Given a Geometric Lorenz Flow X on \'R POT. n+2\' of class \'C POT. k+1\'; by definition there exists a Poincaré map \'P IND. X\' of class \'C POT. k+1\'; often so-called Lorenz-type map [ABS83]. The main purpose in this dissertation is to show that under certain conditions the Lorenz-type map \'P IND.X\' can be associate to it a one-dimensional transformation \'f IND. X\' of class \'C POT. k\' (defined on an interval). This association is so-called the reduction transformation R; so we have \'RP IND. X\' = \'f IND. X\'. This association would allow us to study the dynamical properties for the original flow using techniques of one-dimensional dynamics of class \'C POT. k\' / Dado um Fluxo Geométrico de Lorenz X em \'R POT. n+2\' de classe \'C POT. k+1\'; por definição, existe uma aplicação de Poincaré \'P IND. X\'\' de classe \'C POT. k+1\'; frequentemente chamado aplicação do tipo Lorenz [ABS83]. O objetivo principal desta tese é mostrar que, sob certas condições a aplicação do tipo Lorenz \'P IND. X\' pode ser associado a ele uma transformação unidimensional \'f IND. X\' de classe \'C POT. k\' (definida em um intervalo). Esta associação é chamada de transformação de redução R; assim temos que , \'RP IND. X\' = \'f IND. X\'. Esta associação nos permitiria estudar as propriedades dinâmicas do fluxo original utilizando técnicas da dinâmica unidimensional de classe \'C POT. k\'

Cheung, Chun Ngai. / "August 2011." / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 55-57). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Coding the Lorenz knots --- p.10 / Chapter 2.1 --- Lorenz words --- p.10 / Chapter 3 --- Lorenz links and positive braids --- p.15 / Chapter 3.1 --- Lorenz braids --- p.15 / Chapter 3.2 --- Properties of Lorenz links as the closure of a positive braid --- p.17 / Chapter 4 --- T-Links and the braid index --- p.28 / Chapter 4.1 --- T-links --- p.30 / Chapter 4.2 --- Symmetries --- p.35 / Chapter 4.3 --- Trip number and the braid index --- p.39 / Chapter 5 --- Modular knots --- p.47 / Chapter 5.1 --- The Modular flow --- p.47 / Chapter 5.2 --- Modular Knots --- p.49 / Bibliography --- p.55

Thesis.

Thesis. / Title from cover. "Inaugural-Dissertation zur Erlangung der Doktorwürde der Hohen Philosophischen Fakultät der Universität Leipzig." Includes bibliographical references (p. [195]-197).

Inaugural-Dissertation--Halle, 1908. / "Verzeichnis der Werke von Lorenz von Stein ..."--P. [7]-17. Lebenslauf. Includes bibliographical references.

Inaug.-diss.--Würzburg. / Lebenslauf. "Literaturverzeichnis": p. [7]-13.

Thesis.

Given a Geometric Lorenz Flow X on \'R POT. n+2\' of class \'C POT. k+1\'; by definition there exists a Poincaré map \'P IND. X\' of class \'C POT. k+1\'; often so-called Lorenz-type map [ABS83]. The main purpose in this dissertation is to show that under certain conditions the Lorenz-type map \'P IND.X\' can be associate to it a one-dimensional transformation \'f IND. X\' of class \'C POT. k\' (defined on an interval). This association is so-called the reduction transformation R; so we have \'RP IND. X\' = \'f IND. X\'. This association would allow us to study the dynamical properties for the original flow using techniques of one-dimensional dynamics of class \'C POT. k\' / Dado um Fluxo Geométrico de Lorenz X em \'R POT. n+2\' de classe \'C POT. k+1\'; por definição, existe uma aplicação de Poincaré \'P IND. X\'\' de classe \'C POT. k+1\'; frequentemente chamado aplicação do tipo Lorenz [ABS83]. O objetivo principal desta tese é mostrar que, sob certas condições a aplicação do tipo Lorenz \'P IND. X\' pode ser associado a ele uma transformação unidimensional \'f IND. X\' de classe \'C POT. k\' (definida em um intervalo). Esta associação é chamada de transformação de redução R; assim temos que , \'RP IND. X\' = \'f IND. X\'. Esta associação nos permitiria estudar as propriedades dinâmicas do fluxo original utilizando técnicas da dinâmica unidimensional de classe \'C POT. k\'

BACKGROUND: Differences in disease-modifying therapy (DMT) prescribing patterns between different groups of neurologists have not been explored. HYPOTHESIS: MS-specialist neurologists use a broader range of DMTs in contrast to generalist neurologists who preferentially prescribe Avonex. METHODS: Ontario neurologist demographic and geographical characteristics were linked to 2009 DMT prescription data. Lorenz curves and Gini coefficients were constructed to examine prescribing patterns; separating neurologist characteristics dichotomously and separating Avonex from the other DMTs. Gini Coefficients were compared using jack-knife statistical techniques to derive 95% confidence intervals. RESULTS: Prescriptions are highly concentrated with 12% of Ontario neurologists prescribing 80% of DMTs. High-volume prescribers show a broader range of DMT use while low-volume prescribers tend to use a particular DMT. CONCLUSIONS: The majority of DMTs are prescribed by a small subset of neurologists. High-volume prescribers show more variability in DMT use while low-volume prescribers tend to individually focus on a narrower range of DMTs.

BACKGROUND: Differences in disease-modifying therapy (DMT) prescribing patterns between different groups of neurologists have not been explored. HYPOTHESIS: MS-specialist neurologists use a broader range of DMTs in contrast to generalist neurologists who preferentially prescribe Avonex. METHODS: Ontario neurologist demographic and geographical characteristics were linked to 2009 DMT prescription data. Lorenz curves and Gini coefficients were constructed to examine prescribing patterns; separating neurologist characteristics dichotomously and separating Avonex from the other DMTs. Gini Coefficients were compared using jack-knife statistical techniques to derive 95% confidence intervals. RESULTS: Prescriptions are highly concentrated with 12% of Ontario neurologists prescribing 80% of DMTs. High-volume prescribers show a broader range of DMT use while low-volume prescribers tend to use a particular DMT. CONCLUSIONS: The majority of DMTs are prescribed by a small subset of neurologists. High-volume prescribers show more variability in DMT use while low-volume prescribers tend to individually focus on a narrower range of DMTs.