade. Especificamente procura compreender o processo de construção do sistema biotecnológico em face do contexto ao qual está relacionado. A argumentação teórica estrutura-se em torno de questões levantadas pelos estudos sociais da ciência e tecnologia, e tem como marco teórico a teoria dos sistemas sociais de Niklas Luhmann, que parte da diferença sistema/entorno para compreender a relação ciência e sociedade. A questão levantada refere-se à estrutura de reprodução da ciência contemporânea e sua relação com o entorno. A hipótese argumenta que a estrutura do sistema biotecnológico sofreu uma mudança, da reprodução baseada na "verdade" à reprodução baseada no "funcionamento". Esta última forma de reprodução emerge em função das perturbações do entorno da ciência, principalmente em função do contexto caracterizado por exigências tecnológicas. Vinculadas a tais exigências estão ainda exigências de aplicação, legalidade, lucratividade, segurança, inovação. A pesquisa utilizou entrevista semi-estruturada com líderes de grupos de pesquisa em biotecnologia em seis estados da federação, e pesquisa documental, como métodos de coleta de dados, e utilizou técnicas qualitativas de análise, especificamente, a análise de conteúdo temática. De maneira mais específica, a investigação localiza-se na periferia do sistema global de ciência e tecnologia, e apresenta como a diferenciação centro/periferia também incide na reprodução do sistema biotecnológico. Para tanto, constrói-se o conceito de regime de produção de conhecimento, um regime de perturbações recíprocas entre sistemas, limitado pelas configurações institucionais dos Estados nacionais. Tal regime, no Brasil, foi caracterizado pelos sistemas do direito, da economia, da política e da ciência, e as perturbações dos três primeiros na biotecnologia é o que se investiga nesta pesquisa. Conclui-se que a pesquisa biotecnológica produz um outro tipo de verdade, a saber, a verdade eficaz. / This thesis deals with the relationship between science and society. It particularly seeks to understand the process of construction of biotechnology and its context. Beyond this, it searches to link biotechnology research to the global society and to the specific context of peripheral science The theoretical argument is structured around issues raised by social studies of science and technology, and uses the theoretical framework of the theory of social systems of Niklas Luhmann, who considered the difference system / environment to understand the relationship between science and society. The main question raised refers to the structure of the reproduction of contemporary science and its relation with the environment. Therefore, our hypothesis argues that the structure of the biotechnology has changed from a reproduction based on "truth" to a reproduction based on "operation". The latter form of reproduction emerges in the light of disturbances around the science, especialy in a context characterized by technological requirements. Besides theses, there are requirements for application, legality, profitability, safety and innovation. This research was conducted using semi-structured interviews with leaders of biotechnology research groups from six brazilian states. Besides, a documentary research was conducted and a thematic content analysis was performed. Particularly, this research is located at the periphery of the global system of science and technology, and presents how the differentiation center/periphery also affects the reproductive system of biotechnology. In this sense, we construct the concept of knowledge production regime, a regime of mutual disturbances between systems, which is limited by the institutional configurations of national states. In Brazil, such regime was characterized by systems of law, economy, policy and science. This research has focused on the disturbance of the first three on biotechnology. It is concluded that research biotechnology produces another kind of truth, namely truth effectively.

