Thesis (Ph. D.)--University of Wisconsin--Madison, 1966. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

Este trabalho tem como objetivo principal aplicar elementos de teoria dos conjuntos no estudo de sistemas biortogonais em espaços de Banach. Inicialmente, estudamos o Teorema de Markushevic, que garante que todo espaço de Banach separável admite um sistema biortogonal enumerável. Assim, partimos para o estudo de espaços de Banach não separáveis, mais especificamente, estudamos a existência de sistemas biortogonais não enumeráveis em espaços de Banach da forma C(K), com K compacto Hausdorff não metrizável. Nesta direção, estudamos dois teoremas devido a S. Todorcevic. O primeiro teorema nos dá condições que um compacto Hausdorff K deve satisfazer de tal modo que o respectivo espaço de Banach C(K) possua sistemas biortogonais não enumeráveis. O segundo teorema nos diz que, assumindo o Axioma de Martin, todo espaço de Banach não separável da forma C(K) possui um sistema biortogonal não enumerável. Em seguida, consideramos algumas funções cardinais definidas por P. Koszmider para espaços de Banach, associadas aos sistemas biortogonais e estudamos suas relações com funções cardinais conhecidas. Em particular, obtemos um resultado original que relaciona o peso de um espaço compacto Hausdorff K com o tamanho de tipos especiais de sistemas biortogonais em C(K), generalizando um resultado de S. Todorcevic sobre álgebras de Boole. Finalmente, construímos um espaço de Ostaszewski K usando o Princípio Diamante. O espaço K é um compacto disperso não metrizável tal que todas suas potências finitas são hereditariamente separáveis. Este espaço é um exemplo consistente de um espaço compacto Hausdorff não metrizável tal que o respectivo espaço de Banach C(K) não admite sistemas biortogonais não enumeráveis. / The main purpose of this work is to apply elements of set theory to the study of biorthogonal systems in Banach spaces. Initially, we study Markushevic\'s Theorem, which ensures that every separable Banach space has a countable biorthogonal system. With this result, we focus our attention to the study of nonseparable Banach spaces, more especifically, we study the existence of uncountable biorthogonal systems in Banach spaces of the form C(K), with K a nonmetrizable compact Hausdorff space. In this direction, we study two theorems of S. Todorcevic. The first one gives us sufficient conditions that a compact Hausdorff space K must satisfy in order to get that the respective Banach space C(K) has an uncountable biorthogonal system. The second one tells us that under Martin\'s Axiom, every nonseparable Banach space of the form C(K) has an uncountable biorthogonal system. Next, we consider some cardinal functions defined by P. Koszmider for Banach spaces, related with biorthogonal systems, and we study its relations with well - known cardinal functions. In particular, we obtain an original result relating the weight of a compact Hausdorff space K to the size of certain biorthogonal systems in C(K), generalizing a result of S. Todorcevic for Boolean algebras. Finally, we construct an Ostaszewski space K using the Diamond Principle. The compact space K is a scattered nonmetrizable Hausdorff space such that all its finite powers are hereditarily separable. This space is a consistent example of a nonmetrizable compact Hausdorff space such that the respective Banach space C(K) does not have an uncountable biorthogonal system.

O principal objetivo desse trabalho é o estudo da questão da existência de isomorfismos entre as classes de Baire sobre [0,1]. Para isso, desenvolvemos os principais resultados concernentes às relações entre as classes de Baire sobre [0,1]. A saber: (1) As classes de Baire são isométricas como álgebras de Banach a espaços da forma C(K); (2) As classes de Baire são subespaços próprios umas das outras, até o primeiro ordinal não enumerável, onde elas estabilizam; (3) As classes de Baire não são subespaços complementados umas das outras; (4) As classes de Baire não são isométricas umas às outras como espaços de Banach. Por fim, apresentamos as respostas conhecidas para a questão isomórfica, sendo que para tal, utilizamos os resultados mencionados acima. / The main purpose of this work is the study of the question about the existence of isomorphisms between the Baire classes on [0,1]. In order to do that, we develop the most important results concerning the relations between the Baire classes on [0,1]. Those results are: (1) The Baire classes are isometric as Banach algebras to spaces of the form C(K); (2) The Baire classes are proper subspaces each one of the others, until the first uncountable ordinal, when they stabilise; (3) The Baire classes aren\'t complemented subspaces each one of the others; (4) There aren\'t linear isometries between the Baire classes. Finally we presente the known answers to the isomorphic question, using for this the results mentioned above.

