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All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

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Articles 1201 - 1230 of 1427

Full-Text Articles in Physical Sciences and Mathematics

Petrology And Regional Relationships Of The Ordovician Kinnikinic Formation And Equivalents, Central And Southern Idaho, William Calvin James May 1973

Petrology And Regional Relationships Of The Ordovician Kinnikinic Formation And Equivalents, Central And Southern Idaho, William Calvin James

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Kinnikinic Formation of central Idaho is a sedimentary unit consisting principally of orthoquartzite. From its maximum measured thickness of 2285 feet in the central Lemhi Range near Gilmore, Idaho, it thins westward to 376 feet at the type section and southward to 326 feet near Arco, Idaho. Northeast of the Lemhi Range it occurs only as erosional remnants, due to pre-Devonian erosion. Both the lower and upper contacts of the Kinnikinic Formation are disconformable.

The Kinnikinic Formation is light colored, predominately fine to medium grained, thin to medium bedded, and largely cemented by silica overgrowths. Some metamorphic recrystallization has …


Field Measurements Of Photosynthesis And Leaf Growth Rates Of Three Alpine Plant Species, Douglas A. Johnson May 1973

Field Measurements Of Photosynthesis And Leaf Growth Rates Of Three Alpine Plant Species, Douglas A. Johnson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Leaf photosynthetic measurements using a portable 14Co2 field system were carried out and correlative leaf relative growth rates, RGR, were determined at different leaf positions of three alpine plant species throughout the growing season. Initially there was a period of high leaf RGR associated with a period of increasing photosynthetic activity. Following this stage was a long period of no net change in length of the living leaf. During this period, photosynthetic activity generally increased to a maximum level and then decreased steadily. The final ontogenetic stage was a period of negative leaf RGR denoting leaf senescence which …


Mechanisms Of Population Regulation In Confined Colonies Of Peromyscus Maniculatus (Wagner) And The Response To Exploitation, Donna Corn Olsen May 1973

Mechanisms Of Population Regulation In Confined Colonies Of Peromyscus Maniculatus (Wagner) And The Response To Exploitation, Donna Corn Olsen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Wild-trapped and laboratory-reared Peromyscus maniculatus (Wagner) were raised as confined colonies indoors with various stocking densities ranging from 0.026 to 0.100 mice per sq. ft. in pens of 40, 77, and 154 sq. ft. The animals were individually tagged and all pens were censused at weekly or semi-monthly intervals to record animals present, body weights, food consumption, and overt reproductive condition. At the termination of each experiment, all mice were necropsied and organ weights of gonads and adrenals recorded. Histological sections were made of the testes and ovaries. Half the colonies were subjected to density-independent exploitation by removal of 50% …


The Relationship Of Climatic Factors To Grazing Activities Of Cows On Winter And Spring Ranges, Benton M. Smith May 1973

The Relationship Of Climatic Factors To Grazing Activities Of Cows On Winter And Spring Ranges, Benton M. Smith

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this research was to investigate the effects of climatic variations upon the daily activities of grazing cattle. The activities of individual cows on a partially seeded salt desert shrub range were observed and recorded during three grazing periods. Two of the periods were during consecutive winters and the other during the spring. Climatic variations during the second winter period were quantified and compared to changes in the daily activity patterns of the cattle.

Distinctly different daily routines of cattle activities were evident for the winter and spring seasons. In the spring, the cattle grazed, traveled, and drank …


Habitat Selection By Large Wild Ungulates And Some Aspects Of The Energy Flow In A Sub-Tropical African Savanna Woodland Ecosystem, Stanley M. Hirst May 1973

Habitat Selection By Large Wild Ungulates And Some Aspects Of The Energy Flow In A Sub-Tropical African Savanna Woodland Ecosystem, Stanley M. Hirst

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A study of habitat selection by large wild ungulates was carried out on a 50 cm2 area in the sub-tropical Lowveld region of eastern Transvaal province, South Africa. Estimations were made of herbaceous forage net productivity and ungulate secondary productivity on the same area.

