Physical Sciences and Mathematics Commons^™

A Parameter Perturbation Technique Applied To Multipoint Iteration Functions For The Solution Of Systems Of Nonlinear Equations, Robert N. Delozier

Masters Theses

"The convergence of classical iterative procedures, when applied to a system of nonlinear algebraic or transcendental equations, is highly dependent upon a good initial approximation to the desired roots. Most of the classical iterative schemes have convergence factors between one and two. In this paper iterative schemes of order two and greater are studied in connection with a parameter perturbation process. The parameter perturbation process relaxes the restrictions on the choice of initial values. The procedure divides each problem into a number of subsidiary problems. Each subsidiary system of equations is then solved until a solution is found to the …

Carcinostatic Sulfonic Acid Esters Of Selected 1,4-Diols, Robert A. Earl

Masters Theses

Introduction

The purpose of this research was to prepare the bisarylsulfonic acid esters of 1,4-butanediol and 1,4-but-2-ynediol.

This series of compounds is of interest because of the antitumor activity exhibited by the bismethanesulfonates of 1,4-butanediol and 1,4-but-2-ynediol. The compounds which were prepared were submitted to Cancer Chemotherapy National Service Center for evaluation in their anticancer program.

It was hoped that the compounds synthesized would be of pharmacological value. It was further hoped that the biological test data of these compounds would demonstrate a correlation between types of substituents on the aromatic nucleus and the degree of activity of the compounds. …

Linear And Quadratic Programming With More Than One Objective Function, William John Lodholz

Masters Theses

"A computational procedure is presented for determining optimal solutions to the linear and quadratic programming problem when there is more than one objective function subject to linear constraints. In general a unique solution does not exist and a set of "best" or "efficient" points is determined and presented in graphical or tabular form. To solve the mathematical programming problems the simplex method is used for linear objective functions and Wolfe's method is used for quadratic objective functions"--Abstract, page ii.

I. An Investigation Of The Organic Compounds In The Media And Mycelium Of Naucoria Confragosa. Ii. Study Of The Extra-Cellular Pigments Of An Unknown Fungus, Yueh-Tsun Chen

Masters Theses

"The fungal metabolites excreted into the culture fluid by basidiomycetes growing on synthetic glucose media as well as formed in the mycelia of the organisms were investigated in this thesis. Earlier unpublished work had shown that Maucoria confragosa excreted into the medium compounds which were thought to be phenols. Insufficient material was recovered from an ethyl acetate extract of the medium in the present study for further investigation. Colorimetric methods were employed both for the quantitative estimation of reducing sugar not consumed by the microorganisms as well as for a measure of the total organic solids present in the spent …

Petrology And Mineralogy Of The "Old Workings Area," El Salvador, Chile, Bertis James Vander Schaaff

Masters Theses

"The 'Old Workings Area,' so called for its early mining by the Incas, is located 4 1/2 miles northeast of the El Salvador Porphyry copper deposit, the third largest copper producer in Chile. The area mapped in this study is shown to consist of rhyolite pebble conglomerate, two volcanic flows, andesite and rhyolite porphyry, and two intrusions. Quartz porphyry and tourmaline-bearing breccia. Petrographic study of surface and drill core rock samples confirms the field nomenclature used for the five rock types. All of the rock types are altered, but the quartz porphyry and andesite are the most intensely altered. Both …

Separation Of Optical Isomers By Solvent Extraction, George Truett Mccloud

Masters Theses

The purpose of this research was to develop a solvent extraction method to resolve optical isomers. Earlier work²⁵ done in this laboratory has indicated that partial resolution had been obtained by using D(+)-diisopropyl tartrate and water as the immiscible solvent system. Further work done by the author indicates that this method can be used to partially resolve racemic modifications. Before this method is discussed in detail, a summary of the known methods of resolution should be presented.

Investigations Of Neutron Collimators And Detector Systems Used In A Neutron-Capture Internal-Conversion Apparatus, William Charles Johnston

Masters Theses

Preface

During the past six decades considerable effort has been devoted to investigating and explaining the phenomena associated with the atomic nucleus. However, many important features of the nucleus still are not understood. Among these are such fundamental aspects as the structural composition of the nucleus, the nature of the forces between nucleons, and several of the basic processes that occur among the nuclear constituents. The goal of nuclear physics is to construct a unified theory which is able to explain all nuclear phenomena.

