The object of this study was to use the relaxation method to find the solution of cavity flow past a two-dimensional roughness element in an open channel with gravity effect included. The method developed is based on an inviscid, irrotational and incompressible flowfield, using a finite-difference representation with stream functions as dependent variables. A computer program is developed to adjust free boundaries systematically and to facilitate numerical computation. The Helmholtz-Kirchhoff cavity model is used in this study, with sixteen primary cases analyzed. The computer results are plotted and the computer listing is given. From the results, it is found that the Helmholtz-Kirchhoff model is not applicable because no finite length of cavity can be obtained. Finally, the use of the Riabouchinsky model is recommended. / Ph. D.

Quadratic minimization problems constitute a significant and important subset of optimization problems. Research has shown that a convex quadratic programming problem can be reduced to a least distance programming problem using a unique and non-singular "linear least distance transformation." A computational algorithm for determining this linear least distance transformation is presented. This algorithm uses a variation of the Cholesky factorization technique for positive definite matrices, since Cholesky factorization is known to be numerically stable. In solving the least distance programming problem it is found that certain special cases, dealing with the orthogonality property of the constraint matrix, lend themselves to a simple solution procedure. Theorems establishing the optimality of such solutions are presented. It is also found that solutions for least distance programming problems having a row orthogonal constraint matrix are easily obtained. A generalization of this result for solving a special case of quadratic programming is also presented. A QR-transformation is found to be of no use in reducing a general least distance programming problem to a row-orthogonal least distance programming problem. It is found that the column orthogonality property of the constraint matrix of a least distance programming problem does not contribute to the solution of the problem. These special cases, though useful in their own right, have limited application to the solution of a general least distance programming problem, Using generalized inverses, a new "generalized dual” of the least distance programming problem is derived. The dual problem is solvable by existing quadratic programming techniques. In addition it is shown that the generalized dual problem can be solved by Ben-Israel's modified Newton method. A special case of the generalized dual problem is considered. It is found that the least distance programming problem, having a generalized inverse of the constraint matrix as a partial isometry, is easily solved. Since it is difficult to identify this latter class of matrices) the results have rather limited applications. Finally, a convergent iterative algorithm for solving the least distance programming problem is presented. This algorithm has wide applications. It is based on a cutting plane technique, and requires the computation of an interior feasible direction at each iteration. The method of Ho and Kashyap may be used to establish this direction. The “e-method” proposed here gives an alternative for computing the feasible directions and generally requires much less computation. A few numerical examples are presented to illustrate these algorithms. / Ph. D.

The purpose of this investigation was to determine the effect of sediments in the Occoquan Reservoir on the water quality. Phosphate determination by the ascorbic acid method was first evaluated for its precision and accuracy. An assay was developed to measure the rate of nutrient phosphate release to the overlying water in a quiescent dark condition. The assay was evaluated to test for its reliability in giving valid conclusions. The assay was an attempt to provide a system similar to the actual system which could be used in the laboratory. Also, the effect of different parameters could be studied by varying conditions one at a time. In this assay, it was found that the rate of release was not affected by normal pH changes, depth of sediment, or depth of overlying water. The rate of release was found to increase with increase in temperature, phosphate content in sediments, and reduced anaerobic condition. The rate was adversely affected by high concentration of salt, drying on sediment surface, thickness of physical barrier, and reduction of bacterial activities. Flushing seemed to decrease the rate of release by a constant ratio. Under normal conditions, sediments release other nutrients besides phosphates. However, it was found that whether the sediment served as a sink or source of phosphate was governed by the critical availability concentration which was different for different sediment. A study of the properties of the reservoir sediment showed that there were variations with respect to time, station, and depth, as well as vicinity within the same station, in this reservoir. / Ph. D.