Esta tese trata, de forma ampla, da relação ciência e sociedade. Especificamente procura compreender o processo de construção do sistema biotecnológico em face do contexto ao qual está relacionado. A argumentação teórica estrutura-se em torno de questões levantadas pelos estudos sociais da ciência e tecnologia, e tem como marco teórico a teoria dos sistemas sociais de Niklas Luhmann, que parte da diferença sistema/entorno para compreender a relação ciência e sociedade. A questão levantada refere-se à estrutura de reprodução da ciência contemporânea e sua relação com o entorno. A hipótese argumenta que a estrutura do sistema biotecnológico sofreu uma mudança, da reprodução baseada na "verdade" à reprodução baseada no "funcionamento". Esta última forma de reprodução emerge em função das perturbações do entorno da ciência, principalmente em função do contexto caracterizado por exigências tecnológicas. Vinculadas a tais exigências estão ainda exigências de aplicação, legalidade, lucratividade, segurança, inovação. A pesquisa utilizou entrevista semi-estruturada com líderes de grupos de pesquisa em biotecnologia em seis estados da federação, e pesquisa documental, como métodos de coleta de dados, e utilizou técnicas qualitativas de análise, especificamente, a análise de conteúdo temática. De maneira mais específica, a investigação localiza-se na periferia do sistema global de ciência e tecnologia, e apresenta como a diferenciação centro/periferia também incide na reprodução do sistema biotecnológico. Para tanto, constrói-se o conceito de regime de produção de conhecimento, um regime de perturbações recíprocas entre sistemas, limitado pelas configurações institucionais dos Estados nacionais. Tal regime, no Brasil, foi caracterizado pelos sistemas do direito, da economia, da política e da ciência, e as perturbações dos três primeiros na biotecnologia é o que se investiga nesta pesquisa. Conclui-se que a pesquisa biotecnológica produz um outro tipo de verdade, a saber, a verdade eficaz. / This thesis deals with the relationship between science and society. It particularly seeks to understand the process of construction of biotechnology and its context. Beyond this, it searches to link biotechnology research to the global society and to the specific context of peripheral science The theoretical argument is structured around issues raised by social studies of science and technology, and uses the theoretical framework of the theory of social systems of Niklas Luhmann, who considered the difference system / environment to understand the relationship between science and society. The main question raised refers to the structure of the reproduction of contemporary science and its relation with the environment. Therefore, our hypothesis argues that the structure of the biotechnology has changed from a reproduction based on "truth" to a reproduction based on "operation". The latter form of reproduction emerges in the light of disturbances around the science, especialy in a context characterized by technological requirements. Besides theses, there are requirements for application, legality, profitability, safety and innovation. This research was conducted using semi-structured interviews with leaders of biotechnology research groups from six brazilian states. Besides, a documentary research was conducted and a thematic content analysis was performed. Particularly, this research is located at the periphery of the global system of science and technology, and presents how the differentiation center/periphery also affects the reproductive system of biotechnology. In this sense, we construct the concept of knowledge production regime, a regime of mutual disturbances between systems, which is limited by the institutional configurations of national states. In Brazil, such regime was characterized by systems of law, economy, policy and science. This research has focused on the disturbance of the first three on biotechnology. It is concluded that research biotechnology produces another kind of truth, namely truth effectively.

Komplexitet och flexibilitet är två faktorer som präglar dagens arbetsplatser, gamla etablerade mönster ersätts med nya och ständigt föränderliga organisations - och anställningsformer. Arbetet är en essentiell del av individens tillvaro som bidrar till inkomsttrygghet såväl som social samhörighet och känsla av identitet. Likaså som förändringar utmanar organisationers och anställdas trygghet skapas också möjlighet för nya infallsvinklar samt strukturella åtgärder. För att hantera dessa förutsättningar är det betydelsefullt att identifiera de områden som lägger grund och främjar arbetsplatsens hållbarhet. Syftet med studien var att utifrån en hälsofrämjande ansats analysera och beskriva medarbetares upplevelser av lärande inom organisationen, samt identifiera faktorer som skapar en hållbar och attraktiv arbetsplats. Den teoretiska referensramen består av teorierna; Senges fem discipliner, Empowerment och WHO- modellen Healthy Workplace. Studien utgår ifrån ett hermeneutiskt förhållningssätt och en abduktiv ansats. Empirin har samlats in genom åtta semistrukturerade intervjuer och analyserades genom en kvalitativ innehållsanalys som resulterade i två huvudkategorier och sex subkategorier. Resultatet redogör för hälsofrämjande faktorer i form av ett starkt