The purpose of this project was to investigate the method of discrete least squares polynomial approximation and to provide an extension of the method which would allow for a reasonable data-fit while lowering the number of undetermined coefficients. Also, computer programs were to be provided so that one may use the extended method. This project is an outgrowth of work done by Dr. R. De an Riess, Mathematics Department, V.P.I.S.U. There exist several areas of investigation of the theory and some extensions of the computer programs which appear to merit future effort. Possible investigations of the theory include the interpolation result that was mentioned in the discussion of the extended problem, and error bound results. Possible extensions of the programs include the introduction of decision making capabilities so that the user need only specify the data and a tolerance level to achieve a good approximation, and the implementation of the extended programs on the central system. / Master of Science

A kinetic study of the suprafacial [1,5]-sigmatropic phenyl rearrangements of 3,4-bis- (para-substituted)-1,2,5-triphenyl-2,4- cyclopentadien-1-ols to 3,4-bis-(para-substituted)-2, 2,5-triphenyl-3-cyclopenten-1-ones, where the substituent were, t-butyl, methyl, hydrogen, chloro and bromo, has been performed at 180, 190, 200 and 210 ± 0.2° in tetraethylene glycol. The rearrangement was observed to be first order throughout the temperature range investigated, and the rate constants (k) at the temperatures used were found to be 8.057, 2.143, 2.930 and 6.456 x 10⁻⁴ sec⁻¹ for the t-butyl substituent; 4 7.700, 2.110, 3.434, and 6.581 x 10⁻⁴ sec⁻¹ for the methyl substituent; 0.909, 2.166, 3.678 and 6.448 x 10⁻⁴ sec⁻¹ for the unsubstituted alcohol; 1.469, 2.992, 5.989 and 11.12 x 10⁻⁴ sec⁻¹ for the chloro substituent; and 1.955, 3.215, 6.215 and 13.01 x 10⁻⁴ sec⁻¹ for the bromo substituent, respectively. . Calculations of the activation energy of this phenyl [1,5]-sigmatropic shift from the Arrhenius equation give values of 28.71, 30.31, 28.01, 29.38 and 27.49 kcal·mol⁻¹ for the above substituents respectively, while ΔH^‡ these phenyl migrations were 27.78, 29.39, 27.93, 28.45 and 26.56 kcal·mol⁻¹ respectively. ΔS^‡ values were also calculated to be -16.6, -13.1, -16.1, -14.0 and -17.8 eu, respectively for a mean temperature range of 453-483 ± 0.2°K. The isokinetic temperature was calculated to be 320°. Calculated rho (ρ) values for the sigmatropic migrations were -0.813, -0.400, -0.690 and -0.658 at 180, 190, 200 and 210 ± 0.2°C. These results are used to discuss both the mechanism of this rearrangement and the transition state for rearrangements in the pentaphenylcyclopentadienol system. Ina much broader sense these results and the results of previously documented sigmatropic rearrangements exhibiting electronic influences were used to formulate a general scheme to predict the outcome of those sigmatropic rearrangements that entail an electronic effect as seen in the rates of the above reactions. This scheme used as its basis the transition state approach invoking inductive and mesomeric arguments to rationalize the observed rates of the sigmatropic rearrangements of this dissertation, those of previously documented sigmatropic rearrangements and finally to predict a relative rate of rearrangements in general. Finally a mass spectral investigation of the fragmentation patterns of 1-para-phenylsubstituted 2,3,4,5-tetraphenyl-2,4-cyclopentadien-l-ols and 3,4-bis(para-substituted phenyl)-1,2,5-triphenyl-2,4- cyclopentadien-1-ols was undertaken. A continuum of two super imposable pathways with the choice of the major decomposition mode being determined by the electron donating or withdrawing ability of the substit- vent was established. Linear free energy relationships for mass spectral decomposition were presented as well as a justification for this behavior. / Ph. D.

Computer Aided Design systems intended for three dimensional solid modelling have traditionally used geometric representations incompatible with established representations in computer vision. The utilization of object models built using these systems require a representation conversion before they can be used in automatic sensing systems. Considerable advantages follow from building a combined CAD and sensing system based on a common geometric model. For example, a library of objects can be built up and its models used in vision and touch sensing system integrated into an automated assembly line to 'discriminate between objects and determine- orientation and distance. This thesis studies a representation scheme, the dual spherical representation, useful in geometric modelling and machine recognition. We prove that the representation uniquely represents genus 0 polyhedra. We show by,example that our representation is not a strict dual of the vertex connectivity graph, and hence is not necessarily ambiguous. However, we have not been able to prove that the representation is unambiguous. An augmented dual spherical representation which is unique for general polyhedra is presented. This graph theoretic approach to polyhedra also results in an elegant method for decomposition of polyhedra into combinatorially convex parts. An algorithm implementation details and experimental results for recognition of polyhedra using a large field tactile sensor are given. A theorem relating the edges in the dual spherical representation and the edge under perspective projection is proved. Sensor fusion using visual and tactile sensory inputs is proposed to improve recognition rates. / Master of Science

