Physical Sciences and Mathematics Commons^™

Tests Of Methods That Control Round-Off Error, Dale M. Rasmuson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Methods of controlling round-off error in one-step methods in the numerical solution of ordinary differential equations are compared. A new Algorithm called theoretical cumulative rounding is formulated. Round-off error bounds are obtained for single precision, and theoretical cumulative rounding. Limits of these bounds are obtained as the step length approaches zero. It is shown that the limit of the bound on the round-off error is unbounded for single precision and double precision, is constant for theoretical partial double precision, and is zero for theoretical cumulative rounding.

The limits of round-off bounds are not obtainable in actual practice. The round-off error …

Reliability And Maintainability Sampling Procedures For Life Cycle Cost Evaluation, Doyle H. Harris

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The intent of this thesis is to investigate, develop, and apply techniques to determine the reliability and maintainability of populations of items. These techniques are to be used in determining the total life-time operating costs of the populations so that those items with the lowest life-time costs can be bought. To do this, the author has explored current techniques for determining compliance to some minimum required Mean Time Between Failure (MTBF) in what is referred to as a Phase I testing. After the requirements of Phase I testing have been met, testing may be continued at the option of the …

The Fundamental Groups Of The Complements Of Some Solid Horned Spheres, Norman William Riebe

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One of the methods used for the construction of the classical Alexander horned sphere leads naturally to generalization to horned spheres of higher order. Let M₂, denote the Alexander horned sphere. This is a 2-horned sphere of order 2. Denote by M₃ and M₄, two 2-horned spheres of orders 3 and 4, respectively, constructed by such a generalization.

The fundamental groups of the complements of M₂, M₃, and M₄ are derived, and representations of these groups onto the Alternating Group, A₅, are found. The form of the presentations …

Measure Theory And Lebesgue Integration, Evan S. Brossard

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The Lebesgue integral is a generalization of the Riemann integral which extends the collection of functions which are integrable.

Lebesgue integration differs from Riemann integration in the way the approximations to the integral are taken. Riemann approximations use step functions which have a constant value on any given interval of the domain corres­ponding to some partition. Lebesgue approximations use what are called simple functions which, like the step functions, take on only a finite number of values. However, these values are not necessarily taken on by the function on intervals of the domain, but rather on arbitrary subsets of the …

Principal Component Factor Analysis, Herbert H. Jolliff

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Factor analysis came into being around 1900 in the field f psychology to explain theories of human ability. Several methods of factor analysis exist; but according to Harman (1967) principal component factor analysis is unique in the mathematical sense, therefore, quite often the preferred method. The centroid method is computationally easier, and it gives close approximations to the principal component method on some data sets. An example of this is shown in Appendixes B and F by comparison.

Factor analysis is being used in many fields. A few of the fields are sociology, meteorology, political science, medicine, geography, business, economics, …

Computer Analysis Of Consumer Attitude And Consumption Data For Fluid Milk Products, James Reed Fisher

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The American public, with a per capita disposable income currently at an all time high, has become a source of vital concern to dairy market researchers. The unique socio-economic structure of the present generation causes the dairy industry to be concerned with how the consumer view its products. Effective education and advertising programs must be developed to attract the taste and meet the demands of the consumer.

Two factors which greatly influence market research and advertising programs are the attitude of the consumer toward a given product and the relationship of attitude to the degree of actual milk consumption. To …

Lake Bonneville History In Cutler Dam Quadrangle, Cache And Box Elder Counties, Utah, G. Glayde Maw

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

When Lake Bonneville spilled through Red Rock Pass at the north end of Cache Valley, the major part of the lake in Salt Lake Valley had to drain from west-to-east through Cutler Dam Quadrangle. Here two major saddles connect the two valleys: (1) Bear River Narrows, at about +4380 feet; and (2) Cache Butte-Wellsville Mountain Pass 4.2 miles south, at about +4970 feet. Spillover levels at both places are cut into older rocks.