medarbetarskap som utgörs av en trygg och stabil arbetsmiljö där sammanhållningen stärker både den inre- och yttre kvaliteten. Kompetensutveckling sker formellt som informellt, där arbetsplatslärande som sker mellan medarbetare lyfts fram som mest framträdande. Det förutsätter vidare en öppen dialog, struktur och ett positivt arbetsklimat. Slutligen visade studiens fynd att medarbetarskapet är kärnan i att utveckla starka attraktionsattribut och är avgörande för vad som håller medarbetarna kvar på arbetsplatsen. Vidare konstaterades att ledarskapet ger förutsättningar för att medarbetare tillsammans arbetar i hållbart samt trivsamt arbetsklimat, med fokus på medarbetarnas välmående och arbetstillfredsställelse. / Complexity and flexibility are two factors that characterize today's labor market; old established patterns are replaced with new and ever-changing forms of organization and employment. Work is an essential part of the individual's existence that consists of income security as well as social affiliation and sense of identity. Just as changes challenge the security of organizations and employees, opportunities for new approaches and structural measures are also created. In order to deal with these conditions, it is important to identify the areas that lay the groundwork and promote the sustainability of the workplace. The aim of the study was to analyze and describe employees' experiences of learning within the organization, as well as identify factors that create a sustainable and attractive workplace based on a health promotion approach. The theoretical frame consists of the theories; Senge's five disciplines, Empowerment and WHO- model Healthy Workplace. The study is based on a hermeneutic and abductive approach. The empirical data was collected through eight semi-structured interviews and analyzed through a qualitative content analysis that resulted in two main categories and six subcategories. The result showed that health-promoting factors in form of a strong co-workership that consists of a safe and stable work environment where good companionship strengthens both the internal and external quality. Competence development takes place formally as informally, where workplace learning that occurs between employees is highlighted as most prominent. It also requires an open dialogue, structure and a positive working climate. Finally, the study's findings demonstrate that the co-workership is the core of developing strong attraction attributes and is crucial to what keeps employees in the workplace. Furthermore, it was found that the leadership provides the conditions for employees to work together in a sustainable and pleasant working climate, focusing on the employees' well-being and job satisfaction.

The theory of the lamellar eutectoid reaction by volume diffusion has been extended to account for solute segregation within the product phases and the effect of dilute third element additions. It has been demonstrated for symmetric binary systems that the segregation can account for 10% or more of the free energy stored in the product phases and can lead correspondingly to a predicted lamellar spacings appreciably greater than those obtained when segregation is neglected. This segregation is relatively high in the systems Cu-In, Cu-Be and Ag-Cd and may account for the fact that a secondary coarse-grained pearlitic reaction follows the initial fine grained one in these systems. The binary theory has been-used to analyse the available data for the eutectoid reaction in the Cu-Al and Fe-C systems and satisfactory agreement is obtained. The theory for ternary systems, while complete in principle, proves to be. intractable in all but the simplest version of the solution thermodynamics. It is concluded that the effect of the third element on the binary eutectoid reaction is mainly through its effect on the phase diagram, the ternary cross effects in the diffusion matrix tending to cancel out. Any additional element which lowers the eutectoid temperature will retard the reaction. / Thesis / Doctor of Philosophy (PhD)

In this article we establish a bridge between dynamical systems, including topological and measurable dynamical systems as well as continuous skew product flows and nonautonomous dynamical systems; and coalgebras in categories having all finite products. We introduce a straightforward unifying definition of abstract dynamical system on finite product categories. Furthermore, we prove that such systems are in a unique correspondence with monadic algebras whose signature functor takes products with the time space. We substantiate that the categories of topological spaces, metrisable and uniformisable spaces have exponential objects w.r.t. locally compact Hausdorff, σ-compact or arbitrary time spaces as exponents, respectively. Exploiting the adjunction between taking products and exponential objects, we demonstrate a one-to-one correspondence between monadic algebras (given by dynamical systems) for the left-adjoint functor and comonadic coalgebras for the other. This, finally, provides a new, alternative perspective on dynamical systems.:1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Preliminaries and Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1 Preliminaries related to topology and measure theory . . . . . . . . 