A travers l’étude du cas d’une entité exploratoire, NCA, nous cherchons à comprendre comment identifier et structurer un champ d’innovation. C’est à dire comprendre comment se fait le choix d’un domaine dans lequel mener une activité de conception innovante, et quels mécanismes permettent de mener un travail de conception innovante dans des directions pertinentes. La littérature donne peu d’éléments sur les mécanismes à l’œuvre qui vont permettre d’identifier et de structurer un champ d’innovation, en l’absence de problème spécifique à résoudre, ce qui est la situation de NCA qui s’intéresse en particulier aux innovations d’usages, pour lesquelles il n’existe pas de demande explicite des clients. Nos résultats relatifs aux processus d’innovation montrent que les activités d’exploration menée par NCA conduisent à un renouvellement des routines utilisées pour les produits historiques. L’exploration renouvelle l’exploitation. Par ailleurs, les difficultés principales rencontrées par NCA tiennent moins aux processus spécifiques à mettre en œuvre qu’à des mécanismes inopérants dans l’identification de champs d’innovation.Sur le plan organisationnel, nos résultats montrent que NCA fonctionne selon une forme d’ambidextrie simultanée, sur le plan individuel et au niveau de l’entité NCA elle même. Cela se traduit par un renouvellement de l’exploitation par l’exploration. Nous mettons aussi en lumière la forme organisationnelle originale de NCA, à la fois business unit et entité exploratoire. Cette forme d’organisation facilite le lancement de nouvelles catégories de produits, et le fait que le marché de la BU ne soit pas défini, conduit NCA à maintenir cette activité d’exploration dans le temps. / Our case study based on an exploratory entity evolving from a small team to a business unit raise questions related to the identification and structuration of an innovation field. The literature gives few elements with regards to the choice of such a field, and the mechanisms to set priorities within a chosen field. Our results related to innovation processes show that exploratory activities leads to a renewal of exploitation, and also that the difficulties encountered by NCA in exploration activities are less related to the existing processes than to the choice of an innovation field. Our results related to organization show that NCA works in a mode of simultaneous ambidexterity, being able at the same time to launch new product categories and to explore new product categories. This also leads to the renewal of existing routines. The structure of NCA has also some original features, being at the same time a business unit and an exploratory entity. This exploratory business unit seems to be able to launch more easily new products categories, because there is no need to look for a landing zone, as it is the case of organisations solely responsible for exploration.

