Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-12T13:00:44Z No. of bitstreams: 1 arquivototal.pdf: 2334284 bytes, checksum: c3d087bb8f68c3b8f619b05f161a3e77 (MD5) / Made available in DSpace on 2017-09-12T13:00:44Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2334284 bytes, checksum: c3d087bb8f68c3b8f619b05f161a3e77 (MD5) Previous issue date: 2016-02-25 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this thesis, we study the influence of gravitating non-Abelian cosmic strings on the spacetime geomerty. In order to develop this analysis, we constructed a set of coupled non-linear differential equations. Because there is no closed solution for this set of equations, we solve it numerically to determine the behaviour for the Higgs, gauge and metric fields. This model under consideration present two bosonic sectors, besides the non-Abelian gauge field. The two bosonic sectors may present a direct coupling. So, we investigate the relevance of this coupling on the system, specifically in the linear energy density of the string and on the planar angle deficit. We also analyze the behaviors of these quantities as function of the energy scale where the gauge symmetry is spontaneously broken. We have extented this analysis to de Sitter and anti-de Sitter spacetimes. In order to do that we construct the complete set of equations of motion considering the presence of a cosmological constant. By using numerical analysis we provide the behavior of the Higgs and gauge fields and also for the metric tensor for specific values of the physical parameters of the theory. For de Sitter case, we find the appearance of horizons that although being consequence of the presence of the cosmological constant it strongly depends on the value of the gravitational coupling. In the anti-de Sitter case, we find that the system does not present horizons. In fact the new feature of this system is related with the behavior of the (tt) and (zz) components of the metric tensor. They present a strongly increasing for large distance from the string. / Nesta tese estudamos a influência das cordas cósmicas não-Abelianas na geometria do espaço-tempo. Para este fim, utilizamos um modelo de Higgs não-Abeliano acoplado com a gravidade e obtemos um sistema de equações diferenciais não-lineares. Como este sistema de equações diferenciais não possui solução analítica, realizamos análise numérica para obter o comportamento dos campos de Higgs, de gauge e métricos em função da distância à corda cósmica. O modelo considerado apresenta dois campos bosônicos e um campo de gauge não-Abeliano. Como os dois setores bosônicos podem apresentar um acoplamento direto, investigamos a relevância deste acoplamento no sistema, especificamente na densidade linear de energia e no déficit de ângulo planar. Também analisamos o comportamento destas quantidades como função da escala de energia onde a simetria de gauge é espontaneamente quebrada. Ampliamos este estudo para as cordas cósmicas não-Abelianas no espaço-tempo de de Sitter e anti-de Sitter. Para isto, construímos um sistema de equações de campo considerando a presença da constante cosmológica. Utilizando a análise numérica, fornecemos o comportamento dos campos de Higgs, de gauge e dos campos métricos para valores específicos dos parâmetros físicos do modelo. Para o caso do espaço-tempo de de Sitter, salientamos o surgimento do horizonte cosmológico que, embora seja consequência da constante cosmológica, está fortemente relacionado ao acoplamento gravitacional. Para o espaço-tempo de anti-de Sitter, encontramos que o sistema não apresenta horizonte. Esta característica do sistema está relacionada às componentes (tt) e (zz) do tensor métrico, que divergem para grandes distâncias da corda cósmica.

