Thesis (M.S.)--Boise State University, 2009. / Includes abstract. Includes bibliographical references (leaves 52-53).

Habilitationsschrift, Bonn, 1971; extra t.p. inserted. / Includes bibliographical references (p. [92-93]).

Thesis (M. Phil.)--Hong Kong University of Science and Technology, 2003. / Includes bibliographical references (leaves 44). Also available in electronic version. Access restricted to campus users.

This report articulates some of the recent research on different methods of optimization. Topics discussed include an implicit differentiation process in which the primary substitution method is not used and a relationship among variables method is introduced. In addition, a finding extrema without limits method is explored. Also included is a discussion on the depth of optimization taught in secondary schools and the different methods and levels of instruction on this topic. / text

The thesis is based on the use of mathematical theories and techniques to gain qualitative and quantitative insight into the transmission dynamics of hepatitis C virus (HCV) in an IDU (injecting drug user) population. A deterministic model, which stratifies the IDU population into eight mutually-exclusive compartments (based on epidemiological status), is considered. Rigorous qualitative analysis of the model establishes, for the first time, the presence of the phenomenon of backward bifurcation in HCV transmission dynamics. Three routes (or causes) to such a dynamic phenomenon have been established. Furthermore, five main parameters that play a dominant role on the transmission dynamics of the disease have been identified. Numerical simulations of the model show that the re-infection of recovered individuals has marginal effect on the HCV burden (as measured in terms of the cumulative incidence and prevalence of the disease) in the IDU community.

Interactive theorem proving provides a general approach to modeling and verification of both finite-state and infinite-state systems but requires significant human efforts to deal with many tedious proofs. On the other hand, model-checking is limited to some application domain with small finite-state space. A natural thought for this problem is to integrate these two approaches. To keep the consistency of the integration and ensure the correctness of verification, we suggest to use type theory based theorem provers (e.g. Lego) as the platform for the integration and build a model-checker to do parts of the verification automatically. We formalise a verification system of both CCS and an imperative language in the proof development system Lego which can be used to verify both finite-state and infinite-state problems. Then a model-checker, LegoMC, is implemented to generate Lego proof terras for finite-state problems automatically. Therefore people can use Lego to verify a general problem with some of its finite sub-problems verified by LegoMC. On the other hand, this integration extends the power of model-checking to verify more complicated and infinite-state models as well. The development of automatic techniques and the integration of different reasoning methods would directly benefit the verification community. It is expected that further extension and development of this verification environment would be able to handle real life systems. On the other hand, the research gives us some experiences about how to automate proofs in interactive theorem provers and therefore will improve the usability and applicability of the theorem proving technology.

Habilitationsschrift, Bonn, 1971; extra t.p. inserted. / Includes bibliographical references (p. [92-93]).

Thesis (doctoral)--Friedrich-Wilhelms-Universität zu Berlin, 1894. / On t.p. "n̳" is superscript. "Sonderabdruck aus Heft 4, Bd. 113 des Journals für die reine und angewandte Mathematik"--P. 17. Vita.

Thesis (M.S.)--Boise State University, 2009. / Title from t.p. of PDF file (viewed June 15, 2010). Includes abstract. Includes bibliographical references (leaves 52-53).

Thesis (doctoral)--University of Tartu, 2006. / This dissertation is based on 3 papers.