Only two morphostratigraphic units are recognized widely in the quadrangle. These represent high stands at the Bonneville level (+5180 ± 20 feet) and at the Provo level …

Atomic Absorption As An Index Of The Silver Concentration In Precipitation, Silver Iodide Plume Studies, Part 1, Joel E. Fletcher, H C. Millar

Reports

The Perkin Elmbver Model 303, equipped with the DCR-1, digital concentration readout, was evaluated as to its ability to provide an index of silver concentration in water solutions, without concentrating in any manner. The procedures, principal settings, and adjustments which must be observed are described.

This instrument can detect the difference between concentrations of 10-15 and 10-12 gm/ml. However, as the concentration of silver decreases the experimental error increases to a point at which the error becomes greater than the differences in readout due to differences in silver concentration.

Water Quality Telemetry First Annual Progress Report, Duard S. Woffinden, Allen D. Kartchner

Reports

No abstract provided.

Feasibility Of Rating Current Meters In A Velocity Field, Gaylord V. Skogerboe, Lloyd H. Austin, Roland W. Jeppson, Chi-Yuan Wei

Reports

Preliminary studies employed an 8-inch (outlet diameter) contracting cone and an 8-inch converging nozzle. The design of the cone is based on an electromagnetic analogy reported by Smith and Wang, while the nozzle was designed assuming potential flow and using numerical methods to obtain the solution. Both designs yielded fairly uniform velocity fields, any deviations being primarily due to either construction or measurement techniques. The towing tank rating for a Pygmy current meter was compared with the submerged jet rating, the difference being 1 or 2 percent. A Prototype system was constructed using a 16-inch contracting cone (d). Two Type …

Solutions To Axisymmetric Seepage From Ponds Through Homogeneous And Nonhomogeneous Porous Media, Roland W. Jeppson

Reports

No abstract provided.

Hydraulic Characteristics Of A Modified Venturi Section, Muhammad Aslam Rasheed

Reports

The measurement of water in open channels on extremely flat grades is difficult because of the head loss that is necessary. A modified venture section, the contraction of which is provided by a top cover section mounted in a rectangular flume, is proposed to meet the requirements of a suitable measuring device for use in canals of flat gradients. The method of finite differences has been used for the mathematical solution to the idealized inviscid flow problem. This was followed by a laboratory investigation to ascertain the hydraulic characteristics of the proposed design. The experiments were conducted in a 3 …

Air Pollution Control And Abatement Proceedings Of A Symposium, Allen D. Kartchner

Reports

No abstract provided.

Linear Programming With Random Requirements, Nak Je Kim

Reports

Linear programming was first developed by George B. Dantzig, Marshall Wood, and associates of the U.S. Air Force, in 1947. At that time, the Air Force organized a research group under the title of project SCOOP (Scientific Computation of Optimum Programs). This project contributed to the developing of a general interindustry model based on the Leontief input-output model, the Air Force programming and budgeting problem, and the problems which involved the relationship between two-person zero sum games and linear programming. The result was the formal development and application of the linear programming model. This project also developed the simplex computational …

A Conceptual Model Of The San Pitch River Basin, James D. Ballif

Reports

To meet future expected needs for water, the State of Utah will have to plan and manage its limited resources in a judicious manner. Comprehensive water resources planning on a river basin basis is necessary to economically plan and develop the best combination of water uses. Efficient use and management of agricultural water is necessary to maximize the amount available for future needs. Irrigation water management must be improved. Improvements in the organization, storage, distribution, and method of application will be required to meet future demands. Consideration should be given to various combinations of conjunctive use of groundwater and surface …

Water Resources Research - A Challenge To The Social Scientists, Dean F. Peterson

Reports

No abstract provided.

Topic From Galois Theory, Pai-Yuan Chang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Galois theory constitutes an excellent introduction group theory and field theory and provides a strong motivation for the introduction of the basic concepts of abstract algebra. This paper explains the basic theory and describes how it is applied to prove the unsolvability "by radicals" of equations of degree n >= 5.

