In this work we present a sistematic exposition of a result due to R. Maiíé and L. Rocha, who proved that the Julia set of a rational map of the Riemann sphere is uniíormly perfect. We start with necessary basic concepts and dose with a proof of a result of C. Pommerenke which allows us to condude the Dirichlet regularity of the Julia set.

Denna uppsats diskuterar Julia Kristevas begrepp det semiotiska i Pipilotti Rists audiovideoinstallation Tyngdkraft, var min vän, som visades på Magasin 3, Stockholm konsthall, 2007. Verket består av ett rum med upphöjda mattskulpturer där betraktaren kan ta av sig skorna och lägga sig ned för att ta del av två filmer som visas i taket ovanför matthögarna. Största delen av filmerna utspelar sig under vattenytan där en kvinna och en androgyn man utforskar ett universum fyllt av sinlighet, närvaro, lekfullhet, kropp, drifter och lugn -ett paradis fyllt av växtlighet och där tyngkraften ibland minskat. Bilder i starka färger och ljus, kaleidoskopiska formationer och ett till viss del uppbrutet bildspråk, möter åskådaren. Det semiotiska beskrivs av Kristeva som den driftsmässiga dimensionen av språket som är kopplat till ett förspråkligt stadium hos det preoidipala barnet innan det hunnit utvecklats till ett eget subjekt. Med detta menar hon den värld nära moderskroppen som barnet befinner sig i och där en icke-språklig kommunikation sker mellan mor och barn. Dock står denna värld inte helt utan lag och ordning eftersom modern (och barnet) alltid befinner sig under en viss språklig och kulturell lagbundenhet, kallad den symboliska ordningen, vilken kommer in även i det semiotiska. Det semiotiska och det symboliska är därför nära kopplade till varandra och kan inte existera utan varandra. Det semiotiska lever kvar även efter att det lilla barnet utvecklats till ett subjekt och trätt in i den språkliga, symboliska ordningen. Detta visar sig som semiotiska spår i bland annat konsten, och när det kommer till språket ser vi det främst i poesin, som är ett mindre lagbundet språk som rör sig i gränslandet mellan det semiotiska och det symboliska. Eftersom Tyngdkraft, var min vän inte innehåller något talat eller skrivet språk görs i uppsatsen en koppling mellan detta verk och det semiotiska genom utforskandet av olika element i verket. Dessa element är tyngdkraften, jorden, vattnet, bildspråket, upprepningen, rytmen, moderskroppen, paradiset, affekterna och drifterna samt gränslandet natur och kultur.

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Many real-world engineering problems require large amounts of data in order to accurately model and predict outcomes. However, this data is often noisy, sampled and discontinuous, making the data difficult to process and giving rise to incorrect models. In order to address this issue, different interpolation techniques are commonly used to make the data continuous. This can then followed by a filtering process in order to reduce noise and further reduce discontinuities. In this report, our approach to filtering is the use of convolution kernels, which smooths out the data. By doing so, a better visual representation of the limited data available can be obtained. For instance, in the specific case of studying streamlines and vortices, filtering techniques have been used to produce more realistic plots. While the use of filters can be beneficial, it is important to note that the choice of filter and its parameters can greatly impact the results obtained. In particular, we found that, for the filters we studied, applying these to analytical functions can actually increase the error. On the other hand, when filters are applied to discontinuous functions, they can improve the accuracy of the data. Overall, when analyzing stream functions with filters, significant improvements can be seen in the quality of the data. This underscores the importance of careful selection and application of filtering techniques in engineering problems that involve large amounts of noisy and discontinuous data.

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This dissertation explores literary-theoretical constructions arising from the consideration of certain non-narrative linguistic strategies and applies them to dance analysis. My intent is not only to provide new, functional tools for dance scholars and writers, but also to alter the theoretical terms themselves: by employing literary critical language beyond its original purpose, I hope to locate the limits of that language as it applies to dance. Moreover, I strive to identify the ways moving bodies complicate concepts normally applied to static and disembodied text. In this way my research moves in two directions: adding a specific theoretical lens to the dance-writing toolbox, and, in turn, using dance to sharpen and focus that lens. I have chosen two theoretical constructs--Julia Kristeva's explication of the semiotic aspect of language and her characterization of the abject--because of the ways they address the unsayable through body, repetition, and rhythm. Kristeva's texts, Desire in Language (1981) and Powers of Horror (1982), provide the dissertation's primary theoretical frameworks. The first text puts forth key concepts about heterogeneous meaning within her conceptualization of the semiotic; the second addresses meaning that exceeds language, and the self, and arises out of the abject (a crisis of the subject when confronted with a breakdown of boundaries between self and other). Both concepts are relevant to dance, emerging from the materiality/substance of language rather than from language as a phantom structure that ideas are placed into. This dissertation grapples with how dance strives to express that which exceeds "paraphrasable" meaning from three vantage points: 1) the assessment of the critical reception of historic choreography (Paul Taylor's Big Bertha) that plays simple narrative against the horror of the unknown; 2) an examination of participants' communications during the choreographic process of innovative choreographer, Gabrielle Lamb, and how research material was transformed during that process; 3) the documentation of my own struggle to express the unsayable during the creation of a hybrid dance/textual piece. These perspectives require different analytic strategies: 1) the casting of an artwork's meaning in historical and cultural contexts, 2) the parsing of the language used to communicate meaning between participants during the creative process, 3) the self-chronicling and reflective analysis of meaning-making during the conception and execution of a hybrid work. My objective is to show how Kristeva's theoretical constructs play out in different types of dance analysis and how the lack of a certain strain of theoretical language in dance discourse has left a hole where discussion might profitably ensue. I seek to use Kristeva's texts and post/modern techniques of the body to offer a multi-layered and technically invested understanding of dance rather than an aphoristic and imagistic one: one that substitutes multiple, specific bodies and their actions for a single idealized institution of the beautiful. / Dance

