This thesis examines the method of forcing in set theory and focuses on aspects that are set aside in the usual presentations or applications of forcing. It is shown that forcing can be formalized in Peano arithmetic (PA) and that consis- tency results obtained by forcing are provable in PA. Two ways are presented of overcoming the assumption of the existence of a countable transitive model. The thesis also studies forcing as a method giving rise to interpretations between theories. A notion of bi-interpretability is defined and a method of forcing over a non-standard model of ZFC is developed in order to argue that ZFC and ZF are not bi-interpretable. 1

Hiponimia ni uhusiano wa kifahiwa unaodhihirika baina ya leksimu ya jumla (hipanimu) na mahususi (hiponimu). Kama vile hipanimu mzazi hujumuisha hiponimu baba na mama. Uhusiano huu wa kihiponimia ulidhukuriwa na wanaisimu wa awali kuwa unahusisha leksimu nomino pekee. Hata hivyo, tafiti za hivi punde zinadhihirisha kuwa hiponimia huweza kudhihirika pia miongoni mwa kategoria za vivumishi, vielezi na vitenzi. Ingawa kuna midhihiriko ya hiponimia za vitenzi vya Kiswahili, wataalamu kadha wameelekea kushughulikia hiponimia za nomino na kutotilia maanani vitenzi. Hivyo basi, makala hii imechanganua uhusiano wa kihiponimia unaodhihirika miongoni mwa vitenzi teule vya Kiswahili. Katika kushughulikia suala hili, hipanimu vitenzi 24 kutoka kamusi za Kiswahili zimeteuli¬wa kimakusudi na hiponimu husika kutolewa. Nadharia ya Uchanganuzi Vijenzi kwa mujibu wa Katz na Fodor imezingatiwa katika uchanganuzi wa hiponimia hizi. Katika nadharia hii, sifa bainifu za hiponimu husika huonyeshwa kwa kutumia alama maalum za [+, -]. Data kuhusu hiponimia za vitenzi ilipekuliwa kutoka kamusi za Kiswahili kwa kuzingatia mwelekeo wa kiishara au kisintaksia kwa mujibu wa Hearst, na Snow na wenzake ili kuweza kutambua hipanimu na hiponimu husika katika sentensi. Hiponimia hizi zimechanganuliwa na kuwasilishwa kwa mtindo wa nadharia ya seti. / Hyponymy is a sense relation existing between general lexemes (hypernym) and the specific ones (hyponym). For instance, a hypernym parent includes hyponyms like father and mother. The hyponymy relation was regarded by earlier linguists that it could exist only amongst nouns. However, recent studies indicate that hyponymy can also be manifested in other categories such as adjectives, adverbs and verbs. Though there is hyponymy relation existing amongst Kiswahili verbs, various scho¬lars have tended to focus on nominal hyponymy and disregard verbal hyponymy. Therefore, this article has analyzed the hyponymy relation existing amongst selected Kiswahili verbs. In this regard, 24 verbal hypernyms from Kiswahili dictionaries were purposively sampled and their specific hyponyms indicated. Componential Analysis theory by Katz and Fodor has been used in the analysis of these hyponyms. The theory focuses on distinctive features of specific hyponyms that are normally shown by the use of specific signs [+, -]. The data on verbal hyponymy was observed from the Kiswahili dictionaries by the application of symbolic or syntactic approach propounded by Hearst, and Snow et al in order to identify the hypernyms and specific hyponyms in a sentence. These hyponymy relations are analyzed and presented using the set theory style.

Esta tese busca, de início, pesquisar comparativamente, com a abrangência possível, os métodos e processos pelos quais as empresas componentes do setor siderúrgico nacional avaliam - sob o ponto de vista da viabililidade - a tomada de suas decisões relativamente a seus peculiares e vultosos investimentos em equipamentos de tecnologia avançada de manufatura. Revisita primária e metodologicamente amplo repertório de métodos de avaliação consagrados pela prática e pela literatura, tendo como cenário o setor em referência representado pelas várias modalidades industriais que o suportam. A pesquisa é realizada com base no estudo de múltiplos casos realizados em grandes empresas siderúrgicas, a partir de visitas a suas instalações e entrevistas com seus especialistas de análise de viabilidade de projetos de investimento. Ao final, oferece modelo de avaliação a ser adotado complementarmente aos critérios utilizados pelo setor em referência, a partir das observações e discussões efetuadas em campo. / This thesis initially seeks to search, in a comparative basis and with the permissible largeness, the methods and procedures through which the companies comprising the national siderurgic sector appraise their decisions referring to their peculiar and huge investments in AMT equipments, under a feasibility point of view. A primary review is made, in a comparative way, of a large well known evaluation methods repertoire, in a background at which act the various concerned industrial modalities. The search is accomplished based on the study of multiple cases realized at big siderurgic companies, by visiting their installations and by interviewing their specialists in investment feasibility project analysis. Eventually offers an evaluation model to be adopted by this sector, based upon the observation and discussions made in the related field research.

