In this thesis we shall examine the role of measurability in the theory of Lebesgue Integration. This shall be done in the context of the real line where we define the notion of an integral of a bouuded real-valued function over a set of bounded outer measure without a prior assumption of measurability concerning the function and the domain of integration

The main contribution of this thesis, is to define similarity measures between two images with the main focus on content-based image retrieval (CBIR). Each image is considered as a set of visual elements that can be described with a set of visual descriptions (features). The similarity between images is then defined as the nearness between sets of elements based on a tolerance and a fuzzy tolerance relation. A tolerance relation is used to describe the approximate nature of the visual perception. A fuzzy tolerance relation is adopted to eliminate the need for a sharp threshold and hence model the gradual changes in perception of similarities. Three real valued similarity measures as well as a fuzzy valued similarity measure are proposed. All of the methods are then used in two CBIR experiments and the results are compared with classical measures of distance (namely, Kantorovich, Hausdorff and Mahalanobis). The results are compared with other published research papers. An important advantage of the proposed methods is shown to be their effectiveness in an unsupervised setting with no prior information. Eighteen different features (based on color, texture and edge) are used in all the experiments. A feature selection algorithm is also used to train the system in choosing a suboptimal set of visual features.

Thesis (MA)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: In this thesis I will look at the way in which power relationships are presented in Shakespeare's dramas, with specific reference to the so-called ''Henriad'', Measure for Measure and The Tempest. Each play consists of a network of power relationships in which different forms of power interact on different levels. Different characters in the above-mentioned plays have access to different forms of power according to their position within these networks. The way in which the characters interact could also cause or be influenced by shifts and changes in the networks of power relationships that occur in the course of the action. I will use Michel Foucault's theories on the relationship between power, knowledge and discourse as a guide to my analysis of Measure for Measure. I will also use selected aspects of Mikhail Bakhtin's theories on language and literature, with specific references to the concepts of "dialogism" and "heteroglossia" or "manyvoicedness", as well as his concept of carnival, which implies a temporary inversion in power relationships in an unofficial festive context, as a guide to my analysis of the Henriad. I will use a combination of the theories of Foucault and Bakhtin in my analysis of The Tempest. I have chosen the terms "discourse" and "dialogue" as key terms in the title of this thesis not only because they play an important role in the theories of Foucault and Bakhtin respectively, but also because they play an important role in the analysis and representation of power relationships. According to Robert Young, Foucault relates ''the organisation of discourse ...to the exercise of power" (10). One could also say that the power relationships in a society are reflected in the portrayal of a dialogue between different voices representing different sections of or classes in that society as in Bakhtin's principles of dialogism. I will explain the overall importance of these terms in more detail in the Introduction and the other relevant chapters. In the introductory chapter I will first provide a theoretical background for the thesis as a whole. Then I will look at the specific theoretical principles that are relevant to each chapter. In the chapter on the Henriad I will look at the way in which an alternative perspective on power relations and the role of the king are created by looking at them from the perspective of Bakhtin's concept of carnival. In the next chapter, I will show how Measure for Measure presents us with an evaluation of different strategies of power, which I will look at from the perspective of Foucault's theories on power, knowledge and discourse. In my chapter on The Tempest I will combine aspects of both theories in my analysis of a play that presents us with a complex analysis of power relationships as a social phenomenon. In the concluding chapter I will look at the different perspectives on power relationships that emerged from my previous chapters and attempt to see what its implications are for the representation of power relationships in Shakespeare's work and