Physical Sciences and Mathematics Commons^™

On The Calculation Of Multicenter Two-Electron Repulsion Integrals Involving Slater Functions, Russell A. Bonham, Jerry Peacher, Henry L. Cox

Physics Faculty Research & Creative Works

Integral transforms are used to evaluate many-center two-electron repulsion integrals involving Slater s-type functions. The reduction of a general four-center integral of this type to a form convenient for computational purposes is presented. The technique described has the important advantage that all lesser many-center and one-center integrals can be obtained from the four-center case by proper choice of constants. The form of the result is such that simple single-precision numerical techniques yield rapid and accurate evaluations of many-center integrals. Several numerical examples are presented.

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.

A New Determination Of The Homogeneous Nucleation Rate Of Water In Helium, Edward Francis Allard

Doctoral Dissertations

"The object of this investigation is to apply the best known cloud chamber techniques to the study of condensation phenomena, directed mainly toward the development of a precise method for the determination of homogeneous nucleation rates. A secondary object is to investigate the properties of re-evaporation nuclei so that adequate precautions may be taken to eliminate their detrimental effect in the homogeneous nucleation experiments"--Statement of Problem, page 10.

Stratigraphy Sedimentation And Petroleum Possibilities Of The Middle Ordovician (Kimmswick-Galena) Rocks Of Missouri, Illinois And Iowa, Krishna Kant Misra

Doctoral Dissertations

"Detailed surface and subsurface studies of the Kimmswick Limestone and the Galena Formation of Middle Ordovician age in eastern Missouri, western Illinois, and southeastern Iowa were conducted in order to examine their stratigraphic relations, geological history, environment of deposition, and petroleum possibilities.

The main objective of this study was to seek a stratigraphic subdivision of the Kimmswick Limestone in Missouri, based on its gross lithology and thin section study, and its correlation with the Galena Formation in Illinois and Iowa. As a result of this study, based on the examination of twelve surface sections and 92 thin sections a three-fold …

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

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 …

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

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

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 …

The Origin Of The Bedded Arkansas Barite Deposits (With Special Reference To The Genetic Value Of Sedimentary Features In The Ore), Richard A. Zimmermann

Doctoral Dissertations

"The objective of this study has been to determine the geometric and mineralogic relationships existing between the barite and related sediments in the Stanley Shale in Arkansas and also to establish geometric, mineralogic, petrographic, and geochemical criteria for the interpretation of the origin of the barite and associated minerals. In addition, comparisons with German deposits have been made"--Introduction, Objective and Outline of Study, page [1].

On The Kirkwood Superposition Approximation, Russell V. Cochran Jr.

Doctoral Dissertations

"When the Kirkwood superposition approximation for the triplet distribution function is used in the Born-Green equation for the pair distribution function of a liquid, the fourth virial coefficient is given incorrectly. In view of this, two suggestions for improving the approximation have been investigated. A suggestion, due to G.H.A. Cole, that better results could be obtained by using a second-order integro-differential equation of the Born-Green type with the superposition approximation used for both the triplet and quadruplet distribution functions has been investigated, and results for a hard-sphere model show that this method gives considerably less reliable results than those obtained …