Thesis (Ph.D)--Management, Georgia Institute of Technology, 2009. / Committee Co-Chair: Kavadias, Stylianos; Committee Co-Chair: Toktay, L. Beril; Committee Member: Ferguson, Mark; Committee Member: Gaimon, Cheryl; Committee Member: Saleh, Joseph. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--University of Queensland, 2002. / Includes bibliographical references.

Thesis (M. Eng. Sc.)--University of Queensland, 2002. / Includes bibliographical references.

Thesis (doctoral)--Universität für Bodenkultur Wien, 2008. / Includes bibliographical references (p. 261-273).

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The objective of the thesis is to compare polynomials and finite Blaschke products, and demonstrate that they share many similar properties and hence we can establish a dictionary between these two kinds of finite maps for the first time. The results for polynomials were reviewed first. In particular, a special kind of polynomials was discussed, namely, Chebyshev polynomials, which can be defined by the trigonometric cosine function cos ?. Also, a complete classification for two polynomials sharing a set was given. In this thesis, some analogous results for finite Blaschke products were proved. Firstly, Chebyshev-Blaschke products were introduced. They can be defined by re- placing the trigonometric cosine function cos z by the Jacobi cosine function cd(u; ? ). They were shown to have several similar properties of Chebyshev polynomials, for example, both of them share the same monodromy, satisfy some differential equations and solve some minimization problems. In addition, some analogous results about two finite Blaschke products sharing a set were proved, based on Dinh's and Pakovich's ideas. Moreover, the density of prime polynomials was investigated in two different ways: (i) expressing the polynomials of degree n in terms of the zeros and the leading coefficient; (ii) expressing the polynomials of degree n in terms of the coefficients. Also, the quantitative version of the density of composite polynomials was developed and a density estimate on the set of composite polynomials was given. Furthermore, some analogous results on the the density of prime Blaschke products were proved. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Background: Type 2 diabetes mellitus is one of the most prevalent chronic diseases worldwide, currently affecting about 3 million global populations. The incidence of Type 2 diabetes has been increasing particularly in recently developed Asian settings including Hong Kong. Dairy product, as a part of dietary guidelines, has been hypothesized to help reduce risks of Type 2 diabetes. However different types of dairy product might have different effects on Type 2 diabetes given their varying content in fat, sugar and vitamins. Objective: To review literature on the examination of the association between consumption of different types of dairy products (total dairy, high-fat dairy, low-fat dairy and fermented dairy) and the risk of type 2 diabetes Methods Relevant studies were searched and identified through database of PubMed and Google Scholar using combination of keywords. Studies examining the association between consumption of total dairy and subtypes of dairy products and the risk of type 2 diabetes were included. Results: Of the 163 papers identified, 10 studies were finally included in this systematic review. All studies were prospective cohort study from Western countries. Findings for different kinds of dairy products varied. For high-fat dairy products consumption, nine out of the ten studies found there was no association with type 2 diabetes risks. For low-fat dairy products, six out of ten studies found an inverse association after adjusted for confounders like age, sex and total energy intake; among these six studies, three still reported an inverse association after further adjusted for confounders like education level, smoking status and alcohol intake, physical activities and family history of type 2 diabetes. For fermented dairy products (mainly yoghurt), among seven studies which examined this, three studies found an inverse association between yogurt consumption and Type 2 diabetes risk before and after adjusted for multivariate confounders (age ,sex, total energy drink, education level, social class, physical activities, smoking status, alcohol intake and family history of type 2 diabetes, etc) . One of the three studies also found that, other than yogurt, there was an inverse association between low-fat fermented dairy and total fermented dairy consumption and type 2 diabetes risks after adjusted for age and sex. However, after further adjustment, the association became null for total fermented dairy products while it remained for low-fat fermented dairy products. All of the 10 studies that examined subtypes of dairy product also reported total dairy product consumption. For total dairy product, six out of ten studies found an inverse association. Conclusion: Overall, total dairy consumption might be associated with lower risks of type 2 diabetes, but the associations may be varied by subtypes of dairy products. Across different types of dairy products, low-fat dairy consumption was associated with lower risk of type 2 diabetes while high-fat dairy consumption was clearly not associated with type 2 diabetes risk. Results for subtypes of fermented dairy consumption remain unclear. Further prospective cohort study in other non-Western populations may provide are required. / published_or_final_version / Public Health / Master / Master of Public Health

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No description available.