La thèse étudie le pouvoir génératif de la structuration des connaissances pour la conception innovante. Partant d’une analyse de la générativité des structures de connaissances non-verbales, et notamment du dessin d’architecte, elle identifie un nouveau mode de conception en montrant comment une revisite des rapports entre connaissances favorise la génération de nouveaux concepts. En particulier, une restructuration des connaissances visant à rendre la structure splitting, c’est-à-dire, sans rapports modulaires ou déterministes entre connaissances, possède un fort pouvoir génératif. En session collective, les médias non-verbaux, tels que le dessin, les images ou encore le prototypage 3D, se révèlent ainsi particulièrement favorables à la restructuration des connaissances : trois conditions nécessaires présentées dans la thèse doivent cependant être réunies afin de garantir la performance du non-verbal en session collective. Par ailleurs, ce phénomène de restructuration générative - aussi appelée K-preordering – diffère de l’exploration classique par génération de concepts alternatifs. Les deux modes de conception ne sont pas pour autant incompatibles : la thèse propose ainsi un processus de conception alternant phases de K-preordering et phases de génération de concepts. Ce processus est notamment testé à travers deux cas de recherche-intervention visant à provoquer la réorganisation des structures de connaissances stabilisées et partagées à l’échelle de l’organisation. Ces deux cas montrent en particulier comment un tel processus favorise la conception de programmes de recherche transdisciplinaires. / The thesis investigates the generative power of knowledge structuration for innovative design. Analyzing the generativity of non-verbal knowledge structures - especially, architectural drawings -, this work identifies a new design method by showing that the transformation of links between knowledge bases fosters concept generation. In particular, a restructuration that aims to design a splitting structure - a structure avoiding modular and deterministic links between knowledge bases - has a strong generative power. During collective creativity sessions, non-verbal tools such as sketches, pictures or 3D-printing, can enhance knowledge restructuration: however, three necessary conditions, which are presented in the thesis, have to be met in order to ensure performance of the non-verbal tools used during the session. Moreover, this generative restructuration - also called K-preordering - differs from the classic design exploration by alternative concepts generation. But the two design modes are not mutually exclusive: the thesis proposes a design process that alternates K-preordering and concept generation. This process is applied in two studies, which were led as action research and intended to foster the reorganization of knowledge structures that were both stabilized and shared at the organizational level. In particular, these studies show how such a process helps enhancing the design of transdisciplinary research programs.

La notion de développement durable est aujourd’hui une préoccupation centrale des populations et des pouvoirs publics. L’entrepreneuriat durable représente une forme de réponse à cette préoccupation à travers l’intégration des normes de développement durable dans le cœur de métier de l’entreprise. Ce type d’entreprise vient répondre à des objectifs économiques, sociaux et environnementaux. La recherche en entrepreneuriat durable s’est particulièrement intéressée au profil de l’entrepreneur durable. Cependant, la recherche ne s’est pas suffisamment interrogée sur la façon dont il procède. Il est considéré comme l’agent de rupture à travers l’introduction d’éco-innovations. L’innovation apparait donc comme une solution aux problématiques sociales et environnementales. Mais ceci n’est pas suffisant pour considérer ce phénomène entrepreneurial comme une forme innovante. Cette thèse tente de combler ces manquements en modélisant, le processus entrepreneurial durable. Par ailleurs, l’emprunt d’une théorie de l’innovation « C-K Theory » permet de rapprocher le processus entrepreneurial durable du processus de conception innovante CK dans l’objectif de déterminer le caractère innovant de l’entrepreneuriat durable. / The notion of sustainable development is today a central concern of the population and the public authorities. Sustainable entrepreneurship is a form of response to this concern through the integration of sustainable development standards into the core business of the company. This type of business comes to meet economic, social and environmental objectives. Sustainable entrepreneurship research has been particularly interested in the profile of the sustainable entrepreneur. However, the research did not ask enough about how it works. It is considered the breaking agent through the introduction of eco-innovations. Innovation therefore appears as a solution to social and environmental issues. But this is not enough to consider this entrepreneurial phenomenon as an innovative form. This thesis attempts to fill these gaps by modeling, the sustainable entrepreneurial process. In addition, the borrowing of a theory of innovation "C-K Theory" makes it possible to bring the sustainable entrepreneurial process closer to the CK innovative design process in order to determine the innovative nature of sustainable entrepreneurship.

