The purpose of this paper is to investigate the integrability, measurability, and summability of certain set functions. The paper is divided into four chapters. The first chapter contains basic definitions and preliminary remarks about set functions and absolute continuity. In Chapter i, the integrability of bounded set functions is investigated. The chapter culminates with a theorem that characterizes the transmission of the integrability of a real function of n bounded set functions. In Chapter III, measurability is defined and a characterization of the transmission of measurability by a function of n variables is provided, In Chapter IV, summability is defined and the summability of set functions is investigated, Included is a characterization of the transmission of summability by a function of n variables.

Call number: LD2668 .T4 1957 E32 / Master of Science

by Kam Siu Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Includes bibliographical references. / Chapter Chapter I --- On a generalized Kuratowski's closure theorem / Chapter §0. --- Introduction --- p.1 / Chapter §1. --- Counter examples and the idea of migration --- p.1 / Chapter §2. --- The use of immigration regulations --- p.11 / Chapter §3. --- Remarks on the boundary function and the complementary function --- p.35 / Chapter Chapter II --- A problem in number theory / Chapter §1. --- Introduction --- p.37 / Chapter §2. --- Preliminaries --- p.37 / Chapter §3. --- Technical Lemmas --- p.41 / Chapter §4. --- Main Theorems --- p.45 / Chapter §5. --- Closing Remarks --- p.49 / Chapter Chapter III --- Stiff elements in semigroups and their expansions / Chapter §1. --- Introduction --- p.51 / Chapter §2. --- String expansions of semigroups --- p.51 / Chapter §3. --- Stiff Semigroups --- p.59 / Chapter §4. --- Construction of examples --- p.71 / Chapter §5. --- Partition of semigroups by stiffness --- p.74

This research was conducted as part of the Strategic Highway Research Program (SHRP) A-003A contract at Oregon State University to validate the findings of SHRP contracts A-002A and A-003B with regard to aging of asphalt-aggregate mixtures. One short-term and four long-term aging methods were used to simulate aging of asphalt-aggregate mixes in the field. Four aggregates and eight asphalts for a total of 32 different material combinations were tested using different aging methods. Results of the aging studies are compared with the A-002A and A-003B studies of asphalt binder or asphalt mixed with fine aggregate. This research concludes that aging of asphalt mixes cannot be predicted by tests on asphalt binder alone since results show that aggregates have considerable influence on aging. / Graduation date: 1995

Thesis (Ph.D.)--York University, 2004. Graduate Programme in Mathematics. / Typescript. Includes bibliographical references (leaves 77-83) and index. Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://wwwlib.umi.com/cr/yorku/fullcit?pNQ99185

This article is an investigation of a recently developed method of deriving a topology from a space and an elementary submodel containing it. We first define and give the basic properties of this construction, known as X/M. In the next section, we construct some examples and analyse the topological relationship between X and X/M. In the final section, we apply X/M to get novel results about Lindelof spaces, giving partial answers to a question of F.D. Tall and another question of Tall and M. Scheepers.

This article is an investigation of a recently developed method of deriving a topology from a space and an elementary submodel containing it. We first define and give the basic properties of this construction, known as X/M. In the next section, we construct some examples and analyse the topological relationship between X and X/M. In the final section, we apply X/M to get novel results about Lindelof spaces, giving partial answers to a question of F.D. Tall and another question of Tall and M. Scheepers.

Methods are described that implement a branch-and-price decomposition approach to solve the maximum weight independent set (MWIS) problem. The approach is first described by Warrier et. al, and herein our contributions to this research are presented. The decomposition calls for the exact solution of the MWIS problem on induced subgraphs of the original graph. The focus of our contribution is the use of chordal graphs as the induced subgraphs in this solution framework. Three combinatorial branch-and-bound solvers for the MWIS problem are described. All use weighted clique covers to generate upper bounds, and all branch according to the method of Balas and Yu. One extends and speeds up the method of Babel. A second one modifies a method of Balas and Xue to produce clique covers that share structural similarities with those produced by Babel. Each of these improves on its predecessor. A third solver is a hybrid of the other two. It yields the best known results on some graphs. The related matter of deciding the imperfection or perfection of a graph is also addressed. With the advent of the Strong Perfect Graph Theorem, this problem is reduced to the detection of odd holes and anti-holes or the proof of their absence. Techniques are provided that, for a given graph, find subgraphs in polynomial time that contain odd holes whenever they are present in the given graph. These techniques and some basic structural results on such subgraphs narrow the search for odd holes. Results are reported for the performance of the three new solvers for the MWIS problem that demonstrate that the third, hybrid solver outperforms its clique-cover-based ancestors and, in some cases, the best current open-source solver. The techniques for narrowing the search for odd holes are shown to provide a polynomial-time reduction in the size of the input required to decide the perfection or imperfection of a graph.

The rapid growth of new wireless and mobile devices accessing the internet has led to an increase in the demand for multimedia streaming services. These home-based wireless connections require efficient distribution of shared network resources which is a major concern for the transport of stored video. In our study, a set-top box is the access point between the internet and a home network. Our main goal is to design a set-top box capable of performing network flow control in a home network and capable of quality adaptation of the delivered stream quality to the available bandwidth. To achieve our main goal, estimating the available bandwidth quickly and precisely is the first task in the decision of streaming rates of layered and scalable multimedia services. We present a novel bandwidth estimation method called IdleGap that uses the NAV (Network Allocation Vector) information in the wireless LAN. We will design a new set-top box that will implement IdleGap and perform buffering and quality adaptation to a wireless network based on the IdleGap’s bandwidth estimate. We use a network simulation tool called NS-2 to evaluate IdleGap and our ActiveSTB compared to traditional STBs. We performed several tests simulating network conditions over various ranges of cross traffic with different error rates and observation times. Our simulation results reveal how IdleGap accurately estimates the available bandwidth for all ranges of cross traffic (100Kbps ~ 1Mbps) with a very short observation time (10 seconds). Test results also reveal how our novel ActiveSTB outperforms traditional STBs and provides good QoS to the end-user by reducing latency and excess bandwidth consumption.

Thesis (doctoral)--Georg-Augusts-Universität zu Göttingen, 1910. / Vita. Includes bibliographical references.