Study of covering properties in fuzzy topology

This work is devoted to the study of covering properties both in L-fuzzy topological spaces and in smooth L-fuzzy topological spaces , that is the fuzzy spaces in Sostak's sense, where L is a fuzzy lattice . Based on the satisfactory theory of L-fuzzy compactness build up by Warner, McLean and Kudri, good definitions of feeble compactness and P-closedness are introduced and studied. A unification theory for good L-fuzzy covering axioms is provided. Following the lines of L-fuzzy compactness, we suggest two kinds of L-fuzzy relative compactness as in general topology, study some of their properties and prove that these notions are good extensions of the corresponding ordinary versions. We also present L-fuzzy versions of R-compactness , weak compactness and 0-rigidity and discuss some of their properties. By introducing 'a-Scott continuous functions', a 'goodness of extension' criterion for smooth fuzzy topological properties is established. We propose a good definition of compactness, which we call 'smooth compactness' in smooth L-fuzzy topological spaces. Smooth compactness turns out to be an extension of L-fuzzy compactness to smooth L-fuzzy topological spaces. We study some properties of smooth compactness and obtain different characterizations. As an extension of the fuzzy Hausdorffness defined by Warner and McLean, 'smooth Hausdorffness' is introduced in smooth L-fuzzy topological spaces. Good definitions of smooth countable compactness, smooth Lindelofness and smooth local compactness are introduced and some of their properties studied

A fractal approach to mixing-microstructure-property relationship for rubber compounds

The research is concerned with· exploration of the utility of fractal methods for characterising the mixing treatment applied to a rubber compound and also for characterising the microstructure developed during mixing (filler dispersion). Fractal analysis is also used for characterisation of the fracture surfaces generated during tensile testing of vulcanised samples. For these purposes, Maximum Entropy Method and Box Counting Method are developed and they are applied to analyse the mixing treatment and the filler dispersion, respectively. These methods are effectively used and it is found that fractal dimensions of mixer-power-traces and fracture surfaces of vulcanised rubber decrease with the evolution of mixing time while the fractal dimension of the state-of-mix (filler dispersion) also decreases. The relationship of the fractal dimensions thus determined with conventional properties, such as viscosity, tensile strength and heat transfer coefficient are then explored For example, a series of thennal measurements are carried out during vulcanisation process and the data are analysed for determining the heat transfer coefficient Nuclear Magnetic Resonance is used to obtain the properties of bound rubber and a quantitative analysis is also carried out and possible mechanisms for the relationships between the parameters are discussed based on existing interpretations. Fmally, the utility of the fractal methods for establishing mixing-microstructureproperty relationships is compared with more conventional and well established methods. For this purpose, the fractal dimension of the state-of-mix is compared to conventional methods such as the Payne Effect, electrical conductivity and carbon black dispersion (ASTM D2663 Method C). It is found that the characterisation by the fractal concept agrees with the conclusions from these conventional methods. In addition, it becomes possible to interpret the relationships between these conventional methods with the help of the fractal concept

Foundations of Quantum Theory: From Classical Concepts to Operator Algebras

Quantum physics; Mathematical physics; Matrix theory; Algebr

Announcement of courses

"June 20, 1958."The University catalog is issued in three parts. The first part, The University-Its Schools and Colleges, contains general information on administration, facilities, regulations, requirements for admission, and on the various schools and colleges. The second part, Announcement of Courses, contains descriptions of all courses of instruction for the schools and colleges for the divisions at Columbia and lists officers of administration and instruction. The third part, entitled Aids and Awards, contains information on scholarships, loan funds, employment, and other aids to students.--Foreword

General catalog, with description of courses, 1970-71

"March 24, 1970."The General Catalog of the University of Missouri - Columbia, contains information on administration, facilities, programs of study and degrees offered, regulations and requirements for admission, as well as facts about student welfare and activities. It includes a description of all courses offered in the schools and colleges for the divisions at Columbia, and lists the officers of administration and faculty members.--Foreword.Revised to July 1, 1969