L’ingénierie agroécologique vise à produire des savoirs actionnables, pour concevoir des systèmes de cultures économiquement et écologiquement performants, par la valorisation de régulations naturelles. Notre problématique est centrée sur la santé des cultures, et plus particulièrement sur la bactérie phytopathogène Ralstonia solanacearum, agent du flétrissement bactérien alors qu’une souche extrêmement agressive menace la production de tomates en plein champ en Martinique. La nécessité d’explorer et de développer des alternatives aux méthodes conventionnelles de protection des plantes (variétés résistantes, pesticides), actuellement inefficaces, invite à la mise en œuvre d’une démarche de conception innovante. Nos travaux montrent que la mobilisation d’une barrière rhizosphérique est une stratégie de régulation biologique alternative. Différents processus y contribuent, telle que la mycorhization, symbiose entre racines et champignons mycorhiziens à arbuscules, présents dans la plupart des sols. Nous montrons que la mobilisation de réseaux de mycorhizes indigènes à partir d’un sol agricole permet une mycorhization précoce de la tomate. De plus, l’association de plantes aux propriétés mycorhizotrophes et assainissantes en conditions contrôlées montre des effets bioprotecteurs partiels et ouvre de nouvelles perspectives de combinaisons entre processus. Ces combinaisons sont mobilisables par des leviers d’actions multi-scalaires. Nous avons produit une grille d’analyse générique de ces leviers d’action pour la conception, par des trajectoires d’innovation multidirectionnelles, de « systèmes de culture bioprotégés ». Dans le contexte agricole martiniquais, une démarche d’apprentissage permet en effet l’émergence d’une dynamique de co-conception de systèmes de cultures recourant aux plantes mycorhizotrophes. Nos travaux proposent des outils pour une exploration collective de nouvelles stratégies de gestion durable de la santé des cultures. / Agroecological engineering aims to produce actionable knowledge to design economically and environmentally efficient cropping systems, based on the exploitation of natural regulation mechanisms. Our issue is centered on crop health, especially on the plant pathogenic bacterium Ralstonia solanacearum (bacterial wilt agent), of which an extremely aggressive strain threatens field tomato production in Martinique. The need to explore and develop alternatives to conventional methods of plant protection (resistant varieties, pesticides), ineffective in our case, calls for the implementation of an innovative design approach. Our work shows that the protection of the roots via the formation of a self-sustaining rhizospheric barrier may be an alternative biological control strategy. Different processes contribute, such as mycorrhizal symbiosis between roots and arbuscular mycorrhizal fungi, which are present in most soils. We show that the mobilization of indigenous mycorrhizal networks from an agricultural soil allows early mycorrhization of tomatoes. In addition, the association of plants with mycorrhizal and sanitizing properties in controlled conditions showed partial bioprotective effects and opens up new prospects for combinations between processes. These combinations may be exploited in various ways. We produced a generic analysis grid of key levers to design "healthy cropping systems " through multi-directional innovation trajectories. In Martinique's agricultural context, a learning process allows the emergence of a dynamic co-design of cropping systems using mycorrhizal plants. Our work thus provides tools for collective exploration of new sustainable management strategies for crop health.