A seleção de fornecedores tem impacto significante no custo e na qualidade de produtos manufaturados. Por isso, a seleção de fornecedores passou a ser vista como uma atividade bastante crítica para o desempenho da empresa compradora. Muitos estudos da literatura propõem o uso dos métodos multicritério fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) e fuzzy AHP (Analytic Hierarchy Process) para apoiar a seleção de fornecedores. Contudo, não são encontrados estudos que avaliem o desempenho destes métodos quando usados neste domínio de problema. Diante desta lacuna, este estudo compara os métodos fuzzy TOPSIS (CHEN, 2000) e fuzzy AHP (CHANG, 1996) no apoio à seleção de fornecedores. Esta pesquisa utiliza uma abordagem quantitativa descritiva empírica, baseada em modelagem e simulação. Os métodos fuzzy TOPSIS e fuzzy AHP foram aplicados em um caso ilustrativo de seleção de fornecedores. O desempenho dos fornecedores e o peso dos critérios foram avaliados por um especialista de uma empresa. Modelos de simulação foram implementados usando MATLAB® e aplicados na seleção de fornecedores de uma empresa de uma cadeia de suprimentos automotiva. Cinco fornecedores foram avaliados em relação à qualidade, custo, entrega, perfil e relacionamento. O peso dos critérios e o desempenho dos fornecedores foi avaliado por meio da opinião de um especialista da empresa. Posteriormente, os métodos fuzzy TOPSIS e fuzzy AHP foram comparados em relação à capacidade de apoiar a decisão em grupo, qualificação de fornecedores, escolha final de fornecedores, situações de compra e modelagem de decisões sob incerteza. A eficiência dos métodos em relação à complexidade computacional e à interação requerida com o usuário também foi comparada. Os resultados mostraram que o fuzzy TOPSIS é mais flexível e mais adequado que o fuzzy AHP para modelar diferentes tipos de cenários de seleção de fornecedores. A realização desta discussão é sugerida por Ertugrul e Karakasoglu (2008), e é relevante para ajudar pesquisadores e gestores na escolha de abordagens efetivas para lidar com diferentes cenários de seleção de fornecedores. / Supplier selection has a significant influence on the cost, quality and delivery of products of the buying company. Therefore, supplier selection has become a very critical activity to the performance of the buying company. Several studies presented in the literature propose the use of fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) and fuzzy AHP (Analytic Hierarchy Process) to aid the decision process of supplier selection. However, there are no comparative studies of these two methods when applied to the problem of supplier selection. Thus, this paper presents a comparative analysis of the methods fuzzy TOPSIS (Chen, 2000) and fuzzy AHP (Chang, 1996) applied to the problem of supplier selection. A descriptive quantitative approach was adopted as the research method. Algorithms of the methods fuzzy TOPSIS and fuzzy AHP were developed in Matlab© and applied to the selection of suppliers of a company in the automotive production chain. Five suppliers were evaluated regarding quality of conformance, cost, delivery, profile and relationship. The weight of the criteria and the performance of the suppliers were evaluated by specialist opinion from the studied company. The methods Fuzzy TOPSIS e Fuzzy AHP were compared in terms of ability to support the group decision, supplier qualification, final choice of suppliers, buying situations and modeling decisions under uncertainty. The efficiency of the methods with respect to computational complexity and the required user interaction was also compared. The comparative analysis shows that Fuzzy TOPSIS presents better than Fuzzy AHP performance, especially in scenarios in wich many alternatives are evaluated. Thus, Fuzzy TOPSIS is more flexible and appropriate than Fuzzy AHP to deal with supplier selection problem. This paper presents a new study, comparing the methods Fuzzy TOPSIS and Fuzzy AHP. As commented by Ertugrul and Karakasoglu (2008), a study such as this can contribute to the advance of knowledge, helping researchers and practitioners choosing more effective approaches to supplier selection.