perhaps as a social phenomenon. / AFRIKAANSE OPSOMMING: In hierdie tesis gaan ek kyk na die wyse waarop magsverhoudinge uit gebeeld word in Shakespeare se dramas, met spesifieke verwysing na die sogenaamde "Henriad", Measure for Measure en The Tempest. Elke drama bestaan uit 'n netwerk van magsverhoudinge waarin verskillende vorme van mag op verskillende vlakke wisselwerking uitoefen. Verskillende karakters in bogenoemde dramas het toegang tot verskillende vorme van mag volgens hul posisie in die netwerke. Die manier waarop die wisselwerking tussen die verskillende karakters plaasvind kan ook verskuiwings en veranderinge in die netwerk van magsverhoudinge in die loop van die aksie veroorsaak, of daar deur beïnvloedword. Ek gaan Michel Foucault se teorieë oor die verhouding tussen mag, kennis en diskoers as 'n gids tot my analise van Measure for Measure gebruik. Ek gaan ook uitgesoekte aspekte van Mikhail Bakhtin se teorieë oor taal en literatuur, met spesifieke verwysing na die konsepte van "dialogisme" en "heteroglossia" of "meerstemmigheid", sowel as sy konsep van karnaval, wat 'n tydelike ommekeer in magsverhoudinge in 'n onoffisiële feestelike konteks impliseer, as 'n gids tot my analise van die Henriad gebruik. Ek sal 'n kombinasie van die teorieë van Foucault en Bakhtin gebruik in my analise van The Tempest. Ek het die terme "discourse" en "dialogue" as sleutel terme in die titel van hierdie tesis gebruik, nie net omdat hulle 'n belangrike rol in die teorieë van Foucault en Bakhtin onderskeidelik speel nie, maar ook omdat hulle 'n belangrike rol in die analise en uitbeelding van magsverhoudinge speel. Volgens Robert Young verbind Foucault die manier waarop diskoers georganiseer word met die uitoefening van mag (10). Mens kan ook sê dat die magsverhoudinge in 'n gemeenskap gereflekteer word in die uitbeelding van 'n dialoog tussen verskillende stemme wat verskillende dele van of klasse in die gemeenskap verteenwoordig soos in Bakhtin se beginsel van dialogisme. Ek sal die algehele belang van hierdie terme in meer besonderhede bespreek in die inleidingen die ander relevante hoofstukke verduidelik. In die inleidende hoofstuk gaan ek eers 'n teoretiese agtergrond vir die tesis as geheel verskaf Dan sal ek kyk na die spesifieke teoretiese beginsels wat relevant is tot elke hoofstuk. In die hoofstuk oor die Henriad gaan ek kyk hoe 'n alternatiewe perspektief op magsverhoudinge en die rol van die koning geskep word deur hulle te beskou van uit die perspektief van Bakhtin se konsep van karnaval. In die volgende hoofstuk sal ek kyk hoe Measure for Measure 'n evaluasie van verskillende magsstrategieë aan ons voorlê, waarna ek gaan kyk van uit die perspektief van Foucault se teorieë oor mag, kennis en diskoers. In my hoofstuk oor The Tempest gaan ek aspekte van albei die teorieë kombineer in 'n drama wat 'n komplekse analise van magsverhoudinge as 'n sosiale verskynsel aan ons voorln sosiale verskynsel aan ons voorlê. In die laaste hoofstuk gaan ek kyk na die verskillende perspektiewe op magsverhoudinge wat voortspruit uit die voorafgaande hoofstukke en kyk wat die implikasie daarvan vir die uitbeelding van magsverhoudinge in Shakespeare se werk en as 'n sosiale verskynsel is.

Neste trabalho, fazemos um estudo das correntes e das medidas transversas invariantes por holonomia, e mostraremos o resultado de D. Sullivan [23] sobre a correspondência biunívoca entre estes dois objetos. Em particular mostraremos um resultado conhecido de J. Plante [17] sobre a existência de medidas transversas invariantes sob a hipótese de crescimento sub-exponencial. Apresentamos também, o resultado devido a Ruelle-Sullivan [19] de que a medida de máxima entropia de um difeomorfismo topologicamente mixing pode-se expressar como o produto de duas medidas transversas invariantes para as folheações estáveis e instáveis. Por último, mostramos que os difeomorfismos de Anosov topologicamente mixing, que preservam a orientação das folhas estáveis e folhas instáveis induzem elementos da cohomologia de DeRham / In this work, we make a study of currents and holonomy invariant transverse measure, and we will show the result of D. Sullivan [23] about the biunivocal correspondence between these two objects. In particular we show a known result of J. Plante [17] about the existence of invariant transverse measures under the hypothesis of sub-exponential growth. Also we will present, the result due to Ruelle-Sullivan [19] that the maximum entropy measure of a diffeomorphism topologically mixing can be expressed as the product of two invariant transverse measures for stable and unstable foliations. Finally, we show that the Anosov diffeomorphisms topologically mixing, which preserve the orientation of the leaves stable and unstable induce elements DeRham cohomology

