Tübingen, Univ., Diss., 2008.

archives@tulane.edu / Many symbolic integration methods and algorithms have been developed to deal with definite integrals such as those of interest to physicists, theoretical chemists and engineers. These have been implemented into mathematical softwares like Maple and Mathematica to give closed forms of definite integrals. The work presented here introduces and analytically investigates an algorithm called Method of brackets. Method of brackets consists of a small number of rules to transform the evaluation of a definite integral into a problem of solving a system of linear equations. These rules are heuristic so justification is needed to make this method rigorous. Here we use contour integrals to justify the evaluation given by the algorithm. / 1 / Tri Ngo

AIM: To analyze staining properties of aesthetic brackets. MATERIAL & METHODS: A total of 400 tooth-coloured brackets from 10 brands 5 ceramic and 5 plastic) were investigated. Cumulative effects of staining agents were analyzed at simulated light and heavy consumption levels. Study groups were immersed in the staining agents consecutively at 37°C. The control group was exposed to artificial saliva. Samples were analyzed digitally to obtain the L*, a*, and b* (lightness, red-green, and yellow-blue) colour readings. Using these values total colour change (ΔE*) was also calculated. A general linear model (ANOVA) test was used for statistical comparisons. RESULTS: Significant differences were observed in L*, and b* values of ceramic brackets at all consumption levels (p≤.0001). All values had significant differences amongst the plastic brackets (p≤.0001), except for L* with heavy exposure. Total ΔE* values for ceramic and plastic brackets were 11 and 26, respectively. CONCLUSIONS: Both plastic and ceramic brackets showed changes in colour when exposed to staining agents, with plastic brackets being the most affected.

AIM: To analyze staining properties of aesthetic brackets. MATERIAL & METHODS: A total of 400 tooth-coloured brackets from 10 brands 5 ceramic and 5 plastic) were investigated. Cumulative effects of staining agents were analyzed at simulated light and heavy consumption levels. Study groups were immersed in the staining agents consecutively at 37°C. The control group was exposed to artificial saliva. Samples were analyzed digitally to obtain the L*, a*, and b* (lightness, red-green, and yellow-blue) colour readings. Using these values total colour change (ΔE*) was also calculated. A general linear model (ANOVA) test was used for statistical comparisons. RESULTS: Significant differences were observed in L*, and b* values of ceramic brackets at all consumption levels (p≤.0001). All values had significant differences amongst the plastic brackets (p≤.0001), except for L* with heavy exposure. Total ΔE* values for ceramic and plastic brackets were 11 and 26, respectively. CONCLUSIONS: Both plastic and ceramic brackets showed changes in colour when exposed to staining agents, with plastic brackets being the most affected.

Thesis (M. Sc.)--University of Manitoba, 1998. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M. Sc.)--University of Manitoba, 1998. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Louisville, 1998. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M. Sc.)--University of Manitoba, 1996. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 162-164). Also available via the Internet.

Thesis (M. Sc.)--University of Manitoba, 1996. / Includes bibliographical references.