Fourteen vegetation types, varying in composition and structure from open savanna to dense woodland, were delineated by association analysis. Structural and vegetational characteristics which were considered to influence ungulate distribution were measured within each vegetation type.

The study area supported resident populations of seven ungulate species during the wet season; drv season densities were higher …


The Foods And Feeding Habits Of Botulism Intoxicated And Healthy Waterbirds On The Bear River Refuge, Utah With Emphasis On The American Avocet And Blacknecked Stilt, George W. Wilson May 1973

The Foods And Feeding Habits Of Botulism Intoxicated And Healthy Waterbirds On The Bear River Refuge, Utah With Emphasis On The American Avocet And Blacknecked Stilt, George W. Wilson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Primary objectives of this study were: (1) to compare the food habits of healthy and botulism intoxicated American avocets and blacknecked stilts for qualitative and quantitative differences, (2) to determine which invertebrates found in the tracts of intoxicated and healthy birds contained type C toxin, and (3) to explain apparent susceptibilities among different sexes, ages and species of birds.

Based on percent utilization and occurrence of food items in the esophagus, the diets of healthy and intoxicated birds were similar. However, intoxicated avocets consumed higher proportions of Gastropoda and intoxicated stilts more Hydrophilidae larvae than did healthy birds. Because of …


Analysis Of Case Histories By Markov Chains Using Juvenile Court Data Of State Of Utah, Soo-Hong Uh May 1973

Analysis Of Case Histories By Markov Chains Using Juvenile Court Data Of State Of Utah, Soo-Hong Uh

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to analyze juvenile court data using Markov Chains. A computer program was generalized with a single array orientation for analyzing realizations of a Markov Chain to the kth order within machine limitations. The data used in this paper were gathered by the Juvenile Court of the State of Utah for administrative purposes and limited to District II. The results from the paper, "Statistical Inference About Markov Chains" by Anderson and Goodman, were applied for testing hypotheses. The paper is divided into five chapters: introduction, statistical background, methodology, analysis and summary, conclusions.


A Relativistic One Pion Exchange Model Of Proton-Neutron Electron-Positron Pair Production, William A. Peterson May 1973

A Relativistic One Pion Exchange Model Of Proton-Neutron Electron-Positron Pair Production, William A. Peterson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Proton-neutron electron-positron pair production cross sections are calculated in the framework of the pseudoscalar one-pion exchange model in a fully relativistic manner.

A computer program has been developed to evaluate invariants and Dirac traces for a given data point.

The sections for symmetric coplanar events for laboratory kinetic energies of 10 to 250 MeV were calculated for pair angles of 20° to 120°.

Frequency distributions were also calculated, at a laboratory energy of 200 MeV, using a random number generator to select data points. The frequency distributions are illustrated by curves.

It was noted that the inclusion of heavier bosons …


Mineral And Chemical Content Of The Deep-Water Sediment Sequences Of Bear Lake, Utah-Idaho, James C. Biesinger May 1973

Mineral And Chemical Content Of The Deep-Water Sediment Sequences Of Bear Lake, Utah-Idaho, James C. Biesinger

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Twenty-five piston cores 6 to 12 feet long were obtained from the deepwater sediments of Bear Lake, Utah-Idaho. Analyses of these cores revealed that the deep-water sediments of the lake are divided into two major sequences: a younger sequence rich in carbonate minerals, here called the carbonate sequence, and an older sequence rich in silicate minerals, referred to in this paper as the silt sequence. The carbonate sequence is composed of clay-sized quartz, aragonite, calcite, dolomite, montmorillonite, illite, kaolinite, chlorite, and amorphous material. The silt sequence consists of both silt- sized and claysized particles of quartz, calcite, dolomite, montmorillonite, illite, …


A Comparison Of Consumer's Surplus And Monopoly Revenue Estimates Of Recreational Value For Two Utah Waterfowl Marshes, C. Holden Brink May 1973