Surface and bulk properties have been studied in terms of composition and morphology of siloxane containing block copolymers and their blends with homopolymers. X-ray Photoelectron Spectroscopy (XPS) has been used to obtain the compositional information from the top 60 angstroms or so at the surface. Transmission Electron Microscopy (TEM) was utilized to probe the bulk morphology. An attempt is made to compare the bulk and the surface and find possible mechanisms governing them. It is found that solvent-cast neat block copolymers have a uniform layer at the surface that is rich in siloxane whereas their bulk has a microphase-separated domain structure. In case of blends, siloxane enrichment is quite pronounced even at bulk concentrations as low as 0.05% w/w siloxane. Amount of surface siloxane as a function of bulk content is studied with the help of XPS. At the same time, the bulk morphology of these blends is studied by TEM. The changes occurring in the surface and the bulk are found to have similar patterns. It is shown that the observed surface behavior may be related to the bulk morphology. Molecular weight of the blocks in the copolymers is found to be a very important parameter governing both the surface and the bulk properties in the neat copolymers as well as their blends. / Master of Science

The operating characteristics of a boiler prove that pressure can usually be maintained by the supply of fuel and air, regardless of the combustion efficiency; however, to achieve the desired efficiency the burning of the fuel must take place with a minimum amount of excess air. Thus the criterion for boiler operation becomes percent co. in the flue gas. With a CO₂ meter on the control board of the Number Six Boiler it became desirable to acquaint the boiler operators with the conditions in the boiler for a corresponding reading on the CO₂ meter. The percent CO₂ in the flue gas of Number Six Boiler has four effects on the operating characteristics of the boiler when operating under a steam demand of 50,000 pounds per hour. First, it effects the energy loss due to dry exit gases; second, it effects the energy loss due to unconsumed carbon in the refuse; third, it effects slagging and possible deterioration of the refractory walls in the combustion space, and last, it effects the temperature of the refuse as it is discharged from the grate. From a survey of the data obtained from the test runs a decrease in the energy loss due to dry flue gas is seen with an increase in the percentage of CO₂ in the exit gases. This indicates the desirability of operating the boiler at as high a CO₂ as possible in regard to losses occurring from dry flue gases. Similarly, the energy loss to unconsumed carbon in the refuse decreased with an increase in CO₂. Though this is contrary to results obtained in most boilers, the low CO₂, indicating a high excess air, resulted in the boiler being cooled below maximum combustion temperature; consequently, a high percentage of carbon in the refuse occurred with the low CO₂ This too indicates the desirability to operate the boiler at a high percent CO₂. The limiting factors on the maximum percent CO₂ at which the boiler can be operated, with a steam demand of 50,000 pounds per hour, occurred at 12.9 percent CO₂. At this condition the walls began to Slag. This can be harmful to the walls, eventually causing their replacement, an economical loss which would outweigh the slight advantage of increased efficiency when operating at this percent CO₂ over a long period of time. The test runs were not long enough to determine the maximum effect slag would have on the boiler walls; nevertheless, it was noted during the test that slag running off the walls caused the fuel bed to become distorted and that the slagging has necessitated replacing parts of the front wall. Another economical loss would result from the increase temperature of the refuse discharged from the grate when operating at a higher CO₂. Since the refuse is manually removed from the ash pit to the vacuum ash removal system, and since there is a limit to the temperature the operator can withstand and still remove the ashes efficiently, the hotter refuse requires a longer time to be pulled from the ash pit. An additional load of 4,000 pounds of steam per hour, therefore, must be carried over the prolonged period. The optimum percentage of CO₂ for a single boiler is that which will minimize the total losses due to dry flue gases and unconsumed carbon in the refuse and yet keep the refractory deterioration and temperature of the refuse as low as possible. The desirable percentage of CO₂ to be maintained in Number Six Boiler for operation at a load of 50,000 pounds of steam per hour is 12 percent. This allows a maximum feasible boiler efficiency of 73 percent and corresponds to an excess air of 39 percent. It is not feasible to operate the boiler above 12 percent CO₂ because of the increase cost of maintenance due to the formation of slag on the walls and the increased time required to remove the refuse. A CO₂ recorder is a desirable method of obtaining combustion efficiency when the same type of fuel is fired, but it requires periodical checks to maintain it in proper adjustment. / Master of Science