Le raisonnement de la fertilisation azotée du blé a, depuis 40 ans, été largement orienté par le consensus autour de la méthode du bilan, avec comme principes fondamentaux : une nutrition azotée non limitante tout au long du cycle et l’estimation, de manière indépendante, des différents termes de l’équation du bilan pour caractériser la fourniture du sol et les besoins en azote de la plante. Au regard des enjeux de réduction des pollutions environnementales, de l’évolution des exigences qualitative du marché, ainsi que des difficultés de mise en oeuvre de la méthode, on s’interroge sur l’opportunité de renouveler ce paradigme. Pour proposer une nouvelle méthode qui réponde aux divers enjeux concernant l’azote, qui valorise au mieux les connaissances disponibles et dont la mise en oeuvre est cohérente avec les moyens des acteurs, nous avons mis en oeuvre une démarche de conception innovante, structurée en 3 étapes : un diagnostic des usages des outils actuels, une phase de conception, incluant des ateliers de conception et la mise au point de règle de décision à l’aide d’un modèle, et un test d’usage du prototype conçu.Le diagnostic des usages a mis en évidence plusieurs obstacles à la mise en oeuvre de la méthode du bilan, dont la fixation de l’objectif de rendement, ce qui a orienté la phase de conception vers l’exploration d’un concept de méthode de fertilisation azotée permettant de s’en affranchir. La méthode mise au point est basée sur le suivi régulier de l’état de nutrition azotée de la plante, l’acceptation de carences en azote non préjudiciables et des règles de décision tenant compte des conditions météorologiques au moment de l’apport. Nous montrons que la conception a rendu nécessaire la production de nouvelles connaissances, mais aussi la diversification des ressources et des compétences habituellement mobilisées. Ce travail enrichit les méthodes de conception d’outils d’aide à la décision en montrant comment l’articulation des 3 étapes permet de sortir du paradigme qui domine la fertilisation azotée depuis des décennies et d’élaborer un outil palliant les défauts des outils actuels. / Decisions about nitrogen fertilizer application on wheat have, for the last 40 years, been based on the balance sheet method, with the following underlying principles: non-limiting nitrogen nutrition throughout the crop cycle, and independent estimation of the various terms of the equation, to characterize soil nitrogen supply and plant nitrogen needs. Environmental pollution, changes in the qualitative requirements of the market and difficulties implementing this method have raised questions about whether it might be appropriate to switch to new ways of managing nitrogen fertilizer. We developed a new method meeting the diverse constraints relating to nitrogen use, making the best use of available knowledge and easily applicable by users, through a 3-steps innovative design approach: a diagnosis of the use of current tools, a design phase including design workshops, production of new knowledge, a modelbased prototyping, and the testing of a prototype method.The diagnosis of uses identified several barriers to the implementation of the balance sheet method, including the need to set a target yield. This directed the design phase towards the exploration of new ways of managing nitrogen fertilizer that did not require the fixing of a target yield. The method developed is based on the regular monitoring of plant nitrogen nutrition, the toleration of periods of nitrogen deficiency that are not prejudicial and the use of decision rules taking weather conditions at the time of nitrogen application into account.This design required the generation of new knowledge and a diversification of the resources and skills usually mobilized. This work enriches the methods for designing decision support tools and shows how a combination of 3 steps can be used to develop a tool for managing nitrogen fertilizer applications completely different from the dominant paradigm of the last 40 years, and compensating the defects of current methods.