4 2.2 Basic notions from category theory . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Classical dynamical systems theory . . . . . . . . . . . . . . . . . . . . . . 23 3 Dynamical Systems in Abstract Categories . . . . . . . . . . . . . . . . . . 30 3.1 Monoids and monoid actions in abstract categories . . . . . . . . . . 31 3.2 Abstract dynamical systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3 Nonautonomous dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4 Dynamical Systems as Algebras and Coalgebras . . . . . . . . . . . . . .38 4.1 From monoids to monads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.2 From abstract dynamical systems to monadic algebras . . . . . . . 48 4.3 Connections to coalgebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.4 Exponential objects in Top for locally compact Hausdorff spaces . . 52 4.5 (Co)Monadic (co)algebras and adjoint functors . . . . . . . . . . . . . .56

Made available in DSpace on 2016-04-26T20:26:03Z (GMT). No. of bitstreams: 1 Jurandir Zangari Junior.pdf: 433448 bytes, checksum: 3d60f421a8b0e5367c956430b31fac0f (MD5) Previous issue date: 2007-10-05 / The purpose of this study is to determine the feasibility of establishing a differentiated juridical treatment to small-sized and micro companies within the scope of labor laws. Despite this segment major importance within the Brazilian economic context, accounting for a large part of current jobs, it is in this segment that traditional paradigms of labor law such as the rigidity in the classical protectionism, and the existence of mandatory rules impose their major negative impact, ending up by boosting informality and unemployment. For the analysis of the proposed purpose, the economic context in which microcompanies and small-sized companies was examined together with the status of applicable national, international and foreign laws, and a research was conducted about its concept. The differentiation regarding the applicability of labor law regulations on existing occupational relationships in small undertakings generates, however, some impacts that were examined in light of Niklas Luhmann´s systems, in addition to related doctrines and laws. In short, after the analysis of the aforementioned topics, it is concluded that it is possible to establish a juridical labor system differentiated for microcompanies and small-sized companies, emphasizing, however, that the dynamics of the law follows its own procedures which, only after verified will cause social and economic facts to become part of the juridical system / O presente estudo tem por escopo verificar a viabilidade de se estabelecer tratamento jurídico diferenciado às empresas de pequeno porte e microempresas no âmbito do direito do trabalho. Embora tal segmento tenha enorme relevância no contexto econômico brasileiro, sendo promotor de grande parte dos empregos da atualidade, é nele em que a incidência dos paradigmas tradicionais do direito do trabalho, tais como, a rigidez do protecionismo clássico e a existência de normas imperativas, tem maior impacto negativo, o que acaba por fomentar a informalidade e desemprego. Para a análise do objetivo proposto foram verificados: o contexto econômico em que estão inseridas as microempresas e empresas de pequeno porte; a situação das legislações nacional, internacional e estrangeira relativa ao tema; sendo realizada, ainda, a pesquisa sobre seu conceito. A diferenciação relativa à incidência de normas do direito laboral nas relações de trabalho existentes nos pequenos empreendimentos gera, porém, alguns impasses, que foram analisados à luz da teoria dos sistemas de Niklas Luhmann, além da doutrina e legislação pertinentes. Em síntese, após a análise dos tópicos mencionados, conclui-se que é possível se estabelecer um sistema jurídico trabalhista diferenciado para microempresas e empresas de pequeno porte, ressaltando-se, porém, que a dinâmica do direito obedece a procedimentos próprios, que, somente depois de verificados, farão com que os fatos sociais e econômicos se integrem ao sistema jurídico

Made available in DSpace on 2016-04-26T20:20:59Z (GMT). No. of bitstreams: 1 Paulo Antonio Fernandes Campilongo.pdf: 1454277 bytes, checksum: 1d4e82c20f61e046d8da8eb9f8a9b8df (MD5) Previous issue date: 2012-05-24 / This research aims to carry out the confrontation between the tax administrative procedure, in particular regarding the correlation between the proceeding fact and the decision to be produced in each of those procedural modalities. Facing this analysis, it intends to verify whether the informant principles of the criminal process can be imported, subsidiarily, to the tax administrative procedure, without any communication rumor, so as to authorize the tax release review by the administrative authorities in the exercise of atypical trial activities. To do so, it resorts, under the scientific-theoretical approach, of both the logicalsemantic constructivism and the theory of autopoietic systems, in order to achieve an approximation of those theories and, thus, better understand how the syntactical closure and the semantic and pragmatic opening of the legal systems would occur, as well as the operational closure and the cognitive opening, defended by the mentioned theories. This provides the understanding and reasoning about how the communication