Physical Sciences and Mathematics Commons^™

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

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 …

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 …

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 …

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), …

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 …

Decay Of Intensity Of Certain Hg Lines In An Hg-Ar Discharge, Edward E. Stepp, Richard A. Anderson

Physics Faculty Research & Creative Works

The afterglow of four mercury spectral lines was examined in a mercury-argon electric discharge. The 2537- Å line decays in a complex fashion with three definite modes of decay. The 4077-, 4358-, and 5461- Å lines exhibited an even more complicated decay. These lines exhibited an initial rapid decay followed by an increase in intensity. Finally the intensity of these lines went through two maxima before they decayed in intensity at a slow constant rate. The actual intensity behavior of the 2537- Å line was masked by the imprisonment of resonance radiation. It is postulated that the main processes governing …

Theory Of The Effect Of Temperature On The Electron Diffraction Patterns Of Diatomic Molecules, Russell A. Bonham, Jerry Peacher

Physics Faculty Research & Creative Works

The effect of temperature on the electron diffraction pattern of a diatomic molecule is considered from the standpoint of the simple kinematic scattering theory utilizing a quartic vibrational potential. The potential is obtained by an expansion of ħ²J( J+1)/2μr²+D exp[-2a(r-r_e)]-2D exp[-a(r-r_e)] about its minimum value r₀. The second-order wavefunction for the nth vibrational and 7th rotational state of the system has been obtained, and expressions for the electron diffraction quantities r_g, l_e ², and M (s) have been computed. General results for the quantity M (s) …

Magnetic Structure Investigations At The Nuclear Center, R. Ballestracci, E. F. Bertaut, J. Coing-Boyat, A. Delapalme, William Joseph James, R. Lemaire, R. Pauthenet, G. Roult

Chemistry Faculty Research & Creative Works

The magnetic structure of the compounds UOS, ß-CoSO₄, YCO₅, and HoCO₅ is briefly described.

UOS is antiferromagnetic. The Néel temperature is T_n=55°K. The magnetic cell is doubled in the c direction with a ++ - - sequence of U moments along c. The apparent spin is S∼1. The negative interaction corresponds to U-O-U links.

In ß-CoSO₄ (high-temperature modification, space group Pbnm), Co atoms are in 000, 00½, ½½½, ½½0. Here three different antiferromagnetic spin modes, mutually perpendicular, A_x(+ - - +), G_y(+-+-), and C_z(++ - - …

Geology Of The Northern Half Of The Ellington Quadrangle Missouri., Robert Charles. Thornton

Masters Theses

"Geologic mapping has been completed for the northern half of the Ellington Quadrangle, Missouri. Rocks exposed in the thesis area are Precambrian and Paleozoic in age. The Precambrian rocks are granites and felsite. The Paleozoic rocks include the Potosi and Eminence Formations, of Upper Cambrian age, and the Gasconade Formation of Ordovician age. Distinction between the Potosi and Eminence Formations is difficult because of conformable and transitional relationships. In the thesis area sufficient evidence was available to separate the dolomites of the Potosi and Eminence as mappable units. This mapping should be useful as a basis for more detailed geologic …

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 Sacajawea Formation And The Darwin Sandstone In The Southeast Wind River Mountains, Wyoming, Denny N. Bearce

Masters Theses

"The area under study is located along the southeast flank of the Wind River Range in Fremont County, Wyoming, Beds overlying the Madison Group are measured and described in six locations within this area. These locations are: Worth Fork Popo Agie River, Sink’s Canyon, Crooked Creek, Canyon Creek, Little Popo Agie River, and Cherry Creek.

Laboratory studies are used as an aid in correlating the sandstone and dolomite sequences described In the six sections. These studies include sieve and heavy mineral analyses and thin section examination.

Sorting factors, obtained from the sieve analyses, and heavy mineral suites indicate that the …

Stereoradiography As Applied To Problems Of Petrology., Martin Goldstone

Masters Theses

"Stereoscopic examination of radiographs of rock and ore samples allows a rapid, cursory determination of texture and structure without time consuming preparation and use of thin sections. In addition, volumetric estimates of known mineral components can be made providing they possess significantly different x-ray absorption characteristics.

Stereoscopic effect was most pronounced for specimens having well defined components of structure such as bedding, banding, lineation, inclusions, textural variations and moderate to large x-ray absorption differences. In general, these conditions were best met by ores or ore minerals with their related gangue minerals.