Five interrelated experiments were conducted to study aspects of the mechanisms underlying the genetic variation of mating behavior in bidirectionally selected lines of chickens. Birds utilized included the Athens-Canadian random bred population and lines that had undergone 13 and 14 generations of selection for high and low cumulative number of completed matings. The enzymatic reduction of tetrazolium by Δ5,3β hydroxysteroid dehydrogenase was employed to identify the sites of steroid biosynthesis in developing embryos of all three lines. The histochemical procedure proved insufficiently precise for determining the onset of steroidontogenesis or for quantifying steroid biosynthetic rates. Mating behavior was studied in capons, in males receiving testicular autotransplants, and in intact males. Androgen therapy was utilized and consisted of intramuscular injections of 12.4, 44.8, 89.6, or 179.2 mg. testosterone cypionate (TC). Mating behavior of intact males, as measured by the cumulative number of courts, mounts, treads, and completed matings, was greater in the high mating than in the low mating line with unselected control population being intermediate and significantly different from each of the selected lines. TC injections into capons increased the frequencies of mating behavior traits over the levels attained by birds receiving carrier oil only; 89.6 mg. TC failed to increase the mating behavior frequencies over those attained by capons receiving the 44.8 mg. TC level. Caponization decreased mating activity while testicular autotransplantation increased mating activity in the high mating line. In caponized chickens TC injections elicited courting behavior in all lines and sexual behavior in the high mating and control lines. In the low mating capons TC dosages (12.4 - 179.2 mg.) did not significantly increase the frequency of sexual behaviors. No apparent line differences were found in the time period required after TC therapy for attaining maximal behavioral responses. The duration of mating activity was affected by TC dose levels and line differences in the duration of behavioral responses were indicated. Based on the results of this series of interrelated experiments and because of the insensitivity to exogenous androgens demonstrated by the mating lines, it was suggested that selection in the high and low mating lines has been directed primarily towards an inhibitory mating center and secondarily towards a stimulatory mating center. The inhibitory mating center was presumed to operate independent of the steroid hormones, explaining the lack of response to exogenous androgens. / Ph. D.

Diazotized 3-aminopyridine adenine dinucleotide has been found to modify four sulfhydryl groups per molecule of enzyme during the complete inactivation of yeast alcohol dehydrogenase. The reaction of sulfhydryl groups was indicated by titration studies with 5,5'- dithiobis (2-nitrobenzoic acid) as well as isolation and quantification of the cysteinyl derivative released by acid hydrolysis of the modified enzyme. The cysteinyl derivative was identified as S-(3-pyridyl) cysteine. Authentic S-(3-pyridyl) cysteine was synthesized and structurally characterized for these studies. Diazonium-sulfhydryl reactions were demonstrated for a number of diazonium derivatives with cysteine, homocysteine, glutathione and mercaptoethanol at 0-4° and neutral pH. Second order rate constants were determined in reactions of these sulfhydryl compounds with diazotized l-methyl-3-aminopyridinium chloride, diazotized 3-aminopyridine adenine dinucleotide and diazotized 3-aminopyridine adenine dinucleotide phosphate. Chemical studies of the diazonium-sulfhydryl reaction of diazotized p-aminobenzoic acid with cysteine indicated the initial formation of a diazomercaptide which can then decompose to yield the thioether. / Ph. D.

Using a detector developed in a VPI-BNL collaboration, we have searched for multi-photon events from pp interactions at 300 GeV/c. We measured the multiplicity, energy and angular distributions of approximately 340,000 events. Of the 80,000 events that have been analysed, the angular distributions are consistent with photon production by known processes. The energy distribution of photons shows a rise in cross-section at approximately 150 GeV, an anomaly which can not be explained by known processes. / Ph. D.

