Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. Includes bibliographical references (leaf 145).

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Luis A. Caffarelli. Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1983. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 121-123).

Thesis (doctoral)--Karolinska Institutet, Stockholm, 1984. / Extra t.p. with thesis statement inserted. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (p. 34-42).

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 638-661).

Thesis (doctoral)--Karolinska Institutet, Stockholm, 1984. / Extra t.p. with thesis statement inserted. Includes bibliographical references (p. 34-42).

Thesis (Ph. D.)--University of Missouri-Columbia, 2005. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (July 18, 2006) Vita. Includes bibliographical references.

Differential geometry is deceptively simple. It is surprisingly easyto get the right answer with unclear and informal symbol manipulation.To address this problem we use computer programs to communicate aprecise understanding of the computations in differential geometry.Expressing the methods of differential geometry in a computer languageforces them to be unambiguous and computationally effective. The taskof formulating a method as a computer-executable program and debuggingthat program is a powerful exercise in the learning process. Also,once formalized procedurally, a mathematical idea becomes a tool thatcan be used directly to compute results.

Made available in DSpace on 2015-12-10T14:24:01Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-01-30. Added 1 bitstream(s) on 2015-12-10T14:30:09Z : No. of bitstreams: 1 000853553.pdf: 673227 bytes, checksum: 15daa91b83cef03ccc49628600fefa0f (MD5) / Realizamos um estudo sobre a função exponencial, analisando as principais propriedades desta função e a construção de seu grá co. Para isso, foi realizada uma pesquisa detalhada sobre alguns subconjuntos dos números reais, servindo de base para compreendermos as propriedades envolvidas na potenciação de um número real. Ao nal do trabalho, destacamos algumas aplicações da função exponencial, que podem servir de motivação para se iniciar o ensino de tal função na educação básica do Brasil / We conducted a study of the exponential function, analysing the main properties of this function and the construction of its graph. For this, a detailed research on some subset of the real numbers was carried out, providing the basis for understanding the properties involved in the potentiation of a real number. At the end of the work, we highlight some applications of the exponential function, which can serve as motivation to start teaching this in basic education in Brazil

Made available in DSpace on 2014-06-11T19:33:28Z (GMT). No. of bitstreams: 0 Previous issue date: 2002-09-05Bitstream added on 2014-06-13T21:06:15Z : No. of bitstreams: 1 trentin_ms_dr_arafo.pdf: 461820 bytes, checksum: e0251a43f7587a82128f9f0494efd863 (MD5) / O objetivo deste estudo foi avaliar clinicamente a influência do cálculo subgengival nas medidas de profundidade de sondagem com sonda manual e eletrônica de força controlada. Para tanto, foram avaliados 614 sítios com cálculo subgengival visível em radiografias periapicais e detectáveis clinicamente através do índice de cálculo de Greene e Vermillion, 1967. Os exames foram realizados por um profissional calibrado que avaliou o índice de sangramento gengival à sondagem e realizou a sondagem com os dois tipos de sondas em seis áreas de cada dente: mesio-vestibular, vestibular, disto-vestibular, mesio-lingual, lingual e disto-lingual, com o auxílio de um stent oclusal. As sondagens foram realizadas em dois instantes. Inicial: com a presença do cálculo subgengival, imediato: imediatamente após a remoção do cálculo subgengival. Para a análise dos dados obtidos, as profundidades de sondagens foram estratificadas em rasa (=3mm), média (4-6mm) e profunda (= 7mm). Através do teste de Wilcoxon à 5%, observou-se que as medidas de profundidades de sondagens médias (4.78mm para o momento inicial e 4.56mm para o momento imediato) e profundas (7.60mm para o momento inicial e 6.79 mm para o momento imediato) para a sonda eletrônica de força controlada apresentaram diferenças significativas entre os diferentes momentos, porém, o mesmo não ocorreu quando foi utilizada a sonda manual. Da mesma forma, quando o teste t foi empregado para avaliar a influência do sangramento à sondagem sobre as diferenças da sondagem manual e computadorizada, este não apresentou-se como um fator influenciador. Conclusão: O cálculo subgengival interfere na sondagem realizada com a sonda computadorizada, não ocorrendo o mesmo com a sonda manual. / The present investigation assessed the influence of subgingival calculus on clinical probing measurements with manual and constant force electronic probe. The study evaluated 614 sites with visible subgingival calculus, evidenced by radiographic and clinical modified index (Greene & Vermillion, 1967). The evaluation was performed by a calibrated dental examiner, who evaluate gingival bleeding index and probing depth with manual and computarized probe, in six sites per tooth: mesio-buccal, middle-buccal, disto-buccal, mesio-lingual, middle-lingual and disto-lingual with individually acrylic stents. The probing depths measurements were performed in two moments. Inicial: In presence of subgingival calculus, immediate: immediately after removal of subgingival calculus. To data analysis, the probing depths measurements were classified in: shallow depths (=3mm), moderate (4-6mm) and deep (=7mm) and submmited to statistical analysis (Wilcoxon 5%). The results show that moderate measurement (4.78mm at inicial moment and 4.56mm for immediate), and deep measurements (7.60mm at inicial moment and 6.79 for immediate) with a computerized probe were statistically differentes significative for two moments, however, the same difference did not occurre when manual probe was used. Smilary, when the test t assessed the influence of gingival bleeding index to detect differences between computarizade and manual probe, this not represent a source of error in this measurement. Conclusion: The subgingival calculus influenced the probing depth measurements when a computarized probe was used, although that didnþt occurre with manual probe.