Stereoscopic examination was not successful in revealing twinning or …

Mineralogy, Petrography, And Ceramic Properties Of Lower Cabaniss Underclays In Western Missouri, Anthony C. Tennissen

Doctoral Dissertations

The mineral and chemical components, the petrography, and the ceramic properties of the Weir-Pittsburg, Tebo, and Mineral underclays In Barton, Vernon, St. Clair, sod Henry Counties of western Missouri have bean Investigated by x-ray diffraction, differential thermal, spectrographic, microscopic, and certain ceramic testing techniques. The underclays are composed principally of little, kaolinite, end mixed-layer illite-montmorillonite. Illite is the dominant mineral. The principal non-phyllosilicate minerals are quarts sad pyrite. The under clays are mineralogically similar to the underlying shales and contain clay pallets which also are mineralogically similar to the underclays and shales in which they are found. The clay appears …

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 …

A Numerical Approach To A Sturm-Liouville Type Problem With Variable Coefficients And Its Application To Heat Transfer And Temperature Prediction In The Lower Atmosphere., Troyce Don Jones

Masters Theses

No abstract provided.

Mathematical Techniques In The Solution Of Boundary Value Problems., Vincent Paul Pusateri

Masters Theses

"This study was undertaken to present a summary of mathematical techniques as applied to the solution of boundary value problems in partial differential equations.

The techniques that were presented can be considered to be some of the most popular in applied science.

The salient features of the study are that different techniques can present different analytical expressions for a solution to the same boundary value problem, and from the viewpoint of computation and accuracy one solution may prove more desirable than the other.

The study also indicates that in boundary conditions where finite discontinuities exists, a slight perturbation to remove …

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 Reaction Of Sodium Iodide In Acetone With Halogenated Epoxides -- A Mechanism Study, Thomas E. Breuer

Masters Theses

"l-bromo-2,3-epoxybutane reacted with sodium iodide in acetone to give 3-iodo-l,2-epoxybutane in 70.1 per cent yield. 3-bromo-l,2-epoxybutane produced l-iodo-2,3-epoxybutane in 69.9 per cent yield when it was allowed to react with a solution of sodium iodide in acetone. No other product could be isolated after either reaction, although it is possible that another compound may have been produced in very small amounts. The iodoepoxides were oxidized to the corresponding α-iodoacid in approximately ninety per cent yield by silver oxide"--Summary, page 40.

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 …

The Measurement Of The Life-Time Of The 62P3/2 State Of Thallium, Danny Hale Sokolowski

Masters Theses

The measurement of the lifetime of the metastable 6²P_3/2 state of thallium is discussed. Time-sampling equipment techniques and instantaneous methods of display on an oscilloscope for measuring the lifetime are explained. The lifetime is measured as a function of mercury vapor pressure. The decay of the 5350 A thallium line is also measured to give an indication of the effect of the imprisonment of the 3776 A resonance line. This decay of the 5350 A line is also in a mercury atmosphere"--Abstract, page ii.

A Modified Algorithm For Henrici's Solution Of Y' ' = F (X,Y), Frank Garnett Walters

Masters Theses

"The purpose of the present study is to discuss the boundary value problems leading to equations exemplified by the four equations previously mentioned and to write a program for an I.B.M. computer in Fortran II language as a contribution to the numerical solution of an important class of linear and nonlinear differential equations"--Introduction, page 4.

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.

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 …

Investigation Of Measures Of Ill-Conditioning, Thomas D. Calton

Masters Theses

“The object of investigation in this study is that of ill-conditioning in the solution of a system of linear equations. Ill-conditioning arises when the solution is very sensitive to small changes in the coefficients of the unknowns.

A study is made in this paper of the various proposed measures of ill-conditioning for the purpose of finding the most practical method or measure for determining whether a system is ill-conditioned.

The problem of near-singular or ill-conditioned systems is of great importance in the solution of linear systems because of the extensive use made of them in practical situations. Solution of a …

Permeation Of Water Vapor Through Linear Polymer Films, Mohammed S. Rifai

Masters Theses

"Film formation from thermoplastic resin solutions Is Influenced by secondary intermolecular forces. Consider what may happen when organic coatings change from a liquid to a solid state. In the liquid state it is logical to consider the linear polymer molecules as agglomerates being dispersed in the volatile component rather than being present In solution. These molecular agglomerates are referred to as micelles. They have various degrees of orientation depending on the extent and the location of dipole forces in both polymer and solvent molecules.

When a coating is applied the solvent starts to evaporate and the micelles are driven closer …

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 …

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

Masters Theses

No abstract provided.