Estimation Of Parameters Of Normal Populations From Truncated Samples, Kuo-Chung Liang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In statistical experiments, if a random sample of items drawn from a population is tested until all items fail, conventional statistical techniques may be employed but normal frequency distributions may not be satisfied. Failure of the data to satisfy the assumption of normality may lead to an invalid result. Some statistical results, however, have been shown to be robust to the failure of the data to meet normality. When using conventional experimental methods, considerable time and money are required to produce failure of all samples. To be economical, many experiments are concluded before all test items fail. A sample obtained …

Linear Coordinate Systems And Statistical Independence And Vector Spaces And Linear Statistical Models, James B. Mcdonald

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The object of this report is an investigation of statistical independence and linear coordinate systems. It is hoped that this report will give some background for an ultimate investigation of independence and non­linear coordinate systems using tensor analysis.

An additional basic objective is to obtain explicit algebraic expressions for different types of linear trans- formations.

The first concepts to be covered are arbitrary linear transformations, various ways of looking at linear transformations, and the effects of a linear transformation on a vector of normally distributed random variables.

Next orthogonal transformations to independence, and then oblique transformations to independence will be …

The Influence Of Irrigating With Saline Water On The Energy Status Of Water In Soil And Plant, Rolando H. Braun

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

1. Changes in the energy status of water that occurred in Milville silt loam and in bean (Phaseolus vulgaris L.) plants growing on it , during two consecutive 6-day periods while being irrigated with saline solutions, were studied.
2. Total soil water potential (Ψ soil) (measured with thermocouple psychrometers), matric-potential (Ψ_m) (measured with tensiometers) were considered. In leaf samples, the total water potential (leaf) and the osmotic potential (Ψ_π)--after freezing-- were determined with thermocouple psychrometers; by difference, the pressure potential (Ψ_p) was obtained.
3. There is no evidence of close relationship between changes taking place in …

The Alignment Procedure Of A Two Crystal Spectrometer, Jay W. Phippen

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

For the sake of completeness, it was felt that a brief resume' of x-ray scattering theory as it affects the alignment procedure of a two crystal spectrometer would be beneficial.

X-ray diffraction from a single crystal slab.

W. L. Bragg (1912) tried the experiment of reflecting a beam of x-rays from the cleavage surface of a crystal and found on the photo-graphic plate a spot at the angle of reflection. He then replaced the photo graphic plate with an ionization chamber which he mounted so that it could be rotated about the axis upon which the reflecting crystal is …

An Exposition On Bayesian Inference, John Laffoon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Bayesian approach to probability and statistics is described, a brief history of Bayesianism is related, differences between Bayesian and Frequentist schools of statistics are defined, protential applications are investigated, and a literature survey is presented in the form of a machine-sort card file.

Bayesian thought is increasing in favor among statisticians because of its ability to attack problems that are unassailable from the Frequentist approach. It should become more popular among practitioners because of the flexibility it allows experimenters and the ease with which prior knowledge can be combined with experimental data.

Rational Arithmetic As A Means Of Matrix Inversion, Jay Roland Peterson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The solution to a set of simultaneous equations is of the form A^-1 B = X where A^-1 is the inverse of A in the equation AX= B. The purpose of this study is to obtain an exact A^-1 through the use of rational arithmetic, and to study the behavior of rational numbers when used in arithmetic calculations.

This study describes a matrix inversion program written in SPS II, utilizing the concept of rational arithmetic. This program, using the Gaussian elimination matrix inversion method, is compared to the same method written in Fortran. Gaussian elimination …

Design Optimization Using Model Estimation Programming, Richard Kay Brimhall

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Model estimation programming provides a method for obtaining extreme solutions subject to constraints. Functions which are continuous with continuous first and second derivatives in the neighborhood of the solution are approximated using quadratic polynomials (termed estimating functions) derived from computed or experimental data points. Using the estimating functions, an approximation problem is solved by a numerical adaptation of the method of Lagrange. The method is not limited by the concavity of the objective function.