Dans ce travail, nous analysons le concept de manipulation à travers une théorie élargie qui inclut le réalisme des entités et la théorie causale de la manipulation. Dans une seconde étape, nous appliquons cette théorie à plusieurs expériences scientifiques. Cette thèse est articulée autour de quatre parties : Dans la Partie I nous exposons le concept de manipulation. Nous examinons le réalisme structurel en mettant l’accent sur ses difficultés concernant particulièrement les incertitudes ontologiques de la physique. Cet examen du réalisme structurel nous permettra de développer un réalisme des entités qui est susceptible de constituer une alternative au réalisme structurel.La partie II est consacrée aux aspects clés du réalisme des entités, c’est-à-dire ses fondements, ses arguments ainsi qu’une définition aussi précise que possible du concept de manipulation.Dans la partie III, nous élaborons une théorie générale de la manipulation/intervention qui est basée sur le réalisme des entités et la théorie de Woodward sur l’intervention, l’invariance et la profondeur de l’explication des évènements causaux. Nous allons développer trois éléments : 1-un système des conditions de l’intervention, 2- une typologie de l’intervention, 3-l’intervention probabiliste. Ce dernier type de l’intervention est applicable à l’expérience EPR. Dans la partie IV- Nous appliquons cette théorie à cinq expériences scientifiques : l’expérience EPR, l’expérience de l’électrodynamique quantique en cavité, l’expérience sur l’effet Zeeman, l’expérience du Tevatron (collisions de protons) et la dernière est non des moindres, est une expérience d’astrophysique (ondes gravitationnelles). Dans chacune de ces expériences, notre théorie a trouvé une application réussie. Toutes les conditions de l’intervention sont applicables sur les cinq expériences et une typologie bien définie de l’intervention a été élaborée et qui met en évidence les résultats de l’intervention dans les différentes séquences de ces expériences.Par conséquent, notre théorie de la manipulation reflète une utilité authentique et réelle dans différent domaines de la physique et de l’astrophysique. Un pareil résultat est important tenant compte du rôle de la manipulation expérimentale pour la science moderne. / In this work, we analyze the concept of manipulation through a comprehensive theory which includes the entity realism and the causal theory of manipulation. At the second stage, we implement this theory to several scientific experiments. It is divided into four parts:In Part I, we will have a long journey until we will reach the true concept of manipulation. We analyze the structural realism and we explore its difficulties regarding ontological problems of physics. Our survey of structural realism enables to open a new way to developing entity realism instead of structural realism.Part II will be dedicated to the core aspect of entity realism such as its foundations, its arguments and our aim to reach a global definition of manipulation concept.In Part III I will achieve my aim which is elaborating a global theory of manipulation/intervention based on entity realism and the Woodward theory of intervention, invariance and depth explanation of causal events. We will develop three items : 1- a system of intervention conditions 2-a typology of intervention, 3-probabilistic intervention. Such type of intervention is applicable to EPR experiment. In Part IV, we implement our theory to five scientific experiments: EPR experiment, electrodynamics cavity experiment, Zeeman effect experiment, Tevatron experiment (collision of protons) and last but not least an astrophysical experiment (gravitational waves).In each case, our theory is successful. All intervention conditions are applicable to our five experiments and a well defined typology of intervention is developed based on intervention results through different stages of those experiments. Therefore, the theory of manipulation shows a real and genuine application in different domains of physics and astrophysics. Such result is important regarding the role of manipulation in modern science.

La recherche d'une unité entre les contrats privés et les publics revient à vouloir démontrer l'existence d'un socle, d'un droit commun aux contrats privés et aux contrats publics au stade de leur formation. Cependant, si l'unité des éléments essentiels du contrat peut se révéler imparfaite entre le droit privé et le public, deux notions peuvent apporter une cohérence au phénomène juridique d'unité des contrats : la notion générale de contrat en sa qualité de principe fondateur du phénomène d'unité permet la recherche d'une définition unitaire du contrat dont l'expression est la notion de consentement ; alors que les notions d'objet et de cause se révèlent être des instruments d'identification principal et accessoire du phénomène d'unité des contrats. Ainsi, s'il existe une multitude de contrats, il n'existe qu'une notion de contrat. S'il existe une infinité d'objet, de cause et de moyen de consentir, il n'existe qu'une notion d'objet, de cause et de consentement. L'unité des contrats privés et des contrats publics est cela : la réduction d'une pluralité de notions à une notion-cadre fondamentale, la notion de contrat. / Seeking unity between private and public contracts is ultimately intended to demonstrate the existence of a base, a law common to private and public contracts, at the stage of their conclusion. However, if the unity, in terms of private and public law, of the basic elements of the contract may prove to be imperfect, two concepts may bring cohesiveness to the legal phenomenon of the unity of contracts: the general concept of contract in its role as a founding principle of the phenomenon of unity enables a uniform definition for the contract to be sought, the expression of which is the concept of consent whereas the notions of object and cause reveal themselves to be main instruments of identification, ancillary to the phenomenon of the unity of contracts. Thus, if multiple contracts exist, there only exists one concept of the contract. If there are an infinite number of objects, causes and means of consent, there is only one concept of object, cause and consent. The unity of private contracts and public contracts is this: the reduction of a multiplicity of notions into one basic framework, the concept of the contract.

