Computer-Assisted Proofs and Symbolic Computations

We discuss some main points of computer-assisted proofs based on reliable numerical computations. Such so-called self-validating numerical methods in combination with exact symbolic manipulations result in very powerful mathematical software tools. These tools allow proving mathematical statements (existence of a fixed point, of a solution of an ODE, of a zero of a continuous function, of a global minimum within a given range, etc.) using a digital computer. To validate the assertions of the underlying theorems fast finite precision arithmetic is used. The results are absolutely rigorous. To demonstrate the power of reliable symbolic-numeric computations we investigate in some details the verification of very long periodic orbits of chaotic dynamical systems. The verification is done directly in Maple, e.g. using the Maple Power Tool intpakX or, more efficiently, using the C++ class library C-XSC.

Fractal Analysis for Cancer Research: Case Study and Simulation of Fractals

2010 Mathematics Subject Classification: 65D18.

Changes in intraocular pressure in study and fellow eyes in the IVAN trial

PURPOSE: To describe changes in intraocular pressure (IOP) in the 'alternative treatments to Inhibit VEGF in Age-related choroidal Neovascularisation (IVAN)' trial (registered as ISRCTN92166560). DESIGN: Randomised controlled clinical trial with factorial design. PARTICIPANTS: Patients (n=610) with treatment naïve neovascular age-related macular degeneration were enrolled and randomly assigned to receive either ranibizumab or bevacizumab and to two regimens, namely monthly (continuous) or as needed (discontinuous) treatment. METHODS: At monthly visits, IOP was measured preinjection in both eyes, and postinjection in the study eye. OUTCOME MEASURES: The effects of 10 prespecified covariates on preinjection IOP, change in IOP (postinjection minus preinjection) and the difference in preinjection IOP between the two eyes were examined. RESULTS: For every month in trial, there was a statistically significant rise in both the preinjection IOP and the change in IOP postinjection during the time in the trial (estimate 0.02 mm Hg, 95% CI 0.01 to 0.03, p<0.001 and 0.03 mm Hg, 95% CI 0.01 to 0.04, p=0.002, respectively). There was also a small but significant increase during the time in trial in the difference in IOP between the two eyes (estimate 0.01 mm Hg, 95% CI 0.005 to 0.02, p<0.001). There were no differences between bevacizumab and ranibizumab for any of the three outcomes (p=0.93, p=0.22 and p=0.87, respectively). CONCLUSIONS: Anti-vascular endothelial growth factor agents induce increases in IOP of small and uncertain clinical significance.

The influence of study and travel abroad on the personal and professional development of students in architecture design programs

International travel has significant implications on the study of architecture. This study analyzed ways in which undergraduate and graduate students benefited from the experience of international travel and study abroad. Taken from the perspective of 15 individuals who were currently or had been architecture students at the University of Miami and Florida International University or who were alumni of the University of Florida and Syracuse University, the research explored how international travel and study abroad enhanced their awareness and understanding of architecture, and how it complemented their architecture curricula. This study also addressed a more personal aspect of international travel in order to learn how the experience and exposure to foreign cultures had positively influenced the personal and professional development of the participants.^ Participants’ individual and two-person semi-structured interviews about study abroad experiences were electronically recorded and transcribed for analysis. A second interview was conducted with five of the participants to obtain feedback concerning the accuracy of the transcripts and the interpretation of the data. Sketch journals and design projects were also analyzed from five participants and used as data for the purposes of better understanding what these individuals learned and experienced as part of their study abroad.^ Findings indicated that study abroad experiences helped to broaden student understanding about architecture and urban development. These experiences also opened the possibilities of creative and professional expression. For many, this was the most important aspect of their education as architects because it heightened their interest in architecture. These individuals talked about how they had the opportunity to experience contemporary and ancient buildings that they had learned about in their history and design classes on their home campuses. In terms of personal and professional development, many of the participants remarked that they became more independent and self-reliant because of their study abroad experiences. They also displayed a sense of global awareness and were interested in the cultures of their host nations. The study abroad experiences also had a lasting influence on their professional development.^

Revisiting Entrepreneurship Education Literature: Implications for Learning and Teaching Entrepreneurship

Courses and programs about entrepreneurship show so much variation that it is hard to identify typical teaching strategies. Although diversity is good, consistency is needed because the value of entrepreneurship education has not been established. A literature review on teaching and learning in entrepreneurship was conducted; three challenges were identified.

A study of the impact of field experience in hospitality education

The purpose of this study was to find out the impact of field experience in hospitality education and whether such field experience and others such as semi-practicum, the cooperative, and the work study programs will not play an important role of a closer alliance between the academic and the hospitality industry. II. If it is justifiable to say that it is possible to provide field experience which will enhance the professionally oriented course work, while educators and employers strive to design curriculum that is needed to meet the educational and the industry demands and goals.

Food and beverage management

Abstract and faculty adviser information are not available for this thesis.