The purpose of this thesis is to study the concept of completeness in an ordered field. Several conditions which are necessary and sufficient for completeness in an ordered field are examined. In Chapter I the definitions of a field and an ordered field are presented and several properties of fields and ordered fields are noted. Chapter II defines an Archimedean field and presents several conditions equivalent to the Archimedean property. Definitions of a complete ordered field (in terms of a least upper bound) and the set of real numbers are also stated. Chapter III presents eight conditions which are equivalent to completeness in an ordered field. These conditions include the concepts of nested intervals, Dedekind cuts, bounded monotonic sequences, convergent subsequences, open coverings, cluster points, Cauchy sequences, and continuous functions.

The aim of this thesis is to establish the principal properties for the theory of ordered compactifications relating to connectedness and to provide particular examples. The initial idea of this subject is based on the notion of the Stone-Cech compactification.The ordered Stone-Cech compactification oX of an ordered topological space X is constructed analogously to the Stone-Cech compactification X of a topological space X, and has similar properties. This technique requires a conceptual understanding of the Stone-Cech compactification and how its product applies to the construction of ordered topological spaces with continuous increasing functions. Chapter 1 introduces background information. Chapter 2 addresses connectedness and compactification. If (A;B) is a separation ofa topological space X, then (A 8 B) = A 8 B, but in the ordered setting, o(A 8 B)need not be oA 8 oB. We give an additional hypothesis on the separation (A;B) tomake o(A 8 B) = oA 8 oB. An open question in topology is when is X -X = X. Weanswer the analogous question for ordered compactifications of totally ordered spaces. So, we are concerned with the remainder, that is, the set of added points oX -X. Wedemonstrate the topological properties by using lters. Moreover, results of lattice theory turn out to be some of the basic tools in our original approach. In Chapter 3, specific examples and counterexamples are given to illustrate earlierresults.

Thesis (M.S.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Many poor farmers, especially in Africa, have not adopted recent farming innovations to improve their yields. One theory is that poor farmers are risk averse and therefore do not invest in high risk high return innovations and that risk averse farmers will only adopt larger innovations if they experience success with small ones. Risk preferences were measured in two districts in Uganda (Tororo and Kapchorwa) where adoption of agricultural innovations has been slow, and where a program is underway to encourage use of conservation agriculture practices (CAPs) to reduce soil erosion and sequester carbon. An ordered lottery selection was used to measure risk preferences and an ordered probit model was estimated. Thirty five percent of a random sample of 200 farmers in Tororo (and fifty three percent of 200 farmers in Kapchorwa) made lottery choices that implied severe or extreme risk aversion. However there was no indication that risk preferences correlate with willingness to adopt new technologies (such as CAPs). Neither wealth nor previous success with technology adoption were found to correlate with farmers' risk preferences. / Master of Science / CCRA-6 (Economic and Impact Analysis)

It may be said of certain pairs of elements of a set that one element precedes the other. If the collection of all such pairs of elements in a given set exhibits certain properties, the set and the collection of pairs is said to constitute a partially ordered set. The purpose of this paper is to explore some of the properties of partially ordered sets.

Gives the basic definitions and theorems of similar partially ordered sets; studies finite partially ordered sets, including the problem of combinatorial analysis; and includes the ideas of complete, dense, and continuous partially ordered sets, including proofs.

Thesis (Ph. D.)--State University of New York at Binghamton, Mathematical Sciences Department, 2006. / Includes bibliographical references.

This study focuses on identifying communication technology adoption behaviors to provide educational benchmarks for Texas cooperatives. A survey was conducted with questions identifying a range of variables describing adoption behavior of communication technology from the background of cooperative managers to board management policy. The survey categorized 105 different cooperatives by current technology use and management practices. Once the data were collected, a factor analysis to understand underlying relationships of variables was conducted. The survey found that Texas cooperative managers are willing to expand on their current use of communication technology, however a clear definition of how to use new concepts as a powerful tool is needed. In terms of governance, we found that many cooperatives have no stated policies regarding the use of communication technologies. Generally, those cooperatives that had defined technology use policies were more likely to be using more forms of technology. Through a logistic and ordered logistic regression of the data, the study did not reflect our initial hypothesis that age of the respondent and the years working for a cooperative (manger characteristics) would be a significant factor in estimating Texas cooperatives? willingness to adopt new forms of communication technology and social media. However, the cooperatives? technology adoption behavior can best be explained by the data produced from descriptive cooperative information and the existence of employee communication technology policies. Likewise, cooperatives? willingness to adopt social media can best be explained by the data produced from manager attitudes and cooperatives? concerns.

No description available.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Dec. 15, 2008). PDF text: vi, 93 p. ; 616 K. UMI publication number: AAT 3333017. Includes bibliographical references. Also available in microfilm and microfiche formats.