Inspiré par une démarche de droit politique, le présent travail se propose d’envisager la fiction en droit à travers le prisme inédit de la légitimité, afin d’étudier sous un angle théorique son utilité dans la constitution de la réalité juridique, c’est-à-dire dans les fondations du droit en vigueur. Caractérisée en référence à la réalité politique, la fiction constituante est une technique justificative dont la fonction relève soit de la connaissance, soit du gouvernement. En tant qu’instrument de connaissance, la fiction constituante se trouve au coeur de l’épistémologie du positivisme juridique, et sert à reléguer la légitimité en son sens le plus profondément politique à une simple affaire de "Sein", c’est-à-dire « extra-juridique » ; tel est notamment l’objet de la "Grundnorm" de Kelsen. Le propos de la première partie de ce travail est de montrer que cet isolement de la chose juridique empêche d’approfondir la connaissance de ses fondations ; ce faisant, il s’agira de poser les bases de ce que pourrait être une épistémologie de droit politique. En tant qu’instrument de gouvernement, la fiction constituante se trouve au coeur de l’État, et sert à légitimer l’exercice du pouvoir politique par le biais de la représentation. En s’appuyant sur des auteurs classiques tels que Hobbes, Locke et Rousseau, le propos de la seconde partie de ce travail est de montrer que ce sont les caractéristiques de ce système d’organisation politique, quelle que soit au demeurant la forme de gouvernement retenue, qui rendent nécessaire le recours au registre fictionnel "lato sensu" ; celui-ci étant en effet susceptible de s’inscrire dans trois catégories discursives distinctes : la fiction "stricto sensu", le mensonge ou le mythe. / Following an approach inspired by "droit politique", this work aims at considering legal fiction through the unexplored prism of legitimacy in order to study from a theoretical perspective its utility in creating legal reality, i.e. in founding the law in force. Defined through its relation to political reality, constituent fiction is a technique of justification and its function is either a matter of knowledge or of government. As an instrument of knowledge, constituent fiction is at the core of the epistemology of legal positivism. It is used to relegate legitimacy, in its most political sense, to a simple matter of "Sein, i.e". to an “extra legal” matter, as it is notably the case of Kelsen’s "Grundnorm". The first part of this work aims at showing that this isolation of law prevents a deeper understanding of its foundations. In doing so, we will try to lay the grounds for what could be an epistemology of "droit politique". As an instrument of government, constituent fiction is at the core of the State. It is used to legitimize the exercise of political power by the means of representation. Relying on the classical works of Hobbes, Locke and Rousseau, the second part of this study aims at identifying the characteristics of this system of political organization that makes recourse to fiction a necessity; whatever the form of government chosen. This recourse to fiction, considered here in its broadest sense, can relate to three distinct discursive models: fiction in its strictest sense, falsehood, or myth.

In this work we studied magnetic properties of molecular magnets of the new heteropolyanion {Cu20}, dodecanuclear cluster {Ni12}, and the heterometallic {Cr7M} wheels, in which one of the CrIII ions of Cr8 has been replaced by a Fe, Cu, Zn, Ni, ion with this extra-spin acts as local probe for the spin dynamics.Such systems have been synthesized recently and they are well described using the Heisenberg spin Hamiltonian with a Zeeman term of an applied magnetic field along the z-axis. Using the numerical exact diagonalization method, we have calculated the energy spectrum and the eigenstates for different compounds,and we have used them for reexamining the available experimental susceptibility data to determine the values of exchange parameters.We have studied the thermodynamic properties such magnetization, susceptibility, heat-capacity. At low temperature regions molecular magnets act as individual quantum nanomagnets and can display super-paramagnetic phenomena like macroscopic quantum tunneling, ground state degeneracy, level-crossing. A crucial issue for understanding these phenomena is the coupling between magnetic molecular levels and the environment such as nuclear spins. We have modeled the behavior of the proton spin lattice relaxation rate as a function of applied magnetic field for low temperatures as it is measured in Nuclear Magnetic Resonance (NMR) experiments.

