Physical Sciences and Mathematics Commons^™

The Effect Of Matrix Condition In The Solution Of A System Of Linear Algebraic Equations., Herbert R. Alcorn

Masters Theses

"The solution of a system of linear non-homogeneous equations may contain errors which originate from many sources. A system of linear equations in which small changes in the coefficients cause large changes in the solution is unstable and the coefficient matrix is ill- conditioned .

The purpose of this study is to define several measures of matrix condition and to test them by correlation with a measure of the actual errors introduced into a system of equations.

The study indicates that three of the five measures of condition tested were reliable indices of the magnitude of error to expect in …

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 Parameter Perturbation Procedure For Obtaining A Solution To Systems Of Nonlinear Equations., James Carlton Helm

Masters Theses

"For simultaneous nonlinear equations the convergence of the known functional iterative procedures is dependent upon a good initial approximation to the desired roots. In this paper the restriction on the choice of the initial approximation has been circumvented by dividing each problem into a number of subsidiary problems in accordance with a parameter perturbation procedure. The study presents a discussion of the algorithm and the conditions for convergence. The discussion, also, includes the problems which were solved using the parameter perturbation procedure"--Abstract, p. ii

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

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 …

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.

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 …

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 …

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 …

Distribution Of Sodium Perchlorate Between Tributyl Phosphate And Water, John A. Tengler

Masters Theses

"The questions posed by Carroll (23) concerning a TBP-H₂O system and an alkali salt -which is appreciably soluble in TBP have been partially answered by the experiments described in this thesis"--Conclusions, page 38.

Correlation Between Drying Times Of A Vinyl Copolymer Solution And Properties Of Dried Films., Abd El-Rahman M. Naser

Masters Theses

"One of the common methods used in film formation is the solvent evaporation method. As the evaporation starts the viscosity increases due to the inability of the solvent to keep the chains apart, which leads to a drag between molecules.

The rate of evaporation of the solvent (loss of solvent) cannot be equated with the rate of drying, since the latter depends on the results of the loss of solvents in terms of viscosity and plastic properties. The drying time can be defined as the rate at which a film increases its viscosity and thus changes the properties of a …

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

Masters Theses

No abstract provided.

Solubility And Structure Studies Of Nickel (Ii) Acetate, Richard J. Baird

Masters Theses

"The effects of ammonium acetate on the solubility of anhydrous nickel (II) acetate in anhydrous acetic acid was investigated and was found to behave similar to the zinc (II), copper (II), and cobalt (II) systems. Problems with equilibrium, encountered by previous investigators, were overcome. The determination of the structure of nickel (II) acetate hemiacetate was atacked by infrared studies, preparation of adducts, cryoscopic studies, magnetic susceptibility measurements, and absorption spectra. It was found that nickel (II) acetate hemiacetate is octahedrally coordinated with two coordination sites vacant. It was shown that the binuclear cage structure common to copper (II), chromium (II), …

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

A Modified Procedure For The Quantitative Determination Of Fluoride And The Application Of This Procedure To A Fluoride Balance Study In Children, Beatrice Shuang Wu

Masters Theses

Introduction

This research problem was done in connection with the fluoride balance studies on twelve children at Plymouth State Home. The retention balance studies of fluoride by children can be studied indirectly by measuring the amounts of fluoride excreted in the urine and feces after administration of the fluoride in water or in vitamins as sodium fluoride. The fluoride balance study was repeated, because in the previous study (19), there were no samples collected for a base day in which the fluoride was not given. The previous data also indicated that fluoride retention was merely a function of the interval …

Development Of A Two Channel Counter For Measurement Of Faraday Rotations, Donald R. Flach

Masters Theses

Chapter I

Introduction

The rotation of the plane of polarization of plane polarized light when it passes through a substance in a direction parallel to an applied magnetic field is known as the Faraday effect and was discovered by Michael Faraday in 1845.¹ It was found by experimentation that the amount of rotation of the plane of polarization was represented by the equation:

Θ = VH1 cos A

where H = magnetic field in gauss, 1 = simple path length in centimeters, A is the angle between the magnetic field and the direction of the light, and V is …

Benzohydroxamic Acid As A Reagent For The Determination Of Aluminum And Copper, William E. West

Masters Theses

No abstract provided.

A Study Of Methods For Estimating Parameters In Rational Polynomial Models, Thomas B. Baird

Masters Theses

“The use of rational polynomials for approximating surfaces is investigated in this study. In particular, methods for estimating parameters for a rational polynomial model were investigated.

A method is presented for finding initial estimates of the parameters. Two iterative methods are discussed for improving those estimates in an attempt to minimize the sum of the squares of the residuals. These two methods are (1) Scarborough’s Method for applying the theory of least squares to nonlinear models and (2) the Method of Steepest Descent.

Data from two functions were chosen and approximated as illustrations. Each set of data was used two …

Preparation And Properties Of 3,3’-Disubstituted-2,2’ – Three-Carbon-Atom Bridged Biphenyls, Allan E. Nader

Masters Theses

Introduction

The configuration of biphenyl has been treated in numerous articles and reviews (1, 5, 6, 7, 8, 16, 22, 23). In particular the configuration of 2,2'-bridged biphenyl derivatives has obtained attention. The synthesis of an optically active 2,2'-three-carbon-atom-bridged biphenyl possessing an ultraviolet absorption maximum at 250 mμ has been reported by Iffland and Siegel (15). These properties require first, a non-planar configuration for the molecule and second, significant inter-ring conjugation as demonstrated by ultraviolet spectra.