The experimentalist contributes toward this objective by gathering and classifying extensive amounts of experimental data in …

The Reaction To Ketoacylhydrazones With Lead Tetraacetate, Lavern M. Weisenberger

Masters Theses

Introduction

It has been shown that ketohydrazones react with lead tetraacetate to give azoacetates in good yields (11) according to the following equation:

R₂C=N-NH-R + Pb(OAc)₄ → R₂C(OAc)-N=N-R + Pb(OAe)₂ + HOAc

The reaction of the structurally related 4,4- disubstituted ketosemicarbazones with lead tetraacetate quite unexpectedly gave carbamates in good yields (10) presumably according to the following equation:

R₂C=N-NH-Co-NR₂ + Pb(OAc)4 → R₂C-O-CO-NR₂ + N₂ + Pb(OAc)₂ + HOAc

CO

ı

CH₃

Angular Correlation Of Co60, Henry Kuhlman

Masters Theses

Chapter I

Introduction

The probability that a radioactive nucleus will emit a gama ray may depend on the angle between the nuclear spin axis and the direction of emission. The radiation pattern of a sample of randomly oriented nuclei is isotropic. An anisotropic pattern may be observed if the nuclear spin axes are aligned.

A Measurement Of The Spin Relaxation Time Of Optically Pumped Rubidium Vapor, Robert Oliver Breault

Masters Theses

Chapter I

The Problem and Atomic Energy Levels

In 1949 Francis Bitter proposed a method for optcally detecting radio frequency resonance. That same year Alfred Kastler, Fcole Normale Superiéure, Paris, France, introduced a technique, which he called "Optical Pumping", of concentrating atoms in some of the Zeeman sublevels of one of the hyperfine state levels of the ground state. These two experiments are the basis of research involving optical methods of atomic orientation and of magnetic resonance.

A Study Of The Effect Of The Crystal Orientation On The Internal Friction Of Magnesium Single Crystals., Robert Ray Nothdurft

Masters Theses

"The method of growing, etching, and cutting magnesium single crystals is described in some detail. Ten single crystals of magnesium of different orientations were prepared and studied. The internal friction and relative Young’s modulus were measured for each specimen as a function of applied stress on a quartz composite oscillator. The effect of the orientation on the strain amplitude independent decrement, the strain amplitude dependent decrement and the ratio of the strain amplitude dependent decrement to the relative Young's modulus is compared to the theory of the pinned dislocation model of Granato and Lücke"--Abstract, p. ii

Minimization Of Boolean Functions., Don Laroy Rogier

Masters Theses

"A systematic computational procedure is presented for simplifying a Boolean function. The procedure is an extension of the methods presented by W. V. Quine and E. J. McCluskey. Jr. Specific attention is given to the combined use of linear programming and dominance arguments to find a minimum sum of products for large cyclic prime implicant tables"--Abstract, p. ii

Determination Of The Fast Flux Of U.M.R. Reactor, Dave Vibhakar Ratilal

Masters Theses

"Measurements of fast flux of University of Missouri at Rolla, Reactor have been made using: (n,p) reactions in Mg²⁷ and Ni⁵⁸ and (n,α) reactions in Al²⁷. The effective activation cross sections at respective threshold energies for various foils have been obtained from AERE and AECL reports and from literature published by various investigators. A RIDL 400 channel analyzer was used for counting"--Abstract, page 1.

Nature And Lateral Variation Of Lost Rock Limestone In The Tri-State Zinc-Lead District., Adnan A. Saadallah

Masters Theses

"The nature and lateral variation of a host rock limestone in the Tri-State zinc-lead district were petrographically studied within a single horizon, the M bed. This bed is a massive crinoidal limestone in the Tri- State district of southwestern Missouri, northeastern Oklahoma and southeastern Kansas and is a part of the Mississippian Keokuk Formation.

One hundred and twenty specimens from this bed were collected underground from six pull drifts in five mines: West Side, Grace B, Big John, Little Greenback, and Mudd Mines. The specimens were collected at regular intervals, usually ten to twenty feet, beginning at the edge of …

Study Of The Ste. Genevieve Formation At Selected Localities In Southern Illinois And Western Kentucky, Mahlon Jack Apgar Reinhard

Masters Theses

"The carbonate rocks of the Mississippian Ste. Genevieve Formation were studied megascopically in four quarries--Cave in Rock, Franklin, Three Rivers, and Fredonia Valley--within a small area of the Illinois-Kentucky fluorspar district and in a drill-core from the Cave in Rock Quarry. The rocks were studied microscopically in seventy-four thin sections prepared from samples from the quarries and the drill-core. The Ste. Genevieve Formation is typically an extremely oolitic, fragmentally fossiliferous limestone which is very light gray to white. The megascopic descriptions of the quarry exposures are presented as measured sections and columnar sections. A detailed log of the drill-core is …

