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 …

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 …

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

Transverse Spin Relaxation Of Optically Pumped Rubidium., Robert Evans Hufft

Masters Theses

The study of the transverse spin relaxation of rubidium vapor is a continuation of the work done by Kenneth Steinbruegge¹ and that in progress by John Martin² at the University of Missouri at Rolla. The purpose of the experiment is to study the change of intensity of the transmitted pumping light at resonance in the longitudinal direction, and the observation of the high frequency modulation of a second "cross" beam of light perpendicular to the first. Under resonant conditions this "cross" beam will exhibit a phase coherence and a loss of phase coherence when parameters of the experiment …

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 …

A Method To Give The Best Linear Combination Of Order Statistics To Estimate The Mean Of Any Symmetric Population, Robert M. Smith

Masters Theses

“This paper gives a distribution for the ratio of two non-independent normally distributed random variables. The random variables involved are jointly distributed as the bivariate normal with means zero and variance- covariance matrix V.

The sample mean and one-half the sum of the smallest and largest sample observations from the symmetrically truncated Cauchy density function are compared as estimates of the mean of this density function. The reason for this comparison is to determine which of these two estimators gives the best estimate of the mean.

A method to empirically determine the best linear combination of order statistics for any …

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.

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 …

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 …

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

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.

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 …

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), …

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 …

Studies Of An Electrical Method For Generating Ultrasonic Waves, Yung-Yien Huang

Masters Theses

“Ultrasonic waves have proved very valuable in the observation of both the velocity and the absorption coefficient of sound in various media. From the velocity measurements of ultrasonic waves in metals, it is possible to obtain elastic constants, such as the compressibility, and the specific heat. Also, the observed attenuation depends greatly on the type and structure of the material. One of the widely used methods for investigation of the internal losses in solid state physics is the pulse-echo technique. This method is being used almost exclusively in internal friction investigation"--Introduction, page 1.

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.

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

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 …

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 …

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

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.

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 …

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.

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 …

The Anodic Dissolution Of Zinc In Aqueous Solutions, Glenn E. Stoner

Masters Theses

"The increasing demand for protective metals as coatings and non-corrosive alloys has stimulated extensive research on the fundamental behavior of metals in corrosive media.

One of the problems still unsolved is the nature of the mechanism of the anodic dissolution of metals like zinc, magnesium, beryllium, cadmium, and aluminum in aqueous salt solutions. Several schools of investigators have proposed different and opposing theories to explain the discrepancies which often arise between coulometric data and the weight loss of metal electrodes in certain salt solutions.

The purpose of this investigation was to obtain experimental data for the anodic dissolution of zinc …

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 …