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The research literature is replete with relatively small scale studies investigating various theories of reading. This research is often exploratory rather than confirmatory in nature. To avoid such limitations, samples from a large data base were used to examine causal models based on the Goodman theory of reading and the concepts of process and product comprehension. Two separate causal models were created using the following variables: graphic similarity, sound similarity, acceptability with prior text, acceptability with following text, acceptability or correction, the retelling score for the text read, the Comprehensive Tests of Basic Skills Vocabulary and Comprehension scores, and the Degrees of Reading Power (DRP) scores. The sample for one model consisted of 448 Grade Two to Grade Five students enrolled in a Chapter I program in the southwestern United States. The sample for the second model consisted of only the Grade Four and Grade Five students from the larger sample since DRP scores were not available for other students. In the hypothesized models graphic and sound similarity, and acceptability with prior and following were posited to load on a latent factor representing the unitary dimension of reading which in turn was posited to be causally related to process and product variables. Process variables included the acceptable or corrected score (RMI comprehending score) and the DRP score. Product variables included the CTBS scores and the retelling score. Product variables were posited to be dependent upon process variables. Analysis was conducted using the LISREL program. For both models causal pathways were dropped between process and product comprehension variables but were retained between the latent variables of reading and process and product comprehension. In addition, the DRP score loaded on product comprehension more than on process comprehension while retelling loaded more on process comprehension than product comprehension. Variables relating to the Goodman theory appeared to be more interrelated than those external to the theory. Implications for the uses of causal modeling and the constructs of process and product comprehension are discussed.

A new Maximum Likelihood Criterion (MLE) suitable for data which are recorded at unequal time intervals and contain auto-correlated errors is developed. Validation of the new MLE criterion has been carried out both on a simple two - parameter reservoir model using synthetical data and on a more complicated hillslope model using real data from the Pukeiti Catchment in New Zealand. Comparison between the new MLE criterion and the Simple Least Squares (SLS) criterion reveals the superiority of the former over the latter. Comparison made between the new MLE and the MLE for auto-correlated case proposed by Sorooshian in 1978 has shown that both criteria would yield results with no practical difference if equal time interval data were used. However, the new MLE can work on variable time interval data which provide more information than equal time interval data, and therefore produces better visual results in hydrologic simulations.

published_or_final_version / Civil and Structural Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / abstract / Mathematics / Master / Master of Philosophy

published_or_final_version / Civil Engineering / Master / Master of Philosophy

published_or_final_version / Industrial and Manufacturing Systems Engineering / Master / Master of Philosophy

A new mathematical model for the fundamental mode of a propagating Gaussian beam is presented. The model is two-fold, consisting of a mathematical expression and a corresponding geometrical representation which interprets the expression in the light of geometrical optics. The mathematical description arises from the (0,0) order of a new family of exact, closed-form solutions to the scalar Helmholtz equation. The family consists of nonseparable functions in the oblate spheroidal coordinate system and can easily be transformed to a different set of solutions in the prolate spheroidal coordinate system, where the (0,0) order is a spherical wave. This transformation consists of two substitutions in the coordinate system parameters and represents a more general method of obtaining a Gaussian beam from a spherical wave than assuming a complex point source on axis. Further, each higher-order member of the family of solutions possesses an amplitude consisting of a finite number of higher-order terms with a zero-order term that is Gaussian. The geometrical interpretation employs the skew-line generator of a hyperboloid of one sheet as a ray-like element on a contour of constant amplitude in the Gaussian beam. The geometrical characteristics of the skew line and the consequences of treating it as a ray are explored in depth. The skew line is ultimately used to build a nonorthogonal coordinate system which allows straight-line propagation of a Gaussian beam in three-dimensional space. Highlights of the research into other methods used to model a propagating Gaussian beam--such as complex rays, complex point sources and complex argument functions--are reviewed and compared with this work.