A Numerical Study Of Van Der Pol's Nonlinear Differential Equation For Various Values Of The Parameter E., Charles C. Limbaugh

Masters Theses

"This paper briefly reviews the geometric concepts associated with nonlinear differential equations and then proceeds to a study of the homogeneous van der Pol equation. After studying the method of Kryloff and Bogoliuboff for small values of the parameter €, the author makes a numerical study of the equation using Hamrning's Method for the numerical solution. Several trajectories and the phase plane are shown for E = 0.1, 1.0, and 5.0. The author then studies one of the analytic theories, i.e., the method of Cartwright and Littlewood, and indicates some of the other analyses for large €"--Abstract, p. ii

Aging Of The Dielectric Properties Of Some Perovskite Ceramics, Hector Troche-Maldonado

Masters Theses

"The effect of aging upon the dielectric constant and the dissipation factor were investigated for a number of lead titanate zirconate ceramics of varying composition. The ceramics investigated have a perovskite type structure. The materials chosen all have tetragonal symmetry at room temperature but are close in composition to materials of rhombohedral symmetry.

Empirical relations were determined for each specimen giving the rate of aging of the dielectric constant (K) and loss factor in terms of the frequency (f) and the elapsed time (t). The range of frequency was l kcps to l mcps; the range of elapsed time was …

An Investigation Of The Sensitized Fluorescence Of The Mercury-Sodium And The Cesium-Rubidium Systems., Joseph Edward Hueser

Masters Theses

"The experimental apparatus and techniques used for the study of sensitized fluorescence are discussed. In this study both glass and metal absorption cells were employed. Included also is a discussion of the transitions which 11 occur in the mercury-sodium and the cesium-rubidium systems, which were the two systems investigated. Both photographic and photometric techniques were used as means of detecting the sensitized fluorescence. The actual experimental apparatus used are discussed together with conclusions to be drawn and recommendations to be made from the individual experiments. The purpose of the experiments was to better understand the energy exchange processes in a …

Construction And Test Of Equipment For Use In Ultrasonic Pulse Echo Studies., Charles Joseph Reinheimer

Masters Theses

"An ultrasonic pulse generator was constructed with a variable pulse width ranging from 4 microseconds to 10 milliseconds and a repetition period varying from 15 milliseconds to 5 seconds. The oscillator had an almost continuous range from 500 kilocycles to 18 megacycles per second.

Its applicability in studies of internal friction of metals was demonstrated with a single crystal aluminum sample"-- Abstract, p. vi

Estimation And Tabulation Of Bias Coefficients For Regression Analysis In Incompletely Specified Linear Models., Harry Kerry Edwards

Masters Theses

"There is often some uncertainty as to the exact number of predictors to include in the specification of the linear model when the theory of regression analysis is applied to specific data. To aid the experimenter in defining the correct number of predictors, a bias function that estimates the deviation of a linear model from the true model has been defined.

The writer has derived an accurate, economical, numerical method for calculating the bias function associated with an incompletely specified linear model and has tabulated bias function coefficients for a reasonable number of doubtful predictors"--Abstract, page ii.

A Study On Estimating Parameters Restricted By Linear Inequalities, William Lawrence May

Masters Theses

“A comparison of two methods for estimating parameters restricted by linear inequalities in linear statistical models was made.

The first method consisted of finding the least squares estimates of the parameters disregarding the restrictions, and then forcing those parameters that were outside of their allowable ranges to the nearest endpoints of those ranges.

The second method made use of quadratic programming to minimize the same sum of squares that the first method minimized while keeping the parameters inside or at the endpoints of their allowable ranges.

