The context for the development of this work is constructive mathematics without the axiom of countable choice. By constructive mathematics, we mean mathematics done without the law of excluded middle. Our original goal was to give a list of axioms for the real numbers R by only considering the order on R. We instead develop a theory of ordered sets and their completions and a theory of ordered abelian groups. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

Thesis (M. Sc.)--University of Canterbury, 2009. / Typescript (photocopy). Includes bibliographical references (p. 47-48). Also available via the World Wide Web.

No description available.

Thesis (Ph.D.)--Tufts University, 2001. / Advisers: Mauricio Gutierrez; Zbigniew Nitecki. Submitted to the Dept. of Mathematics. Includes bibliographical references (leaves 73-74). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Thesis (Ph.D.)--McMaster University (Canada), 1990. / Source: Dissertation Abstracts International, Volume: 52-10, Section: B, page: 5312. Supervisor: B. Banaschewski.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 240-243).

An important trend in fuzzy group theory in recent years has been the notion of classification of fuzzy subgroups using a suitable equivalence relation. In this dissertation, we have successfully used the natural equivalence relation defined by Murali and Makamba in [81] and a natural fuzzy isomorphism to classify fuzzy subgroups of some finite abelian p-groups of rank three of the form Zpn + Zp + Zp for any fixed prime integer p and any positive integer n. This was achieved through the usage of a suitable technique of enumerating distinct fuzzy subgroups and non-isomorphic fuzzy subgroups of G. We commence by giving a brief discussion on the theory of fuzzy sets and fuzzy subgroups from the perspective of group theory through to the theory of sets, leading us to establish a linkage among these theories. We have also shown in this dissertation that the converse of theorem 3.1 proposed by Das in [24] is incorrect by giving a counter example and restate the theorem. We have then reviewed and enriched the study conducted by Ngcibi in [94] by characterising the non-isomorphic fuzzy subgroups in that study. We have also developed a formula to compute the crisp subgroups of the under-studied group and provide its proof. Furthermore, we have compared the equivalence relation under which the classification problem is based with various versions of equivalence studied in the literature. We managed to use this counting technique to obtain explicit formulae for the number of maximal chains, distinct fuzzy subgroups, non-isomorphic maximal chains and non-isomorphic fuzzy subgroups of these groups and their proofs are provided.

The thesis shows that, under suitable conditions, a pseudo-differential operator, defined on some "nice" set of functions on Rn x Zm, with continuous negative definite symbol q(x,xi,o) extends to a generator of a Feller semigroup. Sections 1-5 are the preliminary sections, these sections discuss some harmonic analysis concerning locally compact Abelian groups. The essence of this thesis are Sections 6-13, which deals with obtaining the estimates required for the fulfilment of the conditions of the Hille-Yosida-Ray theorem.

No description available.

Thesis (Ph.D.)--York University, [2004]. Graduate Programme in [Mathematics]. / Typescript. Includes bibliographical references (leaves 163-166). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ99158