A seleção de fornecedores tem impacto significante no custo e na qualidade de produtos manufaturados. Por isso, a seleção de fornecedores passou a ser vista como uma atividade bastante crítica para o desempenho da empresa compradora. Muitos estudos da literatura propõem o uso dos métodos multicritério fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) e fuzzy AHP (Analytic Hierarchy Process) para apoiar a seleção de fornecedores. Contudo, não são encontrados estudos que avaliem o desempenho destes métodos quando usados neste domínio de problema. Diante desta lacuna, este estudo compara os métodos fuzzy TOPSIS (CHEN, 2000) e fuzzy AHP (CHANG, 1996) no apoio à seleção de fornecedores. Esta pesquisa utiliza uma abordagem quantitativa descritiva empírica, baseada em modelagem e simulação. Os métodos fuzzy TOPSIS e fuzzy AHP foram aplicados em um caso ilustrativo de seleção de fornecedores. O desempenho dos fornecedores e o peso dos critérios foram avaliados por um especialista de uma empresa. Modelos de simulação foram implementados usando MATLAB® e aplicados na seleção de fornecedores de uma empresa de uma cadeia de suprimentos automotiva. Cinco fornecedores foram avaliados em relação à qualidade, custo, entrega, perfil e relacionamento. O peso dos critérios e o desempenho dos fornecedores foi avaliado por meio da opinião de um especialista da empresa. Posteriormente, os métodos fuzzy TOPSIS e fuzzy AHP foram comparados em relação à capacidade de apoiar a decisão em grupo, qualificação de fornecedores, escolha final de fornecedores, situações de compra e modelagem de decisões sob incerteza. A eficiência dos métodos em relação à complexidade computacional e à interação requerida com o usuário também foi comparada. Os resultados mostraram que o fuzzy TOPSIS é mais flexível e mais adequado que o fuzzy AHP para modelar diferentes tipos de cenários de seleção de fornecedores. A realização desta discussão é sugerida por Ertugrul e Karakasoglu (2008), e é relevante para ajudar pesquisadores e gestores na escolha de abordagens efetivas para lidar com diferentes cenários de seleção de fornecedores. / Supplier selection has a significant influence on the cost, quality and delivery of products of the buying company. Therefore, supplier selection has become a very critical activity to the performance of the buying company. Several studies presented in the literature propose the use of fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) and fuzzy AHP (Analytic Hierarchy Process) to aid the decision process of supplier selection. However, there are no comparative studies of these two methods when applied to the problem of supplier selection. Thus, this paper presents a comparative analysis of the methods fuzzy TOPSIS (Chen, 2000) and fuzzy AHP (Chang, 1996) applied to the problem of supplier selection. A descriptive quantitative approach was adopted as the research method. Algorithms of the methods fuzzy TOPSIS and fuzzy AHP were developed in Matlab© and applied to the selection of suppliers of a company in the automotive production chain. Five suppliers were evaluated regarding quality of conformance, cost, delivery, profile and relationship. The weight of the criteria and the performance of the suppliers were evaluated by specialist opinion from the studied company. The methods Fuzzy TOPSIS e Fuzzy AHP were compared in terms of ability to support the group decision, supplier qualification, final choice of suppliers, buying situations and modeling decisions under uncertainty. The efficiency of the methods with respect to computational complexity and the required user interaction was also compared. The comparative analysis shows that Fuzzy TOPSIS presents better than Fuzzy AHP performance, especially in scenarios in wich many alternatives are evaluated. Thus, Fuzzy TOPSIS is more flexible and appropriate than Fuzzy AHP to deal with supplier selection problem. This paper presents a new study, comparing the methods Fuzzy TOPSIS and Fuzzy AHP. As commented by Ertugrul and Karakasoglu (2008), a study such as this can contribute to the advance of knowledge, helping researchers and practitioners choosing more effective approaches to supplier selection.

Atualmente, o ambiente industrial é caracterizado pela intensa globalização, competição entre cadeias de suprimentos, manutenção das competências centrais e terceirização dos demais serviços. Desta forma, a gestão das relações entre os agentes independentes da cadeia de suprimentos e do processo de aquisição são fatores potenciais para o aumento da competitividade empresarial. No contexto da construção civil, a seleção adequada dos parceiros de negócios é um elemento fundamental para o sucesso dos projetos, uma vez que uma grande proporção das atividades podem ser sub-contratadas e possuem relação de precedência entre si. Os suprimentos representam um percentual significativo dos custos das construções, 60%, dado que demonstra o potencial de lucratividade passível de ser atingida ao estruturar o processo de seleção de fornecedores na construção civil. Seleções baseadas no preço prejudicam os sub-empreiteiros e fornecedores mais responsáveis na concorrência, contribuindo para a queda do nível de desempenho e redução da eficiência global do projeto, uma vez que as ineficiências são somadas ao longo da cadeia. Através da estruturação do processo de seleção de fornecedores, é possível mitigar os riscos de suprimentos oriundos de falhas destes contratados ao longo da relação. O objetivo deste trabalho foi desenvolver uma sistemática para seleção de fornecedores críticos, considerando diversos critérios além do preço, entre qualitativos e quantitativos. A abordagem visa também, a eliminação da subjetividade do processo e a extração do melhor fornecedor de forma objetiva. Para tanto, foram definidas dimensões competitivas para avaliar os fornecedores e posteriormente foram utilizados dois métodos quantitativos, Teoria dos Conjuntos Difusos (TCD) e Análise de Componentes Principais (ACP), para selecionar o melhor fornecedor dentre as alternativas, com base na avaliação de múltiplos agentes. / Currently, the industrial environment is characterized by intense globalization, competition between supply chains, maintenance of core competencies and outsourcing of other services. Thus, the management of relationships between independent agents of the supply chain and the procurement process are potential factors for increasing enterprise competitiveness. In the construction context, the proper selection of business partners is a key element for the success of projects, since a large proportion of the activities can be sub-contracted and have precedence relationship between them. Supplies represent a significant percentage of the cost of buildings, 60%, information that demonstrates the potential of profitability that can be achieved by structuring the process of supplier selection in the construction industry. Selection based on price take off from competition the sub-contractors and suppliers more responsible, contributing to the decline in the level of performance and reduction in the overall project efficiency, since inefficiencies are summed through the chain. By structuring the supplier selection process, it is possible to mitigate the supply risk arising from failures of these suppliers during the relationship. The objective of this study was to develop a systematic for selection of critical suppliers, considering several criteria other than price, among qualitative and quantitative. The approach also aims at eliminating the subjectivity of the process and the extraction of the best supplier in an objective way. In order to that, competitive dimensions were set to evaluate vendors and subsequently two quantitative methods, Fuzzy Sets Theory (FST) and Principal Component Analysis (PCA) were used to select the best supplier among the alternatives based on multiple agents evaluation.