A Comparison Of Consumer's Surplus And Monopoly Revenue Estimates Of Recreational Value For Two Utah Waterfowl Marshes, C. Holden Brink

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Demand curves were estimated for waterfowl hunting and nonconsumptive recreational use from use rate and variable expenditure data collected at the Bear River Migratory Bird Refuge and the Farmington Bay Waterfowl Management Area during fiscal 1969. Consumer's surplus and monopoly revenue estimates were then derived from the demand functions. Adjusted estimates of consumer's surplus for waterfowl hunting amounted to $7,260 per year at Bear River and $11,400 per year at Farmington Bay. For nonconsumptive recreation annual consumer's surplus was estimated to be $18,700 at Bear River and $3,760 at Farmington Bay. Monopoly revenue estimates were between one-half and one-fourth the …


Some Aspects Of Conditioning Behavior In Rainbow Trout, Salmo Gairdneri, Reed E. Harris May 1972

Some Aspects Of Conditioning Behavior In Rainbow Trout, Salmo Gairdneri, Reed E. Harris

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Effects of exercise, social facilitation, and delayed conditioning after vi exercise on the learning behavior of 5 to 6-inch rainbow trout, Salmo gairdneri, was measured in a conditioned avoidance response apparatus. The conditioning schedule contained an intertrial interval between alternate presentations of conditioned (light) and unconditioned (shock) stimuli. This randomization eliminated learning losses found in a previous study. Mean percentage avoidance, the measurement of learning, did not decrease significantly during conditioning trials. Exercised fish learned avoidance better than did non-exercised fish. Mean percentage avoidance for fish exercised at 0.5 ft/sec was 66.3; at 1.0 ft/ sec, 1.5 ft/sec, and …


Investigations Of The Algal Productivity Of Selected And Limited Sites Along The Western Shore Of Bear Lake, Utah-Idaho, John William Sigler May 1972

Investigations Of The Algal Productivity Of Selected And Limited Sites Along The Western Shore Of Bear Lake, Utah-Idaho, John William Sigler

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Investigations of limited and selected areas along the western shore of Bear Lake were carried out to determine the relative algal productivity with relation to nutrient concentrations and incident sunlight. The primary objective of the study was to determine the effects of nutrient changes in the littoral zone on the western shore on the algal productivity and to establish a baseline of data.

l4C02 radioisotope was used as the principal measurement of organic carbon production as an estimate of productivity. Chlorophyll extracts were made and used as a secondary method for the estimation of productivity. Chemical analysis of …


Effect Of Early Growth Cultivation On Beans And Sweet Corn, Raymond L. Cartee May 1972

Effect Of Early Growth Cultivation On Beans And Sweet Corn, Raymond L. Cartee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Investigations involving four cultivation treatments were conducted at the Utah State University Greenville Experimental Farm to determine the effect of these treatments on yields of beans and sweet corn. The effects of the different treatments on soil water content, soil temperature, and weed control in beans and corn were investigated. The effect of cultivation on the degree of root rot infection and the effect of different planting dates were also investigated in the bean study.

The pre-emergence treatment (ridged just before the plants emerge) produced a 48 percent greater bean yield and a 40 percent greater corn yield than the …


Petrology Of The Ordovician Swan Peak Formation, Southeastern Idaho And North-Central Utah, Warren J. Schulingkamp Ii May 1972

Petrology Of The Ordovician Swan Peak Formation, Southeastern Idaho And North-Central Utah, Warren J. Schulingkamp Ii

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Swan Peak Formation in southeastern Idaho and north-central Utah is a sedimentary unit consisting of orthoquartzite, sandstone, siltite, shale, and limestone. The formation is divisible into three members, and the lower two members each are divisible into two informal lithologic subunits.

The lower member consists of a lower subunit of gray, calcareous sandy siltite composed of subangular to subrounded quartz grains cemented by quartz overgrowths, calcite, or iron oxide, and an upper subunit of black shale with minor interbedded silty quartzose sandstone and biomicrite (limestone).

