Physical Sciences and Mathematics Commons^™

A Survey In Mean Value Theorems, David A. Neuser

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A variety of new mean value theorems are presented along with interesting proofs and generalizations of the standard theorems.

Three proofs are given for the ordinary Mean Value Theorem for derivatives, the third of which is interesting in that it is independent of of Rolle's Theorem. The Second Mean Value Theorem for derivatives is generalized, with the use of determinants, to three functions and also generalized in terms of n-th order derivatives.

Observing that under certain conditions the tangent line to the curve of a differentiable function passes through the initial point, we find a new type of mean value …

A Fortran List Processor (Flip), Karl A. Fugal

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A series of Basic Assembler Language subroutines were developed and made available to the FORTRAN IV language processor which makes list processing possible in a flexible and easily understood way.

The subroutine will create and maintain list structures in the computer's core storage. The subroutines are sufficiently general to permit FORTRAN programmers to tailor list processing routines to their own individual requirements. List structure sizes are limited only by the amount of core storage available.

Source Rocks And Sediments In Drainage Area Of North Eden Creek, Bear Lake Plateu, Utah-Idaho, Larry W. Mcclurg

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Bear Lake Plateau extends north-south across the north central corner of Utah and the southeastern corner of Idaho. North Eden Creek drains westward through part of the plateau and is crossaxial across both strikes of beds and other structures in the area. The formations in the area mapped are of Triassic, Jurassic, and Tertiary age, although only Jurassic and Tertiary rocks contribute sediments to North Eden Creek. The formations consist of sandstones (Nugget), limestones (Twin Creek), and conglomerates (Wasatch). A local extrusion of basalt occurs in the southwestern part of the drainage area.

Particle-size analyses of 15 samples from …

The Ontogeny Of Social Behavior Of Uinta Ground Squirrels, D. Andrew Saunders

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The social behavior of juvenile Uinta ground squirrels (Spermophilus armatus) was studied for 2 1/2 years in northeastern Utah. The purpose of the study was to describe the developing social behavior of unconfined, marked squirrels. Their behavior was recorded with motion pictures and written descriptions from the time they emerged from the natal burrow until they entered hibernation.

Three phases of behavioral development were apparent. The first phase began when the juveniles appeared above ground and ended 5 weeks later. This was a period of socialization and consisted of behavioral patterns best described as play. The second phase …

Areal And Temporal Variations In Developmental Phases Of Syringa Vulgaris L. Throughout The Western United States, Joseph Michael Caprio

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper presents the results of the analysis of 10 years of information 1957-1966 on three phases-- begin, peak and end bloom-- of the purple common lilac (Syringa vulgaris L.) using data recorded at approximately 1,000 locations throughout the Western Region of the United States.

The pattern of geographical advance of the various bloom phases is determined by both a manual mapping procedure developed by the author and by standard statistical methods. Manually drawn isophanes for the various elevations for begin bloom phase are based entirely upon the first 5 years of record, 1957-1961. A Zones of Adjustment map to …

Transpiration And Dry Matter Response To Atmospheric Humidity, Matric Suction, And Fertility, Gordon Edgar Warrington

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Growth chamber studies showed that a relationship exists between transpiration and dry matter production of spring wheat (Tritiaum Aestivum L. var . Thatcher). A temperature of 27 C for a 16-hour day,and 21 C at night were used throughout the experiment. Relative humidities (RH) of 12, 25, 71, and 83 percent and matric suctions of 1, 3, and 9 bars were used a l ong with six fertility levels and a 20-day growing period. An equation was developed from previous equations by De Wit and Arkley to describe the transpiration ratio (Tr = mass of water transpired/mass of dry …

Magnesium Ion Inhibition Of Calcium Carbonate Precipitation And Its Relation To Water Quality, John J. Hassett

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The effect of Mg⁺⁺ ion on the solubility of calcium carbonate was determined using P. K. Weyls "carbonate saturometer."

The amount of calcium carbonate precipitated or dissolved was measured for five series of waters when equilibrated with solid carbonate.

It was found that the effect of Mg⁺⁺ ion on solubility depend upon the nature of the solid phase: surface area, coprecipitated Mg⁺⁺, minerology, etc.

Pure low area calcite showed an increase in solubility which could be explained by ion-pair formation, while its other carbonates departed from this behavior.

Drift Of Oligophlebodes Sigma And Baetis Bicaudatus In A Mountain Stream, William Dean Pearson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The objective of this study was to clarify the relationships between drift rates, population density, production rates, key environmental factors, and movements of adults within two populations of stream insects (a caddisfly--Oligophlebodes sigma and a mayfly--Baetis bicaudatus).

Samples of benthic invertebrates (424 total) were collected every 28 days at four stations on Temple Fork of the Logan River, Utah, from October, 1967 to September, 1969. Samples of drift invertebrates (181 total) were collected every 14 days at three stations on Temple Fork during the same period. During summer months (June-September) a day and a night drift sample …

Evaluation Of Molting Areas Of Great Basin Canada Geese, Paul D. Arneson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Environmental factors at Neponset and Woodruff Narrows reservoirs were evaluated to determine their effects on molting Canada geese. More geese utilized Woodruff Narrows. Geese apparently favored the larger expanse of open water and adequate food supply.

