Cette thèse est consacrée à l'étude des systèmes d'équations<br />différentielles non linéaires aux dérivées partielles. L'approche choisie est celle de l'algèbre différentielle. Étant donné un système d'équations différentielles, nous cherchons à obtenir des renseignements sur ses solutions. Pour ce faire, nous calculons une famille d'ensembles particuliers (appelés chaînes différentielles régulières) dont la réunion des solutions coïncide avec les solutions du système initial.<br /> <br />Les nouveaux résultats relèvent principalement du calcul formel. Le chapitre 2 clarifie le lien entre les chaînes régulières et les chaînes différentielles régulières. Deux nouveaux algorithmes (chapitres 4 et 5) viennent optimiser les algorithmes existants permettant de calculer ces chaînes différentielles régulières. Ces deux algorithmes intègrent des techniques purement algébriques qui permettent de mieux contrôler le grossissement des données et de supprimer des calculs inutiles. Des problèmes jusqu'à présent non résolus ont ainsi pu être traités. Un algorithme de calcul de forme normale d'un polynôme différentiel modulo une chaîne différentielle régulière est exposé dans le chapitre 2.<br /> <br />Les derniers résultats relèvent de l'analyse. Les solutions que nous considérons sont des séries formelles. Le chapitre 3 fournit des conditions suffisantes pour qu'une solution formelle soit analytique. Ce même chapitre présente un contre-exemple à une conjecture portant sur l'analycité des solutions formelles.

This analysis employs the sociolinguistic framework of status and solidarity (Holmes, 2001) to examine the use of codeswitching on the relational development between the characters in three plays by Cuban-American playwright Dolores Prida. The three plays discussed are Beautiful Señoritas (1978), Coser y cantar (1981) and Botánica (1991). Linguistic scholars recognize the lack of linguistic analysis of literary texts; specifically, codeswitching at present is not fully explored as a linguistic phenomenon in written contexts. Furthermore, Prida's works have never before been appraised using linguistic methodology. Hence, this work aims to add to scholarly research in the fields of codeswitching, discourse analysis, and literary linguistics, using the status and solidarity framework to examine the codeswitching in Dolores Prida's plays. Dolores Prida is a feminist and Hispanic dramatist whose central theme is the search for identity of Hispanic immigrants, specifically women, in the United States today. Due to her ideological stance, it is expected that a strong emphasis on solidarity rather than status and the use of affective rather than referential speech functions are present in the relationships in her plays. Accordingly, the analysis of Botánica reveals that indeed codeswitching between the characters does affect their relational development in maintaining solidarity and intimacy. However, the relationships found in Beautiful Señoritas and Coser y cantar do not offer such conclusions, due to the variable nature of the relationships identified. Further analysis of these and other literary works will more accurately determine benefits of the status and solidarity framework as applied to the codeswitching research.

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This analysis employs the sociolinguistic framework of status and solidarity (Holmes, 2001) to examine the use of codeswitching on the relational development between the characters in three plays by Cuban-American playwright Dolores Prida. The three plays discussed are Beautiful Señoritas (1978), Coser y cantar (1981) and Botánica (1991). Linguistic scholars recognize the lack of linguistic analysis of literary texts; specifically, codeswitching at present is not fully explored as a linguistic phenomenon in written contexts. Furthermore, Prida's works have never before been appraised using linguistic methodology. Hence, this work aims to add to scholarly research in the fields of codeswitching, discourse analysis, and literary linguistics, using the status and solidarity framework to examine the codeswitching in Dolores Prida's plays. Dolores Prida is a feminist and Hispanic dramatist whose central theme is the search for identity of Hispanic immigrants, specifically women, in the United States today. Due to her ideological stance, it is expected that a strong emphasis on solidarity rather than status and the use of affective rather than referential speech functions are present in the relationships in her plays. Accordingly, the analysis of Botánica reveals that indeed codeswitching between the characters does affect their relational development in maintaining solidarity and intimacy. However, the relationships found in Beautiful Señoritas and Coser y cantar do not offer such conclusions, due to the variable nature of the relationships identified. Further analysis of these and other literary works will more accurately determine benefits of the status and solidarity framework as applied to the codeswitching research.

This study examines the concepts of art, politics and art institution departing from three cases of exhibition situations at Moderna Museet in Stockholm, 1998–2008. The cases are considered in relation to different aspects of the museum’s identity as an art institution. The first case, the Pontus Hultén Study Gallery (2008–), is an interactive exhibition space containing 34 mechanical screens for displaying art. It is understood here as a comment on the museum’s identity as a collecting institution. The author critically analyses a number of common oppositions in avant-garde theory regarding museum culture, such as the museum as a place for passivity rather than activity, preservation rather than initiation, and ultimately death rather than life. The second case, the exhibition series Moderna Museet Projekt (1998–2001), was marked by the ambition to integrate artworks into contexts outside the physical museum building. Here case analyses focus on the distinction that the series established between art and a presumed alternative, such as life, reality, or politics. The third and last case, the sound installation Forty-Part Motet (2001) by Janet Cardiff, was installed in an exhibition space that actualised the ideals of the so-called white cube. In the institutional critique of the 1960s and 1970s, this exhibition space was dismissed as isolated and detached from society, an idea that is critically examined. Throughout the different case studies, spectator positions and potential agency are of particular concern. This thesis concludes that the concepts of art and politics are different permeable forms of experiences, visibilities and practices, that cross and intertwine. This conclusion is informed by Jacques Rancière’s notions of aesthetics and politics. In this reading, the art institution is not a barrier separating art from politics, reality or life, but nor is it a dead or deadening space. Rather, the art institution, as a social space and concept of art, is considered as intertwined with other forms of visibilities and experiences. Thus, regarded as a frame for a certain type of visibility, the art institution is capable of establishing a difference that is both unproblematic and urgent.

Max Reger was a prolific composer on the threshold of modernism. The style of his extensive musical output was polarizing among his contemporaries. A criticism of Reger's music is its complex and dense musical structure. Despite writing tonal music, Reger often pushes the boundaries of tonality so far that all sense of formal organization is seemingly imperceptible. In this dissertation, I offer what I observed to be a new way of discerning Reger's motivic relationships and formal structures within and between movements. There are three primary tools and methods I incorporated to make these observations: Schoenberg's developing variation; melodic contour analysis as discussed by Elizabeth West-Marvin and Diana Deutsch; and Janet Schmalfeldt's motivic cyclicism stemming from internal themes. In this dissertation I examine five different musical works by Reger: D minor Piano Quartet, Clarinet Quintet, Piano Concerto, String Quartet, op. 121 and E minor Piano Trio, op. 102. My analysis shows how Reger relies on melodic contours of his motives to connect musical moments across entire movements and entire works with multiple movements. These motives are developed and often mark structurally significant moments providing the organization often perceived as missing in Reger's music.

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