Zeitreisen und Reisen mit Überlichtgeschwindigkeit sind zwei Menschheitsträume; sie beflügeln die Fantasie und bieten Stoff für skurrile Geschichten. Eine Arbeit zum Thema „Zeitreisen und Reisen mit Überlichtgeschwindigkeit“ zwingt zu einer Auseinandersetzung mit dem Begriff der „Zeit“. Die Vielschichtigkeit und der antinomische Charakter dieses Begriffes machen es schwer, „Zeit“ genauer zu fassen. Zeit tritt uns entgegen als Form der Wahrnehmung in ihrer zutiefst subjektiven Seite, als biologischer Rhythmus, als soziales Phänomen im Sinne einer kollektiven Zeitbestimmung, aber eben auch als physikalischer Parameter. Einsteins Relativitätstheorie revolutioniert unsere Vorstellungen von Raum und Zeit, indem sie sich vom newton-mechanischen Konzept des absoluten Raumes und der absoluten Zeit löst. Sie macht aber das, was bei Wells zehn Jahre vorher noch reine Fiktion war, zu einem für die Physik diskussionswürdigen Thema, nämlich das „Problem der Zeitreisen“. Einsteins Spezielle Relativitätstheorie (1905) erlaubt durch den von ihr vorhergesagten Effekt der Zeitdilatation „Reisen in die Zukunft“, und die Einstein’sche Gravitationstheorie lässt geschlossene zeitartige Linien als Lösungen ihrer Gleichungen zu (z. B. Gödel-Kosmos, Anti-de-Sitter-Kosmos). Allerdings würde eine Reise auf einer Zeitschleife sofort ein ganzes Bündel von Paradoxien (z. B. Großvater-Paradoxon, Informationsparadoxon) und semantischen Inkonsistenzen nach sich ziehen. Obwohl erstaunlicherweise die fundamentalen Gesetze der Physik (abgesehen von extrem seltenen und makroskopisch nicht in Erscheinung tretenden quantenmechanischen Effekten) bei einer Zeitumkehr nicht verletzt würden, scheint es in der Natur doch ein grundsätzliches Verbot von Vergangenheitsreisen zu geben. Der Physiker Dieter Zeh, dessen Position im Schlusskapitel der Arbeit näher beleuchtet wird, vertritt die Auffassung, dass die Science-Fiction-Literatur zum Thema „Zeitreisen“ überwiegend auf einfachen begrifflichen Fehlern beruhe. Die in Anlehnung an die Allgemeine Relativitätstheorie konstruierten Vorgänge seien bestenfalls genauso „theoretisch möglich“ wie ein Gas, das sich von selbst in einer Ecke des Gefäßes versammelt. Die vorliegende Arbeit erörtert Ansätze für „Zeitmaschinen“ und superluminale Prozesse, die in Einklang mit der modernen Physik stehen. Besprochen werden u. a. die Tachyonen-Hypothese, Tiplers rotierender Zylinder, der Gödel-Kosmos, der Anti-de-Sitter-Kosmos, die sogenannten „Wurmlöcher“ und die Alcubierre-Metrik. Zugleich sollen Ansätze vorgestellt werden (z. B. Eternalismus, Viele-Welten-Modell, Prinzip der konsistenten Geschichte), die Lösungsversuche für die Paradoxien von Vergangenheitsreisen bieten. Um die Reisen in die Vergangenheit und Reisen mit Überlichtgeschwindigkeit scheint es zu stehen wie mit einer Anfrage an Radio Jerewan; die Antwort lautet stets: „Im Prinzip ja, aber …“ Doch die Faszination dieser Idee wird weiterhin Stoff für die „Fiction“ liefern. / Time travel and superluminal travel are two of mankind's dreams. They inspire our imagination and provide material for bizarre stories. A work on the subject of time travel and superluminal travel forces us to re-examine our concept of "time". The complexity and the contradictory nature this subject makes it difficult to be more precise about "time". On its deepest subjective side, time is a means of perception, a biological rhythm, a social phenomenon in terms of our collective understanding of time. But it is also a physical parameter. Einstein's Theory of Relativity revolutionised our idea of space and time by freeing us from the Newtonian concept of absolute space and absolute time. The "problem of time travel", a subject that Wells wrote about just ten years before as mere fiction, was now a discussion worthy of physics. Einstein's Special Theory of Relativity (1905), by predicting the effects of time dilation, allowed for "travels into the future" and Einstein's Theory of Gravity used closed time-like lines for solutions to calculations about time travel (for example, the Gödel Universe and the Anti-de Sitter Universe). However, a trip to a time warp would immediately involve a whole set of paradoxes (for example, the grandfather paradox and the information paradox) and semantic inconsistencies. Surprisingly, the fundamental laws of physics (apart from extremely rare and non-emergent macroscopic quantum mechanical effects) are not violated by the concept of time reversal. Yet, in nature, there still seems to be a fundamental prohibition against time travel to the past. Physicist Dieter Zeh, whose position is more closely presented in the final chapter of this work, supports the view that science fiction literature on the subject of "time travel" is overwhelmingly based on simple conceptual errors. The processes used in this literature, which are based on the General Theory of Relativity, at best, are just as "theoretically possible" as a gas which gathers itself into the corner of a container. This work discusses approaches for "time machines" and superluminal travel which are consistent with modern physics. Some of the discussions that will be presented are the tachyon hypothesis, Tipler's rotating cylinder, the Gödel Universe, the Anti-de Sitter Universe, so-called "wormholes" and the Alcubierre-metric. At the same time, approaches will be presented (for example, Eternalism, the Many-Worlds Interpretation and the Consistent Histories Approach) that will provide attempts to find a solution for paradoxes regarding time travel to the past. Questions about time travel to the past and superluminal travel are like the questions asked on Radio Yerevan. The answer is always, "In principle yes, but…" But the fascination about time travel will continue to provide material for "fiction".