The major purpose of this study was to determine the effectiveness of using reading strategy lessons as indicated by Reading Miscue Inventory (RMI) profiles of below average readers to increase reading proficiency. Oral reading miscues of ten below average fifth grade readers were analyzed prior to and following (a) a three month period of reading strategy lessons for the five members of the test group and (b) continuation in the regular reading instruction offered by the school for the five members of the control group. Miscues were coded according to the procedures and categories of the RMI, written by Yetta M. Goodman and Carolyn L. Burke (1972). By comparing the pre- and post RMI scores of the test and control groups, the effectiveness of reading strategy lessons used with the test group was determined. Questions investigated by this study included those concerned with both quantity and quality of oral reading miscues. Analysis of miscue quantity indicated that miscues per hundred words of print decreased with both groups, but more with the test group. Analysis of miscue quality provided the following results: 1. Dialect and intonational miscues produced by both groups proved to be relatively insignificant to the study. 2. Although both groups showed gains in graphic and phonemic similarity, the test group made greater increases in both categories. 3. The test group increased, while the control group decreased, in percentage of miscues retaining the same grammatical function as expected responses. 4. The test group showed gains while the control group decreased in the effective use of correction strategies. 5. The test group produced much higher percentages of grammatically and semantically acceptable structures than the control group following the instructional period of the study. 6. Further, the test group increased in percentage of miscues producing no meaning change, while the control group decreased in this category. 7. In loss of comprehension, the test group decreased and the control group increased. 8. The test group produced greater percentages of miscues which indicated a strength in grammatical relationships than the control group. 9. For the test group, gains were made in all categories of the retelling score, while the control group showed losses in points attributable to story retellings. 10. The types of repeated miscues produced by both groups remained unchanged over the period of the study. It was concluded from these results that reading strategy lessons, which facilitate the reader's intuitive knowledge of language and emphasize meaning, were effective in increasing the reading proficiency of below average readers. An investigation of the effects of using initial, mid, final or all codable miscues as the basis for RMI profiles was also included in this study. The results of this investigation indicated no significant difference in the scores obtained by each of these groupings. Specific implications for educational practices and future research were obtained from the descriptive data of this study. / Ed. D.

Problem The purpose of this study was to analyze the effects of multigrade grouping on self-concept, social-emotional development, readiness development, and achievement at the kindergarten level. The need for this study arose from the mandate from the State Board of Education concerning kindergarten education in Virginia. Since school divisions may be inclined to combine kindergarten and first grade children to financially accommodate this mandate, research was needed to assure those making such decisions that there are at least no major detrimental effects on the growth of kindergarten children placed in the multigrade classes. Procedure The study encompassed the entire (N=l83) kindergarten population of Grayson County for the school year 1972-73. The experimental group consisted of (N=31) kindergarten children organized in three multigrade groups with first grade children. The control group consisted of (N=152) kindergarten children arranged in seven singly graded classes. Four instruments were used to secure data for the study. Readiness scores were secured by use of the Metropolitan Readiness Test. The Behavior Inventory was utilized in determining social-emotional development. The Stanford Early School Achievement Test was administered to determine achievement scores. The Self-Concept and Motivation Inventory furnished the scores for the comparison of self-concept. Since the entire population of kindergarten students in both the multigrade and traditional groups were used in this study, inferential statistics were inappropriate. The hypotheses were tested by comparison of population means. The differences between these means were actual differences. Conclusions The seven hypotheses tested to ascertain the effects of multigrade grouping at the kindergarten level on self-concept, social-emotional development, readiness development, and achievement were derived from the thesis that kindergarten children in a multigrade setting will develop a more positive self-concept and progress faster in the areas of social-emotional development, readiness, and achievement than kindergarten students in the traditional setting. The conclusions which emerged from this study were as follows: 1. Kindergarten children in multigrade groups score only slightly higher on self-concept than kindergarten children in traditional classrooms. 2. Kindergarten children with high self-concept score only slightly higher on social-emotional development than kindergarten children with low self-concept. 3. Kindergarten children with high self-concept score only slightly higher on readiness development than kindergarten children with low self-concept. 4. Kindergarten children with high self-concept score only slightly higher on achievement than kindergarten children with low self-concept. 5. Kindergarten children in multigrade groups score only slightly higher on social-emotional development than kindergarten children in traditional classrooms. 6. Kindergarten children in multigrade groups score only slightly higher on readiness development than kindergarten children in traditional classrooms. 7. Kindergarten children in the traditional groups score only slightly higher on total achievement than kindergarten children in multigrade groups. 8. Boys, older children, and children from small families in the multigrade groups score only slightly higher on self-concept, social-emotional development, readiness development, and achievement than boys, older children, and children from small families in the traditional groups. 9. The results of this study lead to the conclusion that the types of classroom organization studied (single grade or multigrade) have little or no effect on self-concept, readiness, social-emotional development or achievement. There would appear to be other variables that result in the development of these factors. / Ph. D.