Most of the molting geese were from the Bear River drainage. Some geese came from scattered areas in Utah, Idaho, Wyoming, and Montana. After molting, the geese flew to migration staging areas in southeastern Idaho before migrating to wintering areas in southern California and Arizona.

Females outnumbered males by 6 percent. The mean annual mortality rate for adult geese was 42 percent. Recovery rates …

A Kinetic Approach To The Inactivation Of Zinc By Various Soil Constituents, Shingara S. Sandhu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The adsorption reaction of zinc onto prochlorite, pyroxene, and biotite minerals, from dilute solution (water) was studied under isothermal conditions by agitated nonflow experiment method. The equilibrium concentration of zinc in the solution was determined both by radioactive tracer technique and adsorption spectrophotometer methods. The data were collected at three temperatures.

The data were treated by the equation:

∂θ/∂t = k₁(1-θ)C - k_-1θ

where θ is the fraction of total surface coverage and C is the equilibrium concentration of zinc in solution, k₁ and k_-1 are the rate constants for the adsorption and reverse …

Some Aspects Of Geochemistry And Mineralogy Of Bear Lake Sediments, Utah-Idaho, Dean F. Davidson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Bear Lake is located in southeastern Idaho and north-central Utah. The lake has a maximum altitude of 5923 feet and an area of approximately 110 square miles. Surrounding the lake are carbonates, shales, and sandstones of lower Paleozoic through middle Mesozoic ages. The many streams and springs that originate in these rocks are probably the main contributors to the chemistry of the lake. Water from Bear River, which flows into the north end of the lake, also contributes to its chemistry.

Quartz, aragonite, dolomite, calcite and clay minerals are the main minerals in the lake-bottom sediments. Quartz is generally the …

A Concept Of Buoyancy In Topological Spaces, With Applications To The Foundations Of Real Variables, Elwyn David Cutler

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Buoyancy Theorem states that a compact set is buoyant if every point of the compact set has a neighborhood whose intersection with the compact set is buoyant. In this paper, the Buoyancy Theorem is used to prove several standard results involving compact sets. The proof of such a result may be a direct application of the Buoyancy Theorem or the proof may rely on a certain compactness argument which follows from the Buoyancy Theorem. The last application in this paper is such an example.

The method used is to, first of all, define a buoyancy on the compact set; …

Analysis Of Contingency Tables, James Joseph Biundo

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two methods of analyzing multi-dimensional frequency data are detailed.

The Second Order Exponential (SOE) model is applicable for dichotomous classifications. The distribution has two sets of parameters, ϴ_i's and ϴ_j's. The ϴ_i's are interpreted as the log of the odds of the marginal probabilities if no two factor relationships exist. Or if all ϴ_ij are not zero, then the ϴ_i's are analogous to a main effect in a 2^m factorial analysis, (m = number of factors or classifications). The ϴ_if's may be interpreted as a measure and direction …

Generation Of Random Numbers, Keith H. Eberhard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Subroutines are written to generate random numbers on the computer. Depending on the subroutine used, the generated random numbers follow the uniform, binomial, normal, chi-square, t, F, or gamma distribution. Each subroutine is tested using the chi-square goodness of fit test to verify that the random numbers generated by each subroutine follow the statistical distribution for which it is written. The interpretation of the test results indicates that each subroutine generates random numbers which closely approximates the theoretical distribution for which it is designed.

The approach used in the subroutine which generates gamma distributed random numbers involves the use of …

Paleoecology Of The Lowermost Part Of The Jurassic Carmel Formation, San Rafael Swell, Emery County, Utah, R. Joseph Dover

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Paleoecology of the lowermost Carmel Formation, San Rafael Swell, Emery County, Utah, was studied at nine localmes 2 to 21 miles apart. Eight of the sections contain fossiliferous calcilutites and oölmc limestones in the basal 35 to 135 feet measured. Thickness of the fossiliferous beds ranges up to 10 feet. Beds of barren calcilutites, calcarenites, oölmc limestones, intraclastic limestones, calcareous sandstones, and bedded gypsum, separate the fossiliferous beds. A parallel-bedded, basal quartz sandstone, 0.5 to 7 feet thick, everywhere overlies the Navajo Formation.

Molluscs dominate faunal assemblages. Shells are recrystallised to calcite, but external sculpture is preserved in sufficient detail …

Structural Geology Of Southeastern Margin Of Bear River Range, Idaho, Clinton L. Davis

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Seven Cambrian formations and two Ordovician formations, with a total thickness of 9,000 feet, crop out west of the Paris thrust fault and comprise the upper plate. Slices of three Ordovician formations, one Silurian formation, two Mississippian formations, and one formation each of Pennsylvanian and Permian age comprise the low plate. Mesozoic units are not present in the mapped area. Two Tertiary formations and unconsolidated Quaternary deposits are also present.