The middle member consists of a lower subunit of interbedded pale green shale and …


Reproduction And Hematology Of The Cache Elk Herd, Thomas B. Follis May 1972

Reproduction And Hematology Of The Cache Elk Herd, Thomas B. Follis

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The initial three years of a 10-year reproductive study of elk involved three major phases. A fourth was added because of convenience. Objective 1 was to ascertain pregnancy rates in yearling and mature elk by rectal palpation, associate these rates with subsequent fall cow/calf ratios, and to test concurrently an ultrasonic fetal heart detector. Rectally observed anatomical changes in gravid uteri of cattle were directly applicable to elk. Ultrasonic detections of pregnancies in elk and deer were unsuccessful.

Pregnancy rates in the 1969-70 winter of 100 and 0 percent, respectively, for 19 adult and five yearling elk were associated with …


Population Biology Of The Black-Tailed Jackrabbit (Lepus Californicus) In Northern Utah, L. Charles Stoddart May 1972

Population Biology Of The Black-Tailed Jackrabbit (Lepus Californicus) In Northern Utah, L. Charles Stoddart

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Population biology of the black-tailed jackrabbit population on a 250-square-mile area in Curlew Valley, northern Utah, was studied from 1962-70. During this period the fall population density index increased from 40.0 in 1962, to 60.6 in 1963, decreased progressively to a low of 21.2 in 1967, then increased the following 3 years to a high of 185.0 in 1970.

Breeding was synchronous with four conception periods each year; in some years a fifth conception period was evident. The first conception period occurred about the last half of January; other periods followed at 40-day intervals indicating a 40-day gestation period and …


Evaluation Of The Filter Paper Method For Estimating Soil Water Potential, Samir Al-Khafaf May 1972

Evaluation Of The Filter Paper Method For Estimating Soil Water Potential, Samir Al-Khafaf

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The filter paper method for measuring soil water potential was evaluated. The method was calibrated using salt solutions (-1.4 bars to -22.4 bars), sample chamber psychrometer (-1 to -50 bars), pressure plate (-0.1 to -15 bars) and soil column at equilibrium (0 to -0.2 bars). It was found that the absolute temperature had little effect on the predicted soil water potential, but a temperature variation had a large effect. It was found that the temperature fluctuation must be small. The predicted water potential was influenced by the type of contact of the soil with the filter paper. It is suggested …


Effect Of Bear River Storage On Water Quality In Bear Lake, Utah-Idaho, Robert L. Nunan May 1972

Effect Of Bear River Storage On Water Quality In Bear Lake, Utah-Idaho, Robert L. Nunan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Since 1912 concentrations of the major anions and cations (except calcium) in Bear Lake water have shown a steady decrease which has been attributed to a dilution of Bear Lake by Bear River water, Bear Lake having been used as a reservoir for Bear River water since 1918. This study examined the changes which have occurred in Bear Lake water chemistry since 1912 and tested the validity of the dilution theory.

Simple water and salinity budgets were determined for the Bear Lake system and used to simulate the effect of Bear River storage patterns since 1918 on the concentrations of …


Model For Estimating Soil Water Flow, Water Content, Evapotranspiration And Root Extraction, Musa N. Nimah May 1972

Model For Estimating Soil Water Flow, Water Content, Evapotranspiration And Root Extraction, Musa N. Nimah

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A mathematical model was developed to predict water content profiles, evapotranspiration, water flow from or to the water table, root extraction and root water potential at the surface as functions of time under unsteady state conditions.