No description available.

This Master thesis explores delinquency of juvenile Czechs and Germans from seventh to ninth grade based on quantitative data. The data comes from an International Self-Report Delinquency study (ISRD-2), which is anchored primarily in the Social control theory (Hirschi, 1969/2002) and the General theory of crime (Gottfredson, Hirschi, 1990). Therefore, in the first section, attention is paid to these and other selected criminological theories; the other theories are mainly the strain theories and the cultural deviance theories. In the second section, the thesis deals briefly with the socio- cultural differences and similarities between the Czech Republic and Germany. The core of the thesis is the third, analytical section, which presents the findings of statistical analysis. A conclusion is reached that the theories studied are by far less contradictory than what the authors of the social control theory and the general theory of crime claimed them to be. It rather seems that the individual theories are complementary and often lead to the same predictions. Hypotheses are confirmed that some characteristics of the pupils` relation to their school are related to delinquency: Pupils who like going to school are somewhat less delinquent than pupils who do not. Pupils who play truant are substantially...

La portée de la liberté contractuelle dans les relations entre associés est régulièrement relativisée, voire anéantie, à l’aune des règles impératives qui régissent les personnes morales. L’hypertrophie de ces dernières est parfois décriée. La liberté serait d’autant plus bridée qu’elle subirait le joug d’un principe d’égalité, lequel s’oppose à ce qu’une différenciation de traitement soit permise, si ce n’est à titre expressément exceptionnel. Pour autant, à l’analyse des textes, la préférence se révèle n’être que l’expression de la liberté contractuelle dans les relations entre associés. Elle en adopte un régime similaire : en dehors des prohibitions expresses – issues tant de la théorie générale du contrat que du droit des sociétés –, et de l’excès d’inégalité – dont l’intérêt social se fait garant spécial en la matière –, dès lors que le consentement des associés aux aménagements est libre et éclairé, le principe est la liberté de stipuler une altérité de traitement. Quelle que soit la forme sociale considérée, les associés bénéficient d’une grande liberté pour aménager l’ensemble de leurs prérogatives à l’image de leurs besoins. Inégalité constructive et dynamique au service de l’intérêt social, la préférence doit être promue : le souhait est alors renouvelé d’une clarification et d’une simplification du cadre normatif offert aux statuts des sociétés françaises. / The impact of contractual freedom in associates’ relations is often contextualized, if not annihilated, with regard to the mandatory rules governing legal entities. The hypertrophy of those rules is sometimes criticized. Not only is freedom limited, it also suffers from a principle of equality, which prohibit unequal treatment, unless it is on exceptional occasions. However, upon a thorough text analysis, the preference turns out to be the expression of contractual freedom in the relations between associates. It adopts a similar system: apart from intentional prohibitions – originating both from the general theory of contract and corporate laws -, and from excessive inequality –to which social interest acts as a protector in that area-, as soon as the consent of the associates to the organization is free and enlightened, the principle is the freedom to stipulate an alterity of processing. Whichever social form is considered, the associates receive an important freedom to build all their prerogatives reflecting their needs. With constructive and dynamic inequality in social interest’s service, preference must be promoted: the wish must be expressed again with a clarification and a simplification of the standard framework offered to French companies statuses.

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 .