This thesis is broadly divided in two parts. In the first part we give a survey of various distances between metric spaces, namely the uniform distance, Lipschitz distance, Hausdor distance and the Gramoz Hausdor distance. Here we talk about only the most basic of their properties and give a few illustrative examples. As we wish to study collections of metric measure spaces, which are triples (X; d; m) consisting of a complete separable metric space (X; d) and a Boral probability measure m on X, there are discussions about some distances between them. Among the three that we discuss, the transportation and distortion distances were introduced by Sturm. The later, denoted by 2, on the space X2 of all metric measure spaces having finite L2-size is the focus of the second part of this thesis. The second part is an exposition based on the work done by Sturm. Here we prove a number of results on the analytic and geometric properties of (X2; 2). Beginning by noting that (X2; 2) is a non-complete space, we try to understand its completion. Towards this end, the notion of a gauged measure space is useful. These are triples (X; f; m) where X is a Polish space, m a Boral probability measure on X and f a function, also called a gauge, on X X that is symmetric and square integral with respect to the product measure m2. We show that, Theorem 1. The completion of (X2; 2) consists of all gauged measure spaces where the gauges satisfy triangle inequality almost everywhere. We denote the space of all gauged measure spaces by Y. The space X2 can be embedded in Y and the transportation distance 2 extends easily from X2 to Y. These two spaces turn out to have similar geometric properties. On both these spaces 2 is a strictly intrinsic metric; i.e. any two members in them can be joined by a shortest path. But more importantly, using a description of the geodesics in these spaces, the following result is proved. Theorem 2. Both (X2; 2) and (Y; 2) have non-negative curvature in the sense of Alexandrov.

La notion de première impression est fréquemment utilisée dans la socio-psychologie mais elle n'a pas été fortement exploitée dans le marketing. Même si cette notion apparait souvent dans le monde du commerce, il n’est pas toujours facile de la mesurer. La comparaison de deux méthodes de mesure nous permet d’affirmer d’une part, que sur un nouveau produit, la première impression est formée dans les 10 premières secondes, et d’autre part, qu’elle apporte sur ce produit une perception minimale. Le processus d’expérimentation a été réalisé sur de nouvelles voitures en voie de commercialisation au Vietnam. Les résultats obtenus sont convergents et cette thèse montre bien les intérêts mais aussi les limites de concept psychologique. / The concept of first impression is frequently used in social psychology, but it hasn’t been forcefully exploited in Marketing. Even though this notion appears daily in the business world, it is not always easily measured. The comparison of two methods allows us to affirm that the first impression of the new products is formed during the first 10 seconds and then, it provides us minimal perception of product. The process of the experiment was seriously carried out among new cars being commercialized in Vietnam. The results are convergent and this thesis shows not only the interests but also the limits of this psychological concept. / Khái niệm về ấn tượng ban đầu thường xuyên được sử dụng trong tâm sinh lý xã hội nhưng vẫn chưa thật sự được khai thác mạnh mẽ trong Marketing. Ngay cả khi ấn tượng ban đầu xuất hiện hàng ngày trong thế giới thương mại, nhưng thật không dễ để đo lường được nó. Một sự so sánh về hai phương pháp đo lường cho phép chúng ta khẳng định rằng ấn tượng ban đầu về sản phẩm mới được hình thành ngay từ 10 giây đầu tiên và đã mang đến cho chúng ta một nhận thức tối thiểu về sản phẩm. Việc xây dựng tiến trình thực nghiệm đã được thực hiện một cách nghiêm túc trên những chiếc xe ô tô mới đang trên đường được thương mại hóa tại Việt Nam. Những kết quả đạt được là hội tụ và cuốn luận án cũng đã chỉ rõ những lợi ích cũng như giới hạn từ khái niệm tâm sinh lý này.

