Digitized by Kansas Correctional Industries

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Digitized by Kansas Correctional Industries

Digitized by Kansas Correctional Industries

Treating the activated complex for unimolecular dissociation as uncoupled fragments simplifies the calculation of transition-state frequencies in the quasi-equilibrium-theory formulation of an isotopic rate-constant ratio. The general method is applied to the specific case of the intramolecular kinetic isotope effect in decarboxylation of malonic acid. The fragment models are further simplified by means of the “cut-off” approximation of Sterm and Wolfsberg. These model calculations are in agreement with the presently available experimental results. Applicability to reactions involving simultaneous multiple bond rupture or formation is noted.

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A graph may he drawn in many different ways. We investigate how to draw a graph nicely, in the sense of being visually pleasing. We discuss the history of this field, and look at several algorithms for drawing graphs. For planar graphs this problem has been algorithmically solved: that is, there is an algorithm which takes a n vertex planar graph and places the vertices at some of the nodes of an n-2 by 2n-4 array so that each edge of the planar graph can be drawn with a straight line. We describe in detail one particular implementation of this algorithm, give some examples in which this embedding is pleasing, and give a number of examples in which this grid embedding is not as visually pleasing another drawing of the same graph. For the more difficult problem of drawing a nonplanar graph, we investigate a spring based algorithm. We give a number of examples in which this heuristic produces more pleasing drawings than those produced by the planar embedding and a few cases where it fails to do so. / Graduation date: 1997

Computing eigenpairs of a matrix corresponding to a specific geometry in the complex plane is an important topic in real time signal processing, pattern recognition, spectral analysis, systems theory, radar, sonar, and geophysics. We have studied the matrix sign and matrix sector function iterations to extract the eigenpairs belonging to various geometries without resorting to computationally expensive eigenanalysis methods. We propose a parallelization of an existing matrix sign function algorithm, which was implemented on a Meiko CS-2 multiprocessor. We obtain a fast and stable algorithm for computing the matrix sector functions using Halley's generalized iteration formula for solving nonlinear equations. We propose a parallel iterative algorithm to compute the principal nth root of a positive definite matrix using Gauss-Legendre integration formula. Furthermore computing functions of square matrices is also an important topic in linear algebra, engineering, and applied mathematics. A parallelization of Parlett's algorithm for computing arbitrary functions of upper triangular matrices is introduced. We propose a block-recursive and a parallel algorithm for fast and efficient computation of functions of triangular matrices. The parallel complexity and cache efficiency of these algorithms for computers with two levels of memory are also analyzed. / Graduation date: 1996

There are many situations in which contact between two bodies is at a single point so there can be no tensile (force). This form of contact only provides a single degree of restraint, and is defined as a unidirectional point contact. The analysis of Reuleaux shows that four suitably placed frictionless point contacts are required to completely restrain an object in a plane. The objective of the thesis is to allow user-placement of three contacts and to find acceptable range for placement of the fourth. If the fourth contact is anywhere in the range, the four forces fulfill the requirement for total planar restraint, i.e. all translations and rotations in a plane are prevented. This project considers the directions and placement allowed for the fourth force but does not take into consideration the magnitudes or friction coefficients of any of the four forces. In this research a program named Planar Restraint Design Assistant (PRDA) was developed to analyze positions of the four restraint forces. A planar object is first specified by the user; the program accepts AutoCAD images for more complex objects. For three given restraint forces PRDA determines a range of the fourth force such that total restraint is achieved. In addition, PRDA allows the user to arrange three restraint forces until a desired range of the fourth restraint force is obtained. Results are shown in visual form with accompanying graphs for numerical interpretation. A program user's guide and a program learning guide are provided as shown in the report with illustrative examples. Program source code in QuickBASIC is included in the report. / Graduation date: 1995

Thesis (M.S.)--Kutztown University of Pennsylvania, 2000. / Source: Masters Abstracts International, Volume: 45-06, page: 2806. Typescript. Abstract precedes thesis title page as [4] preliminary leaves. Includes bibliographical references (leaves 109-112).