operations in the legal system occur, how and at what time the legal facts enter the system and how important is the process in terms of legal safety, for its legitimacy. By taking the moment in time analysis of the insertion of the legal criminal fact and the tax legal fact in the legal system, as well as the legitimate authorities to enter them in a relevant language, the study herein tries to prove that the subsidiary application of the institutes of the amendment or libel change in criminal proceedings do not have the same connotation as the release review by mistake in fact or error straight of law in the course of the tax administrative procedure / Esta pesquisa tem por objetivo realizar a confrontação entre o processo administrativo tributário e o processo penal, em especial no que tange à correlação entre o fato processual e a decisão a ser produzida em cada uma dessas modalidades processuais. Diante dessa análise, busca verificar se os princípios informadores do processo penal podem ser importados, de forma subsidiária, para o processo administrativo tributário, sem qualquer ruído de comunicação, de maneira a autorizar a revisão do lançamento tributário pelas autoridades administrativas no exercício da atividade atípica de julgamento. Para tanto, socorre-se, sob o enfoque teórico-científico, do construtivismo lógico-semântico e da teoria dos sistemas autopoiéticos, buscando uma aproximação dessas teorias, com o propósito de compreender melhor como ocorreria o fechamento sintático e a abertura semântica e pragmática dos sistemas jurídicos, bem como o fechamento operacional e a abertura cognitiva, defendidos, respectivamente, pelas teorias citadas. Isso propicia a compreensão e a fundamentação acerca de como ocorrem as operações de comunicação no sistema jurídico, como e em que momento os fatos jurídicos ingressam no sistema e de qual é a importância do processo, em termos de segurança jurídica, para a sua legitimação. Pelo exame do momento temporal da inserção do fato jurídico penal e do fato jurídico tributário no sistema jurídico, bem como das autoridades legitimadas para inseri-los em linguagem competente, o presente estudo procura demonstrar que a aplicação subsidiária dos institutos da emenda ou mudança do libelo no processo penal não tem a mesma conotação que a revisão do lançamento por erro de fato ou erro de direito no curso do processo administrativo tributário

Der anhaltende Misserfolg des politikgetriebenen Reformstakkatos verstärkt seit einer Dekade die Tendenz zu einem Reformmodus, der Universitäten höhere Autonomie zuspricht und auf deren Selbstorganisation gegen die teilweise dramatisch diskutierte Entfremdung von der Gesellschaft setzt. Mit Experimentierklauseln oder gar Hochschulfreiheitsgesetzen wird die Möglichkeit zur Selbstreferenz geschaffen – die Universität ist fortan für sich selbst verantwortlich. Diese Möglichkeit ist gleichwohl nur eine der notwendigen Bedingungen für erfolgreiche Selbstreferenz. Die Fähigkeit dazu liefert die „Entfesselung“ nicht. Dazu muss sich die Universität eingebettet in die sie umfassenden Zusammenhänge begreifen und mögliche Wechselwirkungen zwischen Organisation und Umwelt berücksichtigen können. Diesen voraussetzungsvollen Fall, dass eine Organisation die Auswirkungen ihrer Operationen auf ihre Umwelt sowie daraus entstehende Rückwirkungen auf sich selbst reflektiert, kann mit LUHMANN (1984, S.617) rationale Selbstreflexion genannt werden. Die Arbeit widmet sich dem Managementinstrument der Leitbildentwicklung und untersucht, wie es zur rationalen Selbstreflexion der Universität beitragen kann. Mit der Perspektive der Theorie sozialer Systeme werden drei Bedingungen herausgearbeitet, die im Prozess der Leitbildentwicklung zu berücksichtigen sind, um das orientierende und koordinierende Nutzenpotential dieses Managementinstruments zu entfalten. / Due to the persisting failure of ever continuing reforms driven by politics a new mode of reform has been established during the last decade: Universities are granted higher autonomie with respect to decisionmaking aiming at strengthening their capability of self-organisation. With flexible clauses in new higher education laws the possibility for self-reference has been created - Universities are responsible for themselves. This possibility is nevertheless just one of the required conditions for sucessful self-reference. The second required condition, the ability for self-reference, is not fulfilled automatically by just "loosening the chains". In order to develop this ability Universities have to recognize themselves as embedded in a tight network of relationships and they have to be able to incorporate reciprocal effects between themselves and its environment into their decisionmaking. This case of an organisation being able to reflect on its impact on its environment as well as on the backlashes created by that, can be termed "rational reflexivity" with LUHMANN (1984, p.617). This paper adresses the management instrument of creating mission statements and analyses, how this instrument can contribute to the rational reflexivity of Universities. Using the theory of social systems three conditions are suggested that should be accounted for when aiming to unreveal the potential of the orienting and coordinating management instrument mission statements.