A micro mechanical finite element model to compute the overall instantaneous stiffness of fiber-reinforced composites in elastic-plastic response is presented. The model is applicable to a periodic diamond array of elastic circular fibers embedded in an elastoplastic matrix subjected to a plane stress loading. This model enforces symmetry and anti-symmetry conditions isolating the smallest unit cell and should greatly increase the speed of doing "built-inn micromechanics within a larger finite element program because of the small number of degrees of freedom (12 to 14 d.o.f.). The matrix plastic behavior is modeled using the endochronic theory without a yield surface. Various off-axis elastoplastic characteristics predicted by the mini grid for a boron/aluminum composite are presented. Comparison with experimental data and a fine grid finite element solution shows very good agreement and demonstrates the effectiveness of the mini model presented. / Master of Science

Master of Engineering

This dissertation examines characteristics of a class of semi-infinite linear programming problems designated as C/C semi-infinite linear programming problems. Semi-infinite programming problems which belong to this class are problems of the form [See document] where S is a compact, convex subset of Euclidean m space and u_i : S→R, i=1,...,n are strictly concave functions while u _n+1 : S→R is convex. Certain properties of the C/C semi-infinite linear programming problems give rise to efficient solution techniques. The solution techniques are given as well as examples of their use. Of significant importance is the intimate relationship between the class of C/C semi-infinite linear programming problems and certain convex fuzzy set programming problems. The fuzzy set programming problem is defined as [See document] The convex fuzzy set programming problem is transformed to an equivalent semi-infinite linear programming problem. Characterizations of the membership functions are given which cause the equivalent semi-infinite linear programming problems to fall within the realm of C/C semi-infinite linear programming problems. Some extensions of the set inclusive programming problem are also given. / Ph. D.

Recent developments in industrial organization and strategic management have conceptualized an industry as being composed of finer groups of firms. The cluster of firms with similar strategic behavior is called the "strategic groups". This concept has important implications for strategy researchers because it offers a systematic way to study the relationships between strategy and performance. A review of the literature on strategic groups reveals that the dynamics and performance implications of strategic groups have not been systematically studied. Thus, the major focus of this study was to examine the dynamic characteristics of strategic groups and performance implications over time, and to understand the nature and pattern of competition. To guide this study theoretically, the concepts of strategy, strategic groups, strategic group movement, and mobility barriers are defined explicitly. Under the guidance of research questions and the theory of strategic groups, three hypotheses on the strategic group dynamics were provided based on the inter-temporal stability of firm members, firm movement pathways, and contextual factors motivating changes in group membership. In addition, three hypotheses on the performance implications of strategic groups were derived from between and within-group analysis and the consequences of mobility dynamics. In order to test these hypotheses, constructs were operationalized in a multidimensional manner. Strategy was operationalized in terms of three dimensions (scope, differentiation, efficiency) each of which were found to be significant in previous research. Performance was operationalized to include the financial and growth dimensions. The data used to perform the empirical tests was obtained from COMPUSTAT II and other objective, secondary sources (e.g., annual reports and 10-K, the Annual Survey of Manufacturers). The U.S. computer equipment industry for the period 1975-1989 served as the setting for this study. Analysis results suggest that strategic groups are a relative part of the competitive structure in an industry. The mobility rate between relatively similar groups is higher than that between less similar groups. Firms that change group membership have different contextual factors than firms that do not change membership. Moreover, no significant performance difference was found among strategic groups over time. Instead, individual firm effects contribute more to explaining the performance differences. The primary contribution of this study is the integration of strategic management, industrial organization, and organization theory to provide a cohesive platform from which to understand the role and value of strategic groups in competitive strategy. / Ph. D.

Total Quality Management (TQM) has become a popular term in quality improvement management. Many organizations, however, frequently implement quality tools that are not well coordinated with the established quality principles or the managerial decisions and actions. This research focuses on studying three major quality management components: quality philosophies, interventions, and tools. The primary desired outcome of this research is to improve the understanding of TQM implementation. The means to accomplish this desired outcome included reviewing quality improvement philosophies of Deming, Juran, Feigenbaum, Crosby, and Ishikawa, and conducting multiple case studies. The eight organizations vary in their organizational type (service or manufacturing), years of experience in their TQM efforts, and their sizes (number of employees). The case studies involved interviewing the quality managers and described how they define and implement TQM. A quality improvement taxonomy, a two-dimensional matrix, is a product developed as a result of this study. The first dimension of the taxonomy describes the quality interventions--the organizational planned changes for improving quality, which are categorized by six quality checkpoints: management of upstream systems, incoming quality assurance, in-process quality management, outgoing quality assurance, proactive assurance of customer satisfaction, and the overall quality management process. The second dimension lists seventeen supporting quality management tools. They include tools such as the Input/Output Analysis, Quality Function Deployment, Competitive Benchmarking, and Statistical Process Control. Organizations can use this quality improvement taxonomy to communicate the TQM concept and to improve coordination of quality management tools with the overall TQM implementation decisions and actions. / Master of Science