A Julia set for a complex function 𝑓 is the set of all points in the complex plane where the iterates of 𝑓 do not form a normal family. A picture of the Julia set for a function can be generated with a computer by coloring pixels (which we consider to be small squares) based on the behavior of the point at the center of each pixel. We consider the accuracy of computer generated pictures of Julia sets. Such a picture is said to be accurate if each colored pixel actually contains some point in the Julia set. We extend previous work to show that the pictures generated by an algorithm for the family λe² are accurate, for appropriate choices of parameters in the algorithm. We observe that the Julia set for meromorphic functions with polynomial Schwarzian derivative is the closure of those points which go to infinity under iteration, and use this as a basis for an algorithm to generate pictures for such functions. A pixel in our algorithm will be colored if the center point becomes larger than some specified bound upon iteration. We show that using our algorithm, the pictures of Julia sets generated for the family λtan(z) for positive real λ are also accurate. We conclude with a cautionary example of a Julia set whose picture will be inaccurate for some apparently reasonable choices of parameters, demonstrating that some care must be exercised in using such algorithms. In general, more information about the nature of the function may be needed. / Ph. D.

Made available in DSpace on 2016-03-15T19:45:56Z (GMT). No. of bitstreams: 1 Edmundo Gomes Junior.pdf: 1012907 bytes, checksum: d9fc3f62b706eeff0f0b3921bc082da9 (MD5) Previous issue date: 2013-12-12 / Universidade Presbiteriana Mackenzie / This essay aims to analyze the film Stranger Than Fiction (2006), directed by Marc Foster, following of the concept of intertextuality, created by Julia Kristeva. It presents a survey of the literary works mentioned in the film and their effects on film narrative, in order to discuss how intertextuality enables the production of meaning. For this analysis the origin of this concept is researched, confronting the dialogism of Mikhail Bakhtin with Kristeva's texts. Kristeva also developed the concepts of ambivalence and transposition, terms that are used later on by other authors. During the analysis it was possible to see through the intertexts in the film the Prometheus theme repeated in the nature of fictional creation, where creator face decay, the similarities between the representations of mentors in fiction in relation with the epic hero's journey, as the use of ecphrasis as an anticipation of the outcome of the story and the formation of the identity of the characters work through dialogue. / Este trabalho tem como objetivo analisar o filme Mais estranho que a ficção (2006), dirigido por Marc Foster, no viés do conceito de intertextualidade, criado por Julia Kristeva. É apresentada uma pesquisa sobre as obras literárias citadas na película e seus efeitos na narrativa fílmica, visando assim discutir de que modo a intertextualidade propicia a produção de sentido. Para essa análise foi levantada a origem desse conceito, confrontando o dialogismo de Mikhail Bakhtin com os textos de Kristeva. A autora elaborou, além da intertextualidade, os conceitos de ambivalência e transposição, termos que são empregados posteriormente por outros autores. Durante a análise foi possível notar, através dos intertextos presentes no filme, a natureza prometaica da criação ficcional, onde criadores enfrentam a decadência, as semelhanças entre as representações dos mestres na ficção em relação à jornada do herói épico, a utilização da écfrase como antecipação do desfecho da estória e a formação da identidade das personagens da obra através do diálogo.

We generalize the notions of structural stability and hyperbolicity for the family of (multivalued) complex maps Hc(z) = zr + c; where r > 1 is rational and zr = exp r log z: We discovered that Hc is structurally stable at every hyperbolic parameter satisfying the escaping condition. Surprisingly, there may be infinitely many attracting periodic points for Hc. The set of such points gives rise to the dual Julia set, which is a Cantor set coming from a Conformal Iterated Funcion System. Both the Julia set and its dual are projections of holomorphic motions of dynamical systems (single valued maps) defined on compact subsets of Banach spaces, denoted by Xc and Wc, respectively. For c close to zero: (1) we show that Jc is a union of quasiconformal arcs around the unit circle; (2) the set Xc is an holomorphic motion of the solenoid X0; (3) using the formalism of Gibbs states we exhibit an upper bound for the Hausdorff dimension of Jc; which implies that Jc has zero Lebesgue measure. / Generalizamos as noções de estabilidade estrutural e hiperbolicidade para a família de correspondências holomorfas Hc(z) = zr + c; onde r > 1 é racional e zr = exp r log z: Descobrimos que Hc é estruturalmente estável em todos os parâmetros hiperbólicos satisfazendo a condição de fuga. Tipicamente Hc possui infinitos pontos periódicos atratores, fato totalmente inesperado, uma vez que este número é sempre finito para aplicações racionais. O conjunto de tais pontos dá origem ao chamado conjunto de Julia dual, que é um conjunto de Cantor proveniente de um Conformal Iterated Function System. Tanto o conjunto de Julia e quanto seu dual são projeções de movimentos holomorfos de sistemas definidos em subconjuntos compactos denotados por Xc e Wc; respectivamente de um espaço de Banach. Para todo c próximo de zero: (1) mostramos que Jc é reunião de arcos quase-conformes próximos do círculo unitário; (2) o conjunto Xc é um movimento holomorfo do solenóide X0; (3) utilizando o formalismo dos estados de Gibbs, exibimos um limitante superior para a dimensão de Hausdorff de Jc. Consequentemente, Jc possui medida de Lebesgue nula.