The model was tested in the field at The Hullinger Farm near Vernal, Utah, in 1970 and 1971. Comparison of water content-depth profiles show excellent agreement at the end of a 9- day run in 1970 on oats seeded to alfalfa. In 1971 with alfalfa as the crop, the data show best agreement, between predicted and computed water content-depth profiles, 48 hours after any …


Selecting The Best Linear Model From A Subset Of All Possible Models For A Given Set Of Predictors In A Multiple Linear Regression Analysis, David L. Jensen May 1972

Selecting The Best Linear Model From A Subset Of All Possible Models For A Given Set Of Predictors In A Multiple Linear Regression Analysis, David L. Jensen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Sixteen "model building" and "model selection" procedures commonly encountered in industry, all of which were initially alleged to be capable of identifying the best model from the collection of 2k possible linear models corresponding to a given set of k predictors in a multiple linear regression analysis, were individually summarized and subsequently evaluated by considering their comparative advantages and limitations from both a theoretical and a practical standpoint. It was found that none of the proposed procedures were absolutely infallible and that several were actually unsuitable. However, it was also found that most of these techniques could still be …


A Two Sample Test Of The Reliability Performance Of Equipment Components, Miki Lynne Coleman May 1972

A Two Sample Test Of The Reliability Performance Of Equipment Components, Miki Lynne Coleman

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this study was to develop a test which can be used to compare the reliability performances of two types of equipment components to determine whether or not the new component satisfies a given feasibility criterion.

Two types of tests were presented and compared: the fixed sample size test and the truncated sequential probability ratio test. Both of these tests involve use of a statistic which is approximately distributed as F.

This study showed that the truncated sequential probability ratio test has good potential as a means of comparing two component types to see whether or not the …


Sequential Analysis For Tolerances Of Noxious Weed Seeds, Seung Tokko May 1972

Sequential Analysis For Tolerances Of Noxious Weed Seeds, Seung Tokko

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The application of a sequential test, the sequential probability ratio test, for the tolerances of noxious weed seeds is studied. It is proved that the sequential test can give a similar power curve to that of the current fixed sample test if the test parameters are properly chosen.

The average sample size required by a sequential test, in general, is smaller than that of the existing test. However, in some cases it requires relatively a larger sample than current test.

As a solution to the problem a method of truncation is considered. A kind of mixed procedure is suggested. This …


An Examination Of The Inorganic Nitrogen Status Of A Soil Of The Alaskan Coastal Tundra Plain, Norton R. Munn May 1972

An Examination Of The Inorganic Nitrogen Status Of A Soil Of The Alaskan Coastal Tundra Plain, Norton R. Munn

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This experiment was designed to measure in situ concentrations of NH4+ and NO3--N in a soil of the arctic coastal tundra plain, to determine if nitrification was taking place in this soil and to determine if the vascular plants growing in this soil could assimilate NH4+-N.

The extractable NH4+-N concentration was approximately 40 μg/g in the 01 horizon and 10 μg/g in the 02 horizon. The NO3--N concentration was approximately 5 μg/g in the 01 horizon and 4 μg/g in the 02 …


Potentiometric Titration Of Sulfate Using A Lead-Mercury Amalgam Indicator Electrode, Charles W. Robbins May 1972

Potentiometric Titration Of Sulfate Using A Lead-Mercury Amalgam Indicator Electrode, Charles W. Robbins

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A lead sensitive indicator electrode was constructed with a 70 percent lead and 30 percent mercury amalgam billet. Sulfate concentrations in pure solutions, natural waters, and soil saturation extracts were determined potentiometrically using the lead-mercury amalgam indicator electrode and a standard calomel reference electrode. Sulfate concentrations over the range 0.4 to 20 milliequivalents sulfate per liter were determined with an automatic titrator and compared to a turbidimetric method for accuracy and precision. The values obtained by the two methods from twelve saturation extracts and three subsurface drainage waters were not significantly different and the potentiometric method was generally more precise. …


Tertiary Igneous Rocks Of Northeastern Cache Valley, Idaho, Parry D. Willard May 1972