A classificação isomorfa dos espaços de Banach separáveis C(K) é devida a Milutin no caso em que K são não enumeráveis e a Bessaga e Pelczynski no caso em que K são enumeráveis. Neste trabalho apresentamos uma extensão vetorial dessa classificação e tiramos várias consequências, por exemplo, considerando o espaço métrico compacto infinito K e Y um espaço de Banach: &nbsp; &nbsp; 1. Sendo 1 < p < &infin; e &Gamma; um conjunto infinito, classificamos, a menos de isomorfismo, os espaços de Banach C(K, Y &oplus; lp(&Gamma;)), quando o dual de Y contém uma cópia de lq, onde 1/p+ 1/q =1. &nbsp; &nbsp; 2. Classificamos os espaços de Banach C(K, Y &oplus; l&infin;(&Gamma;)), quando a densidade de Y é estritamente menor que 2|&Gamma;|. &nbsp; &nbsp; 3. Classificamos os espaços de Banach C(K &times;(S&oplus; &beta;&Gamma;)) e C(S &oplus; (K&times; &beta;&Gamma;)), onde S é um compacto disperso de Hausdorff arbitrário e &beta;&Gamma; é a compactificação de Stone-Cech de &Gamma;. Obtemos, também, algumas leis de cancelamento para espaços de Banach da forma C(K1,X)&oplus; C(K2,Y), onde K1 e K2 são espaços compactos métricos infinitos de Hausdorff e X, Y espaços de Banach satisfazendo condições adequadas. Estabelecemos também um teorema de quase-dicotomia envolvendo os espaços C(K,X), onde X tem cotipo finito. Finalmente, apresentamos algumas majorações nas distorções de isomorfismos positivos de C([0,&omega;k]) em C([0,&omega;]) e também de C([0,&omega;]) em C([0,&omega;k]), k&isin; N, k &ge; 2. / The isomorphic classification of separable Banach spaces C(K) is due Milutin in the case when K are uncountable and to Bessaga and Pelczynski in the case when K are countable. In this work we prove a vectorial extention of this classification and provide several consequences, for example considering the infinite metric compact space K and Y a Banach space: &nbsp; &nbsp; 1. Let 1 < p < &infin; and &Gamma; a infinite set, we classify, up to an isomorphism, the Banach spaces C(K, Y &oplus; lp(&Gamma;)), in the case where the dual of Y contains no copy of lq, where 1/p+ 1/q =1. &nbsp; &nbsp; 2. We classify the Banach spaces C(K, Y &oplus; l&infin;(&Gamma;)), when the density character of Y is strictly less that 2|&Gamma;|. &nbsp; &nbsp; 3. We classify the Banach spaces C(K &times;(S&oplus; &beta;&Gamma;)) and C(S &oplus; (K&times; &beta;&Gamma;)) where S is an arbitrary dispersed compact and &beta;&Gamma; is the Stone-Cech compactification of &Gamma;. We obtain also some cancellation laws for Banach spaces in the form C(K1,X)&oplus; C(K2,Y), where K1 and K2 are metric compact Hausdorff spaces and X, Y Banach spaces satisfying appropriate conditions. We established also a quasi-dichotomy theorem envolving the C(K,X) spaces, where X is of finite cotype. Finally, we present some upper bounds of distortions of positive isomorphisms of C([0,&omega;k]) on C([0,&omega;]) and also of C([0,&omega;]) on C([0,&omega;k]), k&isin; N, k &ge; 2.

Le propos de cette étude est de modéliser une méthodologie de “design augmenté” appliqué à la conception de produit innovant dans un environnement de PME. Cette approche inclut la Théorie C-K dans ce contexte d'innovation de rupture.En général, le processus de design industriel consiste à parcourir quatre pôles complémentaires :1/ la phase d'ego-design, où le designer conceptualise un besoin utilisateur,2/ la phase de techno-design, où le designer et l'ingénieur trouvent des solutions pour matérialiser ce concept,3/ la phase d'éco-design, où les acteurs sociaux concernés l'autorisent et4/ la phase d'ergo-design, où l'utilisateur final adopte le produit final.Une réflexion méthodologique conduit à la modélisation d'un raisonnement innovant de “design augmenté” (où les acteurs principaux sont remplacés par un cortège d'intervenants).Cette méthodologie a été expérimentée dans un contexte de PME. Grâce à l'utilisation du modèle, le management de projet de “design augmenté” fut couronné de succès. Cependant, d'autres validations, plus complexes encore, seront utiles pour sécuriser cette modélisation. L'exploitation de cette approche, par la variété de ses supports, doit guider le chef de projet innovant, en PME, dans le processus général d'innovation de rupture. / The purpose of this study is to model an ‘enhanced design' methodology applied to the conception of an innovative product in a SME environment. This approach includes C-K theory in a context of disruptive innovation.In general, the industrial design process consists of four major steps:1/ the ego-design phase, where the designer conceptualizes a user need,2/ the techno-design phase, where designer and engineer find solutions to materialize the concept,3/ the eco-design phase, where social actors involved authorize it and then4/ the ergo-design phase, where the user adopt the final product.A methodological reflection leads to the modeling of the innovative ‘enhanced design' reasoning (where major actors are replaced by a bunch of various stakeholders).The specific SME's case was successful. Using the model, the enhanced design project management was efficient. But some more complex application cases would help secure it. Using this approach, with appropriate information, should guide the SME design project manager in the general radical innovation process.