Poststructuralism may be broadly characterized as a move away from traditional Western foundationalist thinking. Such thinking is exemplified by post-enlightenment transcendentalism, humanism and subject-centredness. This study aims to contribute to the poststructuralist decentering of the subject by means of the application of the critical practice of deconstruction – a type of analysis named and popularized by Jacques Derrida, who is himself frequently classified as a poststructuralist, in which the ruling logic of the text is undermined and the meaning of the text is therefore shown not to be fully present within it – to four texts by a writer who is arguably among the most prominent within the English literary canon: William Shakespeare. The first deconstructive reading centres around the court scene at the climax of the bond story in The Merchant of Venice. Here the apparent contrast between the restrictive law – which views Shylock’s claim of a pound of Antonio’s flesh as valid – and justice and mercy – which regard adherence to this bond as contrary to the spirit of the law – is collapsed, and justice is shown to be capable of being as restrictive as the law, while mercy becomes embroiled in all the trading that occurs in The Merchant of Venice, and demonstrates the capacity to be mercenary. The Tempest is examined next: the starting point is the apparent Nature/Culture distinction within the play. The reading is influenced by Derrida’s use of the notion of supplementarity in his examination in “… That Dangerous Supplement …” of the Nature/Culture distinction in Rousseau. Particular attention is given first to the wedding masque, where the central figure of Ceres, who is goddess of agriculture and marriage, and also the source of seasonal changes, is shown to problematize any absolute distinctions between Nature and Culture. Such distinctions are further collapsed with reference to Prospero and Miranda’s teaching of language to Caliban, as the latter, who supposedly is representative of natural man, is shown to have had his thought supplemented by language before Prospero’s arrival on the island. Hamlet is approached with a reading that again draws from Derrida – this time his exploration of Mallarmé’s “Mimique” in “The Double Session”. Plato’s theory of forms also becomes involved as this chapter plays with the distinction between Being and imitation, destabilizing this distinction within Hamlet and problematizing Hamlet’s question: “To be, or not to be”. And finally, the chapter on Measure for Measure is concerned with the ideas of restraint and freedom, inspecting Lucio’s suggestion that his restraint arises from “too much liberty”, as well as many other instances in the play where restraint, as well as freedom – which seems at times to function in the same way as restraint – seems significant. The reading draws attention to its own impulse to restrain the reader with the truisms it presents by being written in the form of thirty-four aphorisms, and thus alludes to Derrida’s “Aphorism Countertime”. / Dissertation (MA (English))--University of Pretoria, 2005. / Modern European Languages / unrestricted

Due to the social, political, and religious upheavals occurring across Europe in the Early Modern period, many writers were exploring the proper relationship between citizens and political and religious leaders. While some writers encouraged citizens to give unconditional loyalty to local and national leaders, Shakespeare has a pattern of endorsing citizen rebellion as a moral means to overthrow tyrannical rulers. By exploring Richard III, Measure for Measure, and Julius Caesar, I argue that Shakespeare is developing a taxonomy of citizen responses to a tyrannical leader and teaches citizens that a moral rebellion can be launched against a tyrant when a citizen embraces personal responsibility, accepts the power of rhetoric over violence, and overcomes the filtering effects of nostalgia. To demonstrate that Shakespeare is deliberately entering the conversation about a citizen's reaction to a tyrant, I provide information about how a tyrant is defined in the Early Modern period. I synthesize the scholarship on relevant texts in the period and explain how all three leaders in the aforementioned plays support that definition of tyranny. Then I focus on each play's surrounding characters to discuss the motivations and reactions of rebellious and obedient citizens. Finally, I conclude each section with an analysis of the repercussions of the citizen's actions and evaluate the lessons that Shakespeare is consistently promoting about moral rebellion.

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In this thesis we shall examine the role of measurerability in the theory of Lebesgue Integration. This shall be done in the context of the real line where we define the notion of an integral of a bounded real-valued function over a set of bounded outer measure without a prior assumption of measurability concerning the function and the domain of integration. / Mathematical Sciences / M. Sc. (Mathematics)