Tertiary Igneous Rocks Of Northeastern Cache Valley, Idaho, Parry D. Willard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The tuffs and limestones of the Tertiary Salt Lake Formation in northeastern Cache Valley, Franklin County, Idaho, are intruded by basic and intermediate igneous dikes and sills. The Tertiary intrusives are exposed in an area 10 miles long and 2 miles wide between Bear River and Maple Creek in the foothills of the Bear River Range east of Preston, Idaho. They trend north-northwest. The intrusives are mostly diabase but include a small body of syenodiorite and several small andesite dikes. The intrusives seem to be emplaced along early Basin and Range faults. They are limited to the Cache Valley Member …


Geology Of The Wildcat Hills, Utah, Ronald C. Howes May 1972

Geology Of The Wildcat Hills, Utah, Ronald C. Howes

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Wildcat Hills, located in Curlew Valley of northwestern Utah, are composed of a series of late Tertiary extrusive and dike rocks. Five volcanic rock types have been identified: an andesite, a rhyolite, a perlite, a basalt, and a welded tuff. Hydration of obsidian pellets contained in the flows has produced some of the perlite. Diatremes in the andesite attest to the high-volatile content and the explosive extrusion of some of the lavas. A compound basalt neck indicates that basalt was extruded at the Wildcat Hills and is not an erosional remnant of the basalt flow from the base of …


Model For Predicting Simultaneous Distribution Of Salt And Water In Soils, Satish C. Gupta May 1972

Model For Predicting Simultaneous Distribution Of Salt And Water In Soils, Satish C. Gupta

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Knowledge of water and salt movement in soils is necessary for development of a management scheme for controlling the quality of irrigation return flow. A computer model was developed to predict the distribution of water and salts in the root zone under varying initial and boundary conditions. The model consists of water flow and salt flow sub-models. The water flow sub-model considers the numerical approximation of the general water flow equation with modification for water loss by evapotranspiration (and thus root extraction). The salt flow sub-model considers the mass flow of salts, chemical exchange, precipitation or dissolution of CaCO3 …


An Analysis Of Stock Densities And Harvest Of The Cutthroat Trout Of The Snake River, Teton County, Wyoming, John W. Kiefling May 1972

An Analysis Of Stock Densities And Harvest Of The Cutthroat Trout Of The Snake River, Teton County, Wyoming, John W. Kiefling

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

An intensive creel census and marking program was conducted in 1969 and 1970 to make possible population estimates and estimates of harvest of cutthroat trout in the Snake River in Teton County, Wyoming. Stock density determinations made in one of the five study areas provided an estimate of 400 and 992 cutthroat trout, eight inches or more in length, per mile of stream in 1969 and 1970 respectively.

Harvest data provide an estimate of 5,207 and 5,903 cutthroat trout harvested in 1969 and 1970 respectively. The harvest estimates obtained in this study are not comparable to those made in 1967 …


Stratigraphy And Environmental Analysis Of The Swan Peak Formation And Eureka Quartzite, Northern Utah, George Gregory Francis May 1972

Stratigraphy And Environmental Analysis Of The Swan Peak Formation And Eureka Quartzite, Northern Utah, George Gregory Francis

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Swan Peak Formation in north-central Utah thickens westward, from zero feet near Logan to 687 feet in the Promontory Range. The unit is subdivided into three distinct members: 1) A lower member of interbedded shales, limestones, and quartzites; 2) A middle member of interbedded shales and brown quartzites; and 3) An upper member of white quartzites. The Swan Peak thins southward toward the east-west-trending Tooele Arch in the area of study; this thinning probably reflects both lesser deposition and greater subsequent erosion there than elsewhere. The lower member in northern Utah probably was deposited in shallow-shelf and/or traditional shoreface-shelf …


Integral Representation Theorems, Leiko Hatta May 1971

Integral Representation Theorems, Leiko Hatta

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Since F. Riesz showed in 1909 that the dual of C[0,1] is BV[0,1] (the functions of bounded variation on [0, 1] with || g ||BV = V(g)) via the Stieltjes integral, obtaining representations for linear operators in various settings has been a problem of interest. This paper shows the historical manner of representations, the road map type theorems and representations obtained via the v-integral.