Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Fernando Rodriguez-Villegas. Vita. Includes bibliographical references.

Thesis (Ph. D.)--Institute of Paper Science and Technology, 1989. / Bibliography: leaves 94-100.

published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy

Thesis (Ph. D.)--Carleton University, 2001. / Includes bibliographical references (p. 141-144). Also available in electronic format on the Internet.

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 32-33).

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.

The counting of fuzzy subsets of a finite set is of great interest in both practical and theoretical contexts in Mathematics. We have used some counting techniques such as the principle of Inclusion-Exclusion and the Mõbius Inversion to enumerate the fuzzy subsets of a finite set satisfying different conditions. These two techniques are interdependent with the M¨obius inversion generalizing the principle of Inclusion-Exclusion. The enumeration is carried out each time we redefine new conditions on the set. In this study one of our aims is the recognition and identification of fuzzy subsets with same features, characteristics or conditions. To facilitate such a study, we use some ideas such as the Hamming distance, mid-point between two fuzzy subsets and cardinality of fuzzy subsets. Finally we introduce the fuzzy scanner of elements of a finite set. This is used to identify elements and fuzzy subsets of a set. The scanning process of identification and recognition facilitates the choice of entities with specified properties. We develop a procedure of selection under the fuzzy environment. This allows us a framework to resolve conflicting issues in the market place.

by Ka-hon Yeung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Bibliography: leaves 155-158. / Chapter 1) --- INTRODUCTION --- p.1 / Chapter 2) --- BACKGROUND MATERIALS AND DEFINITIONS --- p.3 / Chapter §1. --- THE RIEMANN ZETA FUNCTION --- p.3 / Chapter §2. --- THE DEDEKIND ZETA FUNCTION --- p.9 / Chapter §3. --- THE DIRICHLET L-FUNCTION --- p.11 / Chapter §4. --- PLACES AND ABSOLUTE VALUES --- p.13 / Chapter §5. --- THE HECKE L-FUNCTION --- p.14 / Chapter §6. --- CLASS FIELD THEORY --- p.17 / Chapter §7. --- LINEAR REPRESENTATIONS OF FINITE GROUPS --- p.19 / Chapter §8. --- THE ARTIN L-FUNCTION --- p.22 / Chapter 3) --- WORKS OF VARIOUS PEOPLE IN THE EVALUATION OF L-FUNCTIONS --- p.28 / Chapter §1. --- CLASS NUMBER FORMULA --- p.28 / Chapter §2. --- WORKS OF SHINTANI --- p.35 / Chapter §3. --- WORKS OF STARK --- p.65 / Chapter 4) --- STARK'S CONJECTURE --- p.90 / Chapter § 1. --- WORKS OF STARK --- p.90 / Chapter §2. --- WORKS OF TATE --- p.102 / Chapter §3. --- WORKS OF SANDS --- p.132 / NOTE --- p.146 / APPENDIX --- p.153 / BIBLIOGRAPHY --- p.155

Thesis (Ph. D.)--State University of New York at Binghamton, Department of Mathematical Sciences, 2009. / Includes bibliographical references.