Inaug.-diss.--Upsala. / "Quellen und literatur": p. [xi]-xix. Also issued online.

In this thesis we will be working with dominating and interpolating sequences. We worked with a geometric approach and used pseudohyperbolic translated to the Euclidean disc in order to show that a sequence within a certain radius of a dominating sequence is dominating as well.

Thesis (M.S.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 8).

Master of Science / Department of Mathematics / Natalia Rojkovskaia / The topic of limits and sequences run through the math syllabi from high school to graduate school. However rigorous proofs of this concept is not seen up until a students second year in college or even later. This text is aimed at presenting proofs of limits of sequences at a level accessible to high school and undergraduate students who are interested in learning such proofs. The ''Epsilon-N" definition of the limit with proofs using this definition is presented in the text. We also look at properties of limits of sequences and their proofs as well as sequences without limits (that is sequences that diverge). We include some graphical representations of some sequences which can help one to determine whether a sequence will converge or diverge. Finally, the text contains a good number of exercises for the reader, some solved and others with hints to direct the reader in solving them.

We investigate a class of minimal sequences on a finite alphabet Ak = {1,2,...,k} having (k - 1)n + 1 distinct subwords of length n. These sequences, originally defined by P. Arnoux and G. Rauzy, are a natural generalization of binary Sturmian sequences. We describe two simple combinatorial algorithms for constructing characteristic Arnoux-Rauzy sequences (one of which is new even in the Sturmian case). Arnoux-Rauzy sequences arising from fixed points of primitive morphisms are characterized by an underlying periodic structure. We show that every Arnoux-Rauzy sequence contains arbitrarily large subwords of the form V^2+ε and, in the Sturmian case, arbitrarily large subwords of the form V^3+ε. Finally, we prove that an irrational number whose base b-digit expansion is an Arnoux-Rauzy sequence is transcendental.

by Wong Oi Ping. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 77-79). / Abstracts in English and Chinese. / Chapter 1 --- LP-minimizing and Stationary Sequences --- p.8 / Chapter 1.1 --- Residual function --- p.8 / Chapter 1.2 --- Minimizing sequences --- p.14 / Chapter 1.3 --- Stationary sequences --- p.17 / Chapter 1.4 --- On the equivalence of minimizing and stationary se- quence --- p.21 / Chapter 1.5 --- Complementarity conditions --- p.25 / Chapter 1.6 --- Subdifferential-based stationary sequence --- p.29 / Chapter 1.7 --- Convergence of an Iterative Algorithm --- p.32 / Chapter 2 --- Minimizing And Stationary Sequences In Nonsmooth Optimization --- p.38 / Chapter 2.1 --- Subdifferential --- p.38 / Chapter 2.2 --- Stationary and minimizing sequences --- p.40 / Chapter 2.3 --- C-convex and BC-convex function --- p.43 / Chapter 2.4 --- Minimizing sequences in terms of sublevel sets --- p.44 / Chapter 2.5 --- Critical function --- p.48 / Chapter 3 --- Optimization Conditions --- p.52 / Chapter 3.1 --- Introduction --- p.52 / Chapter 3.2 --- Second-order necessary and sufficient conditions with- out constraint --- p.55 / Chapter 3.3 --- The Lagrange and G-functions in constrained problems --- p.63 / Chapter 3.4 --- Second-order necessary conditions for constrained prob- lems --- p.73 / Chapter 3.5 --- Sufficient conditions for constrained problems --- p.74 / Bibliography

published_or_final_version / abstract / toc / Mathematics / Master / Master of Philosophy

published_or_final_version / abstract / Mathematics / Doctoral / Doctor of Philosophy

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