Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1993. / Vita. Abstract. Includes bibliographical references (leaves 127-132). Also available via the Internet.

Th.--Sci., anal. numér.--Toulouse 3, 1981. N°: 1015.

No description available.

Universiẗat, Diss., 2001--Duisburg.

Thesis (Ph. D.)--Carleton University, 1995. / Also available in electronic format on the Internet.

Thesis (doctoral)--Rheinischen Friedrich-Wilhelms-Universität, Bonn, 1980. / Includes bibliographical references (p. 252-258).

Semiclassical and Born-Oppenheimer approximations are used to provide uniform error bounds for the energies of diatomic molecules for bounded vibrational quantum number n and large angular momentum quantum number l. Specifically, results are given when (l + 1) < κ𝛜⁻³/². Explicit formulas for the approximate energies are also given. Numerical comparisons for the H+₂ and HD+ molecules are presented. / Ph. D.

Rough sets have been studied for over 30 years, and the basic concepts of lower and upper approximations have been analysed in detail, yet nowhere has the idea of an `optimal' rough approximation been proposed or investigated. In this thesis, several concepts are used in proposing a generalized definition: measures, rough sets, similarity, and approximation are each surveyed. Measure Theory allows us to generalize the definition of the `size' for a set. Rough set theory is the foundation that we use to define the term `optimal' and what constitutes an `optimal rough set'. Similarity indexes are used to compare two sets, and determine how alike or different they are. These sets can be rough or exact. We use similarity indexes to compare sets to intermediate approximations, and isolate the optimal rough sets. The historical roots of these concepts are explored, and the foundations are formally defined. A definition of an optimal rough set is proposed, as well as a simple algorithm to find it. Properties of optimal approximations such as minimum, maximum, and symmetry, are explored, and examples are provided to demonstrate algebraic properties and illustrate the mechanics of the algorithm. / Thesis / Doctor of Philosophy (PhD) / Until now, in the context of rough sets, only an upper and lower approximation had been proposed. Here, an concept of an optimal/best approximation is proposed, and a method to obtain it is presented.

published_or_final_version / Mathematics / Master / Master of Science

published_or_final_version / Mathematics / Master / Master of Philosophy