The quadratic programming gave better estimates of the parameters in the sense that the …

A Study Of A Method For Selecting The Best Of Two Or More Mathematical Models, August J. Garver

Masters Theses

"A method for selecting the best in some sense of two or more mathematical models is investigated in this study. The method is that of using part of the data to estimate parameters and using the resulting equation to predict the additional data which are then compared with the existing data not used in estimating the parameters. In particular the effects produced on the method by the number and location of points used in estimating the parameters and the criterion for determining the best fit are investigated. It was concluded from the results of an empirical investigation that the success …

A Study Of Stability Of Numerical Solution For Parabolic Partial Differential Equations., Tsang-Chi Huang

Masters Theses

"Parabolic partial differential equations hold a very important position in science and technology since they are encountered frequently in the solution of diffusion and heat-conduction problems. Theoretically, it is possible to solve many of these equations by analytical methods, but the modern development of mathematics has revealed that there are numerous difficulties in obtaining the solution. Numerical solutions for most applied problems of a parabolic partial differential equation type are practically necessary, thus methods for numerical solution or approximate solution became more important. Since numerical results are required for most applied problems of a parabolic partial differential equation type a …

A Study Of Methods For Estimating Parameters In The Model Y(T) = A₁E-P₁T + A₂E-P₂T + Ε, Gerald Nicholas Haas

Masters Theses

“In this study, methods for estimating the unknown parameters A₁, A₂, p₁, and p₂ in the model
y(t) = A₁e^-p₁t + A₂e^-p₁t + ϵ
where ϵ ~ N(0, σ) are investigated. In the model investigated, A₁, A₂, p₁, and p₂ are positive.

Four methods, one non-iterative method and three iterative methods, for estimating parameters in this model are investigated. The non-iterative method is known as Prony's Method. The three iterative methods are (1) the Modified Gauss …

The Dielectric Properties Of Thallium Nitrate., Gene E. Gowins

Masters Theses

"The purpose of this research was to investigate the dielectric behavior of thallous nitrate and to determine whether it belongs to space group Pbnm or to Pbn2.

The growing of single crystals of thallous nitrate which are suitable for dielectric measurements is difficult because the crystals are prone to initiate a dendritic growth habit. In the present work single crystals of thallous nitrate were obtained, however, by slow evaporation of an aqueous solution at 55 degrees centigrade. The crystals were plates, not larger than 8 x 8 x 2 mm, whose principal faces were subsequently indentifled as (001) planes. The …

On A Numerical Solution Of Dirichlet Type Problems With Singularity On The Boundary., Randall Loran Yoakum

Masters Theses

No abstract provided.

Longitudinal Spin Relaxation Of Optically Excited Rubidium., John Robert Martin

Masters Theses

"This thesis is intended to be a guide to the theory and experimental procedures of optical pumping in one of its most usual applications. It is also intended to be an extension of the work done here by Steinbruegge¹ in 1963 along with several significant changes and improvements in experimental techniques. A study is made of the optical pumping of rubidium vapor, and results are given stating the most efficient methods with which to produce large populations of optically oriented rubidium atoms, and thereby determine the relaxation properties of a given rubidium system"-- Abstract, p. ii

The Reaction Of Ketosemicarbazones With Lead Tetraacetate, Thomas M. Davies

Masters Theses

Introduction

It has been demonstrated that lead tetraacetate will oxidize ketohydrazones to azoacetates in good yields (11).

R₂C=N-NH-R + Pb(OAc)₄ ------> R₂C(OAc)-N=N-R + Pb(OAc)₂ + HOAc

Since ketosemicarbazones are structurally equivalent to ketohydrazones, it was thought that the reaction of ketosemicarbazones with lead tetraacetate would proceed in a similar manner. Originally the object of this research was to prepare a series of new azo compounds related to semicarbazones by lead tetraacetate oxidation.

Pachycereus Marginatus Alkaloids, John M. Brewer

Masters Theses

Introduction

Serturner's paper, 1817, "Morphis, a New Salt-forming Substance, and Meconic Acid, as the Chief Constituents of Opium", opened a new era of discovery in organic plant chemistry. His isolation of the first alkaloid was soon followed by the isolation or narcotine by Robiquet and strychnine by Pelletier and Caventou. These basic compounds were at first called vegetable alkalies, but were later renamed alkaloids, meaning alkali-like¹¹.

Structural And Magnetic Characteristics Of The Belton Anomaly, Cass County, Missouri, Nagib Chamon

Masters Theses

"A vertical intensity magnetic survey of approximately 156 square miles in Cass County, central-west Missouri, revealed a broad circular anomaly whose magnetic relief exceeds 1000 gammas. Surface rocks are very gently inclined and are of Pennsylvanian age. Crystalline basement rocks are at a depth of approximately 2400 feet. Analysis of the data shows that the Belton anomaly consists of discontinuous smaller magnetic anomalies surrounding the central part of this broad anomaly. The central area of the Belton anomaly is occupied by a magnetic low. Analytical calculation showed that the source of the magnetic disturbance is at least 3650 feet below …