Dans la tradition occidentale, mathématiques et musique ont été étroitement liées depuis plus de 2000 ans. Nonobstant cette longue histoire concernant les relations entre mathématiques et musique, l'intérêt professionnel des mathématiciens dans ce domaine est un phénomène assez récent. Alors que la puissance d'application des mathématiques dans la description de la musique a été reconnue depuis longtemps, c'est seulement grâce a des développements plus récents que la musique commence à occuper également une place stratégique au sein des mathématiques. Ce fait est confirmé par l'émergence d'un nombre croissant de problèmes «~mathémusicaux~». Ces problèmes sont caractérisés par le fait qu'en positionnant un problème à l'origine musical dans un contexte mathématique approprié non seulement on obtient des résultats mathématiques nouveaux mais cela ouvre la voie également à des constructions musicales nouvelles. C'est ce double mouvement, de la musique aux mathématiques et vice-versa, qui suscite l'intérêt de plus en plus de chercheurs dans les deux domaines et qui est au c\oe ur d'une croissante activité de recherche internationale accompagnée de la création de revues internationales à comité de lecture et collections d'ouvrages consacrés à la matière ainsi que d'une prolifération de conférences, séminaires d'études et projets collaboratifs dans le domaine. Dans la première partie de ce mémoire, nous présentons tout d'abord une sélection de problèmes «~mathémusicaux~» sur lesquels nous avons travaillé en montrant les résultats obtenus et les questions qui restent ouvertes. Dans la deuxième partie, nous détaillons trois types d'interactions entre recherche mathémusicale et trois autre disciplines, à savoir les sciences cognitives, l'informatique et la philosophie.

<p>This thesis presents the implementation of a knowledge base system for rough sets [Paw92]within the logic programming framework. The combination of rough set theory with logic programming is a novel approach. The presented implementation serves as a prototype system for the ideas presented in [VDM03a, VDM03b]. The system is available at "http://www.ida.liu.se/rkbs". </p><p>The presented language for describing knowledge in the rough knowledge base caters for implicit definition of rough sets by combining different regions (e.g. upper approximation, lower approximation, boundary) of other defined rough sets. The rough knowledge base system also provides methods for querying the knowledge base and methods for computing quantitative measures. </p><p>We test the implemented system on a medium sized application example to illustrate the usefulness of the system and the incorporated language. We also provide performance measurements of the system.</p>

<p>he focus of this research is to establish whether there is a difference in the way the genders perceive the visualization of mathematics, with specific reference to set theory. The influence of the computing experience of students on their perceptions was also investigated. Interfaces were created for the teaching of set theory for learners in the first class of secondary school. Since the mother tongue of most the pupils is Dari the interface was made available in both Dari and English. The interfaces were used to gather the data for the researc</p>

The compositional technique of cross partitioning is one of Luigi Dallapiccola's most used twelve-tone devices. Through a detailed analysis of three contrapuntal canonic movements from Dallapiccola's Quaderno Musicale di Annalibera, I examine his use of cross partitioning as a motivic tool and as a referential collection. The development of the BACH motive and the derivation of tone-row statements reflects on Dallapiccola's extensive use of cross partitioning and his compositional principles used to achieve a sense of polarity. Upon a preliminary analysis based on set-theory analysis set out by Joseph Straus I draw an interpretive analysis through Alegant's cross partitioning model as well as develop my own set of parameters for interpretation in regards to polarity which is based on intervallic stability.