Made available in DSpace on 2015-03-04T18:51:13Z (GMT). No. of bitstreams: 1 Apresentacao.pdf: 64345 bytes, checksum: 1657601da62e336950fb70b6034a6009 (MD5) Previous issue date: 2005-09-02 / Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Decisions related to the sustainable development involve the following: what to sustain and how to sustain . In general, these decisions are based on assumptions about the permanence of certain characteristics of the systems involved, be them natural or socio-economic. Moreover, these decisions can be only of ethical character or may involve formulations that include mechanisms for effective control, and search to steer the whole system towards a sustainable regime. The formal frameworks and the lines of thought employed in this process generaly relay in the maintenance of natural resources stocks and other factors. They do not consider, however, variations in technological production processes and social preferences. They do not, as well, take into account the spontaneous variability in the structure and components of the natural systems involved. This work aims an analysis of some existing concepts of Sustainability. It looks foward towards a stronger integration between the mathematical models and structures in Sustainability studies, in particular while they relate to the interaction between the ecological, social and production areas. An investigation of Sustainability integrating all these areas has not yet been made, not only due to a lack of perception of variabilities about man-nature systems, but also because their models and representations have diverse nature. The evolution of ecosystems, for instance, is represented as dynamical systems, while the interactions between people or organizations are represented as games and iterations in the productive system always appear as problems of control and allocation. When expressed in mathematical terms, these descriptions confine themselves to areas of mathematics that are not easily integrated and which techniques do not keep, at the moment, a narrower relation. We propose, in this work, the language of general system theory as a means to represent the mutual interactions and influences between the natural, productive and social systems. We search also for a more integrated form to describe mathematically problems in these areas. This allows, at least, for a clearer perception of what to sustain and of the interaction between components and processes in the mutable cases. This, in turn, provides a better stand about how to sustain . / Decisões relacionadas ao desenvolvimento sustentável envolvem as seguintes questões: "o quê sustentar" e "como sustentar". Em geral, as propostas de solução para essas questões baseiam-se em suposições sobre a permanência de determinadas características dos sistemas envolvidos, sejam eles naturais ou sócios econômicos. Além disso, as decisões podem ser de caráter apenas ético ou podem envolver formulações que incluam mecanismos efetivos de controle, e busquem dirigir o uso dos recursos naturais para um regime sustentável. Os esquemas formais e as linhas de pensamento comumente empregados neste processo repousam na manutenção de estoques de recursos naturais e outros fatores. Não consideram, porém, variações nos processos tecnológicos de produção e nas preferências sociais, e tampouco variabilidades espontâneas na estrutura e nos componentes dos sistemas naturais envolvidos. Este trabalho visa analisar vários conceitos existentes de Sustentabilidade. Procura também, buscar uma maior integração entre os vários modelos e estruturas matemáticos usados nestes estudos de Sustentabilidade, em particular os modelos que se referem à interação entre as áreas ecológica, de produção e social. Essa discussão integrada não tem sido feita até o momento, não apenas por falta de uma percepção da variabilidade dos sistemas homem-natureza, mas também porque seus modelos e representações abstratas tem natureza diversa. A evolução dos ecossistemas, por exemplo, é representada por sistemas dinâmicos, enquanto que as interações entre as pessoas ou organizações são representadas como jogos e as interações do sistema produtivo aparecem sempre como problemas de controle e alocação. Quando estão expressas de forma matemática, essas descrições se confinam a áreas da Matemática que não são facilmente integradas e cujas técnicas não guardam, no momento, uma relação mais estreita. Apresentamos neste trabalho formas matemáticas dentro da Teoria Geral de Sistemas para representar as interações e influências mútuas entre os sistemas naturais, produtivos e sociais, [Barbier(1989)], para nos auxiliar nos estudos de Sustentabilidade. Buscamos também uma forma mais integrada de descrever esses sistemas matematicamente. Este intento nos fornece, no mínimo, uma visão mais clara do quê sustentar e da interação dos componentes e processos nos casos mutáveis. Isso, por sua vez, permite uma melhor postura do como sustentar .