The major structural feature is the Paris thrust fault which extends north-south throughout the area. It was active during the Laramide orogeny. This fault involved eastward movement and placed Cambrian …

Salinity And Water Potential Sensor For Evaluation Of Soil Water Quality, Melvin Dee Campbell

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The objective of this study was to evaluate response times of a salinity sensor and a soil psychrometer. Influences of pressure, temperature and molar concentration changes were to be measured.

Salinity sensor response times ranged from 50 to 130 minutes during solution adsorption while desorption response times were perhaps ten times as long. Temperature affected both response times and equilibrium values, but pressure did not affect either.

Soil psychrometer response times ranged from from 40 to 80 minutes for either adsorption or desorption of solution. However, other factors probably related to indirectness of measurement made the soil psychrometer fail to …

Environmental Analysis Of The Swan Peak Formation In The Bear River Range, North-Central Utah And Southeastern Idaho, Philip L. Vandorston

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Swan Peak Formation in the Bear River Range of northern Utah and southeastern Idaho varies in thickness from 0 feet to over 400 feet. It consists of three units: (1) a lower unit of interbedded quartzites, shales, and limestones; (2) A middle unit of interbedded quartzites and shales; (3) An upper unit of nearly homogeneous quartzites. The different sedimentary structures, ichnofossils, body fossils, and mineral compositions of each unit represent different environments of deposition. The lower unit probably was deposited in a shallow-shelf environment, and its sediments grade upward into probably shoreface-, tidal-flat-, and lagoonal deposits of the middle …

A Formula To Express Evapotranspiration As A Function Of Soil Moisture And Evaporative Demands Of The Atmosphere, Aldo L. Norero

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A mathematical expression was developed and tested which describes the relation between evapotranspiration and soil moisture. A general premise of this mathematical model is that the evapotranspiration-soil moisture relationship is determined by interaction of climatic, soil and plant factors. The basic model is

dETa/dYs = -ke[1-(ET_a/ET_mx)]

in which ET_a is the actual evapotranspiration, Ψ_s is the total soil water potential, k is a proportionality coefficient, ∈ is the soil moisture extraction capacity of the atmosphere , and ET_mx is the evapotranspiration that would occur from a particular crop-soil unit when soil moisture was …

Catalytic Effect Of Soil Components On The Nitrite Transformation In Buffer Acid Solutions, Laxman G. Kuratti

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Nitrite decomposition in buffer solutions of pH 3, 4, and 5 was observed to be a first order reaction with rate constants (k) 6.39 x 10^-3, 1.15 x 10^-3, and 0.17 x 10^-3, respectively. When 10 grams of two different soils were introduced, the reaction was catalyzed in all three pH conditions studied. This effect, however, was more pronounced in pH 5.

When 10 grams of soil were introduced, all the added nitrite was not recovered. The deficit ranged from 17 to 30 parts per million when 150 parts per million nitrite nitrogen was …

The Hyrum And Beirdneau Formations Of North-Central Utah And Southeastern Idaho, James F. Eliason

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Hyrum and Beirdneau Formations of North-central Utah and Southeastern Idaho represent rocks of late Middle Devonian (Givetian) to upper Upper Devonian (Famennian) age. They are disconformably underlain by the Early Devonian Water Canyon Formation in most cases and disconformably overlain by the Devonian-Mississippian Leatham Formation or the Mississippian Lodgepole Formation.

The Hyrum Formation is divided into five members based on lithology and color changes. The five members are: (1) Samaria, (2) Lower Dolomite, (3) Lower Carbonate-detritus, (4) Upper Dolomite, and (5) Upper Carbonate-detritus Members. The Samaria Member is the only fossiliferous unit within the Hyrum Formation.

The Beirdneau Formation …

Geologic Feasibility Of Dam And Reservoir Sites, Blacksmith Fork Canyon, Utah, Alfredo Capistrano Buenaventura

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Two areas along the Blacksmith Fork River, in the Bear River Range southeast of Logan, Utah, were studied as sites for a storage dam and reservoir. An earth dam, 150-200 feet high, and a reservoir of 15,000-20,000 acre-feet are contemplated by the Bureau of Reclamation, U.S. Department of Interior.

The lower area, located about 7 miles east of the mountain front, involves two possible dam sites on limestone. Thick overburden is present in the canyon bottom and on the right abutments. The upper area, located about 2 miles south of the headquarters of the Hardware Ranch, includes two possible dam …

Algebraic Properties Of Endomorphisms Of Abelian Groups And Rings, Johnnie George Slagle

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The main objective of the thesis was to extend the definition of an M-Group to what is called an M-Ring. From this extension a system called an expanded ring follows naturally. To facilitate the development of the expanded ring, chapter I is devoted to developing properties on systems that are not quite rings where many interesting examples are constructed. In chapter II the definition of an M-Ring is given and some of its properties are derived. In chapter III some of the properties of expanded rings are proved, and examples of expanded rings are given to show their existence.

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 …

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 …

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 …

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 …