Several 2,2'-three-atom-bridged biphenyls have been prepared by Ahmed and Hall (2, 3) in order to obtain some measure of their specific rotation. The use …

Preparation Of The Cis And Trans Isomers Of Methylcyclohexanecarboxylic Acids And Their 2-Diethylaminoethyl Esters, Paul Allen Meulman

Masters Theses

Introduction

The purpose of this research is to prepare the CIS and TRANS isomers of the 2, 3 and 4-methylcyclohecanecarboxylic acids and their 2-diethylaminoethyl esters.

This series of compounds is of interest because of the anti-tumor activity shown by some ethanolamine derivatives. The compounds to be prepared in this study represent modifications of these structures to determine if further investigation in this area is worthwhile. A pharmacological evaluation of these compounds will be made since many esters of amino alcohols have demonstrated pharmacological activity. The cancer chemotherapeutic and pharmacological test results are not included in this paper, but will be …

Stability Properties Of Various Predictor Corrector Methods For Solving Ordinary Differential Equations Numerically., Charles Edward. Leslie

Masters Theses

No abstract provided.

Hydrogeology Of Reservoir Sites In The Meramec River Basin, Missouri., John H. Anderson

Masters Theses

"Governmental and private agencies have proposed construction of multiple purpose dams in the Meramec River Basin for flood control, conservation, recreation and possible power development. Evaluation of the effects of reservoirs created by these dams on ground water conditions has not been published. Study of possible effects led to the thesis that prediction of changes in ground water conditions could be made.

Several limited applications of ground water geology techniques to the problem of reservoir-ground water relations were studied; no thorough previous studies were found. Apparently, complete studies have not been undertaken by even the larger agencies.

Inspection of the …

Pegmatites Of The Anderson Ridge Quadrangle, Fremont County, Wyoming, Hassan A. Etr

Masters Theses

“The oldest rocks in the area consist mainly of para- schists of low to medium rank and restricted higher rank sillimanite schist. The entire series has been at least double folded. The most apparent are tight north to north- east trending folds. These have been intruded in the northern part of the area by a batholithic body of granitic composition, a granitic stock, a pegmatitic granite, a granitic sill-like body and different types of pegmatite dikes and sills. The youngest intrusions are a series of northeast trending basic dikes and sills. A major easterly trending transverse fault and a series …

An Investigation Of The Acceleration Of Neutrons, Charles Edward Byvik

Masters Theses

"The acceleration of neutrons via their magnetic dipole moment in an axially symmetric magnetic field is considered. Conditions for bunching are derived and expressions for the off-axis forces are developed. It was found that neutrons off axis are forced back onto the axis and that neutrons slightly depolarized remain in their initial state. A calculation of the acceleration is made using the field of a current loop and the conclusion is that under present laboratory capabilities a neutron accelerator is not feasible"--Abstract, page ii.

The Diagenetic Origin Of The Dolomites, Chert, And Pyrite In The Jefferson City Formation., Erik Hans Schot

Masters Theses

"Diagenesis designates all modifications which a sediment undergoes during and following deposition and prior to complete lithification, metamorphism, deep burial, and orogenesis.

Probably the dolomites of the Jefferson City Formation resulted from alteration at, or below the sea floor or the depositional interface and during diagenesis. Diagenetic dolomitization or penecontemporaneous alteration presumably involves a reaction between the calcium carbonate sediments at/or below the sea floor or the depositional interface and magnesium salts in solution or suspension in the basal layer of contacting sea water, or in the initial pr connate water trapped in the sediment.

The cherts of the Jefferson …

The Construction And Analysis Of An Amplifier For Ultrasonic Research, Jerry John Koelling

Masters Theses

“An amplifier to be used for ultrasonic pulse methods was constructed and tested. The frequency range lies between 100 cycles per second and 2 mega-cycles per second and, if tuned circuit plug-in units are used, may be increased to approximately 4 mega-cycles per second. Special demands upon the amplifier are discussed along with basic acoustic attenuation measurements in solid state physics”--Abstract, page ii.

A Study Of Methods For Determining Confidence Intervals For The Mean Of A Normal Distribution With Unknown Varience By Comparison Of Average Lengths, Karl Richard Kneile

Masters Theses

“The purpose of this thesis is to briefly review various properties which may be desirable for a system of confidence intervals; and to empirically determine whether the system of confidence intervals obtained from the Student’s t distribution will produce shorter average lengths than those obtained by other methods which may be used. It was concluded from the results of an empirical investigation that there was no significant difference between the average lengths of confidence intervals obtained from a family of distributions of which the Student’s t is a member"--Abstract, page ii.

The Location Of Underground Points By Means Of A Magnetic Dipole, Anthony Del Prete Jr.

Masters Theses

"The object of this study was to design, construct, and test an electromagnet that could, from an underground location, generate a magnetic field which could be located at the surface, and that was portable enough to be carried through a cave. This could then be used to locate points in a cave relative to the surface.

A 20 foot solenoid composed of four five-foot sections was built and magnetized by a lightweight rechargeable four-cell eight volt battery. The total weight of the equipment was 30 pounds.

The magnet was calibrated by erecting it and measuring its vertical intensity with a …

Sedimentary Petrography And Environments Of Deposition Of The Plattin Group, Cliffdale Hollow, Jefferson County, Missouri., Narendra M. Naiknimbalkar

Masters Theses

"Petrographic and depositional environments studies were completed on selected Plattin Limestone rock-samples from the Drill-cores of Cliffdale Hollow area, Jefferson County, Missouri.

Petrographic analysis of forty-four thin sections and the detailed megascopic study of the samples revealed the different types of limestone rocks which were classified on the basis of Folk's (1959) Carbonate Classification. As to the environments of deposition of the Plattin Limestone determined by petrographic study, it has been concluded that this environment was one of low to medium agitation and low to medium organic activity.

Chemical analysis of the Plattin Limestone samples revealed the presence of the …