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No / This article critically explores the working lives and views of disabled senior staff working in UK organisations. The qualitative research at the core of the article establishes that some disabled people are confounding established notions of disabled people only working in peripheral employment roles by exploring the working lives and perceptions of disabled managers. The findings do, however, point to continued barriers to what disabled staff in senior positions can be seen to do and be organisationally. Here both practical and ontological risk inheres in organisationally induced change, openness about impairment and risky identities. Such ideas, it is argued, present limits to further promotion and workplace inclusion for some disabled managers.

O artigo Weighted forms of Euler's theorem de William Y.C. Chen e Kathy Q. Ji, em resposta ao questionamento de George E. Andrews, matemático estadunidense, sobre encontrar demonstrações combinatórias de duas identidades no Caderno Perdido de Ramanujan, nos mostra algumas formas ponderadas do Teorema de Euler sobre partições com partes ímpares e partes distintas via a introdução do conceito de partição com raiz. A propositura deste trabalho é envolta à apresentação de resultados sobre partições com raiz de modo a posteriormente realizar formulações combinatórias das identidades de Ramanujan por meio deste conceito, procurando estabelecer conexões com formas ponderadas do Teorema de Euler. Em particular, a bijeção de Sylvester e a iteração de Pak da função de Dyson são elementos primordiais para obtê-las. / The article Weighted forms of Euler's theorem by William Y.C. Chen and Kathy Q. Ji in response to the questioning of George E. Andrews, American mathematician, about nding combinatorial proofs for two identities in Ramanujan's Lost Notebook shows us some weighted forms of Euler's Theorem on partitions with odd parts and distinct parts through the introduction of the concept of rooted partition. The purpose of this work involves the presentation of results on rooted partitions in order to make combinatorial formulations of Ramanujan's identities, seeking to establish connections with weighted forms of Euler's Theorem. In particular, the Sylvester's bijection and the Pak's iteration of the Dyson's map are primordial elements to obtain them.

Ce travail se situe dans le domaine du diagnostic des processus défini comme étant l'identification de ses états fonctionnels. Dans le cas où l'obtention d'un modèle précis du processus est délicate ou impossible, la connaissance sur le système peut être extraite à partir des signaux obtenus lors d'un fonctionnement normal ou anormal en incluant des mécanismes d'apprentissage. Cette connaissance s'organise sous l'aspect d'une partition de l'espace des données sous forme de classes (représentant les états du système). Parmi les techniques d'apprentissage, celles incluant de la logique floue ont l'avantage d'exprimer les appartenances d'un individu à plusieurs classes, ceci permet de mieux connaître la situation réelle du système et prévoir des changements vers des états de défaillance. Nonobstant leurs performances adéquates, leur forte dépendance aux paramètres d'initialisation est une difficulté pour l'apprentissage. Cette thèse se situe dans l'amélioration de ces techniques, en particulier notre objectif est l'élaboration d'une méthode permettant de valider et d'adapter automatiquement la partition de l'espace de données obtenue par une technique de classification floue. Elle permet de trouver automatiquement une partition optimale en termes de compacité et de séparation des classes, à partir uniquement de la matrice des degrés d'appartenance obtenue par une classification antérieure. Cette méthode est donc une aide importante donnée à l'expert du processus pour établir les états fonctionnels dans l'implémentation d'une technique de surveillance d'un procédé complexe. Son application est illustrée sur des exemples académiques et sur le diagnostic de 3 procédés chimiques.

Markov partitions provide a 'good' mechanism of symbolic dynamics for uniformly hyperbolic systems, forming the classical foundation for the thermodynamic formalism in this setting, and remaining useful in the modern theory. Usually, however, one takes Bowen's 1970's general construction for granted, or restricts to cases with simpler geometry (as on surfaces) or more algebraic structure. This thesis examines several questions on the algorithmic content of (topological) Markov partitions, starting with the pointwise, entropy-like, topological conjugacy invariant known as orbit complexity. The relation between orbit complexity de nitions of Brudno and Galatolo is examined in general compact spaces, and used in Theorem 2.0.9 to bound the decrease in some of these quantities under semiconjugacy. A corollary, and a pointwise analogue of facts about metric entropy, is that any Markov partition produces symbolic dynamics matching the original orbit complexity at each point. A Lebesgue-typical value for orbit complexity near a hyperbolic attractor is also established (with some use of Brin-Katok local entropy), and is technically distinct from typicality statements discussed by Galatolo, Bonanno and their co-authors. Both our results are proved adapting classical arguments of Bowen for entropy. Chapters 3 and onwards consider the axiomatisation and computable construction of Markov partitions. We propose a framework of 'abstract local product structures'

O artigo Weighted forms of Euler's theorem de William Y.C. Chen e Kathy Q. Ji, em resposta ao questionamento de George E. Andrews, matemático estadunidense, sobre encontrar demonstrações combinatórias de duas identidades no Caderno Perdido de Ramanujan, nos mostra algumas formas ponderadas do Teorema de Euler sobre partições com partes ímpares e partes distintas via a introdução do conceito de partição com raiz. A propositura deste trabalho é envolta à apresentação de resultados sobre partições com raiz de modo a posteriormente realizar formulações combinatórias das identidades de Ramanujan por meio deste conceito, procurando estabelecer conexões com formas ponderadas do Teorema de Euler. Em particular, a bijeção de Sylvester e a iteração de Pak da função de Dyson são elementos primordiais para obtê-las. / The article Weighted forms of Euler's theorem by William Y.C. Chen and Kathy Q. Ji in response to the questioning of George E. Andrews, American mathematician, about nding combinatorial proofs for two identities in Ramanujan's Lost Notebook shows us some weighted forms of Euler's Theorem on partitions with odd parts and distinct parts through the introduction of the concept of rooted partition. The purpose of this work involves the presentation of results on rooted partitions in order to make combinatorial formulations of Ramanujan's identities, seeking to establish connections with weighted forms of Euler's Theorem. In particular, the Sylvester's bijection and the Pak's iteration of the Dyson's map are primordial elements to obtain them.

Let X be a Polish space and Q a measurable partition of X into Gδ equivalence classes. In 1978, S. M. Srivastava proved the existence of a Borel cross section for Q. He asked whether more can be concluded in case each equivalence class is uncountable. This question is answered here in the affirmative. The main result of the author is a proof that shows the existence of a Castaing Representation for Q.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1979 / Vita. / Bibliography: leaves 96-98. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Mathematics

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