Beginning with an initial array of data observations, an initial approximate solution is obtained. Using this approximate solution as a new datum point, the coefficients for …

Fortran Programs For The Calculation Of Most Of The Commonly Used Experimental Design Models, H. Wain Greenhalgh

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two computer programs were developed using a CDC 3100. They were written in FORTRAN IV.

One program uses four tape drives, one card reader, and one printer. It will calculate factorial analysis of variance with or without covariance and/or multivariate analysis for one to eight factors and up to twenty-five variables.

The other program is used for completely randomized designs, randomized block designs, and latin square designs. It will handle twenty-five treatments, rows (blocks), and columns. The program can handle fifteen variables using any number of these variables for covariates.

Geology Of The West-Central Part Of The Malad Range, Idaho, Phillip H. Wach

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The west-central part of the Malad Range is located in south-eastern Idaho. This area was the site of thick marine deposition in the early Paleozoic period. In the Tertiary and Quaternary periods continental deposition occurred, covering the Paleozoic rocks. Quartzite and shale units of the Brigham Quartzite are found near the base of the Cambrian section. Carbonate with shale interbeds is found in the middle and late Cambrian units. Limestone and silty limestone are found in the early and middle Ordovician time overlain by the middle Ordovician Swan Peak Quartzite. The Laketown Dolomite includes units of late Ordovician and Silurian …

Geology Of The Northern Part Of The Malad Range, Idaho, Drew C. Axtell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Rocks of Paleozoic, Tertiary, and Quaternary age are represented in the northern part of the Malad Range. The Paleozoic rocks are represented by thirteen formations that are characterized lithologically by quartzites, shales, and carbonates. The oldest formation in the mapped area of Paleozoic age is the Brigham Formation, and the youngest formation is the Jefferson Formation of late Devonian age.

The rocks of Tertiary age are conglomerates, shales, and limestones and are represented by the Wasatch Formation, the Salt Lake Formation, and boulders. Quaternary rocks include sediments of the Lake Bonneville Group and alluvium.

The faults in the mapped area …

Experiments On The Inactivation Of Zinc By The Mineral Fractions Of The Soil, John J. Hassett

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Zinc deficiency, in many cases, is closely related to organic matter decomposition. DeRemer and Smith (1964) studied the effects of decomposing sugar beet tops on the reactions of Zn⁶⁵ in a Portneuf soil. They found that with time the Zn⁶⁵ associated with lime minerals, exchangeable, and water soluble fractions of the soil decreased, while that found with the organic and mineral fractions increased. This increase in the mineral fraction is of particular interest, since the majority of the Zn⁶⁵ was found to be with this fraction after a period of time. They also showed that the increase …

Movement Of Atrazine In Soil Under Furrow Irrigation, Jyothi Veerabhadrappa

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Movement of atrazine in response to furrow irrigations was studied using the samples of Timpanogos silt loam soil. Distribution in soil profile of surface applied herbicide was determined by drawing samples of water extracts through porous cylinders. Atrazine quantity was determined by spectrophotometer.

It was observed that the herbicide found in the water extracts was an indication of the quantity present in the soil. The herbicide moved readily with the applied water. Irreversible thermodynamic model could not be applied because of the initial and final boundary conditions. The pattern of movement was in conformity with the chromatographic theory.

Topics In Semigroups, Merlin Ray Jenson

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The semigroup theories of fundamental importance were discovered in 1928 with the publication of a paper by A. K. Suschkewitsch. The paper is included in the only book published prior to 1961 dealing primarily with the algebraic theory of semigroups. The book written by the above author and published in 1937 is entitles "The Theory of Generalized Groups."

Since 1940 the number of papers on semigroups has increased to approximately 30 per year. Thus we find ourselves in the midst of a new and expanding area of mathematics. Our interest centers around the structure of semigroups and their representation by …