This study was designed to investigate changes, if any, in the curriculum design of reading and/or language arts and arithmetic, student scheduling, student attendance, staffing patterns, expenditure patterns, reporting procedures and attitudes of parents, students and teachers for three years prior to and one year following implementation of 45-15 year-round programming. A review of the current literature, at that time, revealed that four school districts met the above time criteria. The four school districts were as follows: Francis Howell School District, St. Charles County, Missouri; Mora Public Schools, Mora, Minnesota; Valley View School District, Romeoville, Illinois and the Prince William County Public Schools, Manassas, Virginia. Representatives of the four school districts were then contacted by telephone and by written correspondence as to their (1) willingness to participate and (2) the amount of data available. Only two school districts, Francis Howell and the Mora Public Schools, had sufficient data available to participate. Each school district had one elementary school (grades 1-6) which was operating on a 45-15 year-round schedule. They were the Becky David Elementary School from the Francis Howell School District and Fairview Elementary School from the Mora Public Schools. A Data Collection Instrument was developed and mailed to the two selected school districts. In addition to the Data Collection Instrument, telephone conversations end written communication, district evaluation reports were reviewed and curriculum guides for language arts and/or reading and arithmetic were reviewed. Curriculum guide(s) were developed by both elementary schools. A change in curriculum design occurred when the two schools developed curriculum guide(s) and moved to 45-15 year-round scheduling. The curriculum guide for Becky David Elementary School was designed around a continuous progress concept. Fourteen levels of work for language arts and arithmetic replaced the traditional graded classroom situation. The curriculum guides for reading and arithmetic for Fairview Elementary School were developed around a self contained graded classroom situation. The curriculum guides for reading and arithmetic in each grade did utilize sessions, levels and units. Reporting procedures to parents were modified for the above curriculum areas after 45-15 year-round scheduling was begun. The pupil/teacher ratio for Becky David Elementary School decreased while the pupil/teacher ratio for Fairview Elementary School increased after 45-15 year-round progranuning. Both school districts' budgets increased each year after year-round school operations were begun. District expenditures for curriculum development, in-service education for teachers, instructional materials and instructional equipment were not available for Becky David Elementary School. District expenditures for Fairview Elementary School for instructional equipment and materials and curriculum development were available. The expenditures for instructional. materials and equipment and curriculum development increased with 45-15 year-round programming. A majority of teachers, students and parents of Fairview Elementary School and Becky David Elementary School expressed a favorable attitude toward 45-15 year-round scheduling as determined by appropriate questionnaires. Student attendance remained stable over the five year period of this study. / Ed. D.

A derivation of the equations which govern the deformation of an arbitrarily curved and twisted space beam is presented. These equations differ from those of the classical theory in that extensional effects are included. Other departures from the previous theory are that the strain - displacement relations are derived and that the expressions for the stress resultants are developed from the strain - displacement relations instead of assuming that the resultants are proportional to changes in the curvatures. It is shown that the torsional stress resultant obtained by the classical approach is basically incorrect except when the cross-section is circular. Using a vector approach the exact expressions for the curvature components of a deformed space beam are developed. Because inextension of the beam is not assumed an additional term appears in each of the linearized curvature expressions. These expressions are utilized in the derivation of the strain - displacement relations. The normal and shearing physical components of the strain tensor are given. These relations are not restricted to beams whose cross-sectional dimensions are very small compared to the radius of curvature. Next, a development of the stress resultants is presented. Effects arising from the initial twist of the beam are obtained which are not reflected in the classical theory. Finally, the six equilibrium equations are derived using a vector approach. The governing equations are given in the form of twelve first-order differential equations. A numerical algorithm is given for obtaining the natural vibration characteristics and example problems are presented. / Ph. D.