Physical Sciences and Mathematics Commons^™

Axiomatic Set Theory, Ronald P. Smit

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

An analysis of the well known paradoxes found in intuitive set theory has led to the reconstruction of set theory by axiomatic means. This exposition is devoted to Zermelo-Fraenkel set theory with some changes made by Suppes.

The first order predicate calculus is presupposed. In addition to the usual quantifiers admitted, a unique existential quantifier is used. The primitive notions of the set theory are the empty set and the two place membership predicate.

Fredholm Solution Of Linear Integral Equations, Dewey F. Furness

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

An integral equation of the form

ζ(x) - λ∫ K(x, s) ζ(s) ds = f(x) a ≤ x ≤ b

is called a Fredholm equation. By the method of successive approximations a solution can be obtained if the parameter λ is sufficiently small. If the kernel, K (x, s), is degenerate then a solution can be obtained by reducing it to a system of linear algebraic equations. In the general case the kernel is represented as an infinite Fourier Series. With this representation the solution is obtained by combining the two methods mentioned. The solution is the solution of two …

Laplace, Finite Fourier Sine And Cosine, Transformations, Jan Eugene Wynn

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

The Laplace and finite Fourier sine transforms can be used to solve certain boundary value problems. Also the Laplace transform is a useful took in solving some integral and integrodifferential equations. This report is composed of transform solutions of seventeen such applied problems, while the author's first report is focused towards the theoretical aspect of these transforms.

Several different types of problems are solved in this report. Among these are Bessel's classical differential equation of index n, two electrical circuit problems, a beam problem, a vibrating string problem, a heat flow problem, and a temperature gradient problem.

One of the …

Effect Of Calcium Availability On Alfalfa Grown In Calcareous High Sodium Soils, Harry Irving Nightingale

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In soil science we shall always be confronted with reactions in soils that involve Ca. Early recognition of this led to experimentation in this area. Due to the fact that Ca deficiency is most common in acid soils, the majority of the experimentation has in the past been largely confined to acid soils and their soil-Ca-plant relationships. There has been relatively little research done with Ca and its availability problems associated with alkaline or sodic soils.

Formulation Of Error Structures Under Non-Orthogonal Situations, Justus Frandsen Seely

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

To gain an appreciation or understanding for the title of this study we must first understand what the phrases "non-orthogonal" and "error structure" mean. With an understanding of these terms the title of this study will become clear.

To obtain an understanding of the term non-orthogonal, consider an experiment where differing treatments are applied to groups of experi­mental units in order to observe the differential treatment responses. If an equal number of experimental units are in each group, then we say we have an orthogonal situation. This means that when equal numbers exist among the experimental units, that the variability …

Error Structure Of Randomized Design Under Background Correlation With A Missing Value, Tseng-Chi Chang

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The analysis of variance technique is probably the most popular statistical technique used for testing hypotheses and estimating parameters. Eisenhart (12) presents two classes of problems solvable by the analysis of variance and the assumption underlying each class. Cochran (9) lists the assumptions and also discusses the consequences when these assumptions are not met. It is evident that if all the assumptions are not satisfied, the confidence placed in any result obtained in this manner is adversly affected to varying degrees according to the extent of the violation.

The Kinetics And Mechanism Of The Reaction Of Molybdenum(V) With Iodine, Oxygen And Nitrate, Ervin Park Guymon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Molybdenum compounds present a series of baffling chemical puzzles. By no means are all of these yet even clearly defined and many may never be. This complexity results from the ability of molybdenum to form six different oxidation states, which can possess three different coordination numbers. Furthermore, molybdenum compounds readily disproportionate to yield mixed valence compounds; and finally, molybdate ions readily aggregate in solution to form a variety of polyions by polymerization-condensation reactions which are controlled by pH and the concentration of the system. Molybdenum's complexity can best be summed up in the words of the late Edgar Smith who …

Geology Of The Monte Cristo Area, Bear River Range, Utah, Robert B. Smith

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Monte Cristo area is a 7 1/2-minute quadrangle located in the southeastern. part of the Bear River Range, northern Utah. It is within the Middle Rocky Mountain province and is 10 miles east of the Basin and Range province. Previous to this investigation little was known about the detailed geology of the area except for a reconnaissance study and general geologic map of the Cache County part included in the Geologic Atlas of Utah, Cache County, published by Williams (1958).

The purposes of this investigation were as follows: (1) to determine the formations present in the area and their …

Barypact Topological Spaces, Bradley Y. Maughan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Recently, Kimber [3] has discovered a general class of topological spaces, the members of which are termed barypact spaces, that includes the compact topological spaces. This class is distinct from the set of all compact topological spaces, but its members possess many of the useful properties associates with compactness. As a consequence, several standard compactness theorems become special cases of corresponding theorems in a more general setting and the techniques of proof applied to these extensions provide new, and sometimes remarkably simple, proofs of the very theorems they generalize. The purpose of this paper is to extend to this …

Spectral Analysis Of Time-Series Associated With Control Systems, Karl Leland Smith

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The progress of science is based to a large degree on experimentation. The scientist, engineer, or researcher is usually interested in the results of a single experiment only to the extent that he hopes to generalize the results to a class of similar experiments associated with an underlying phenomenon. The process by which this is done is called inductive inference and is always subject to uncertainty. The science of statistical inference can be used to make inductive inferences for which the degree of uncertainty can be measure in terms of probability. A second type of inference called deductive inference is …

Paleozic Stratigraphy Of The James Peak Quadrangle, Utah, Harley D. King

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

General Statement

The James Peak quadrangle is a topographic map unit of the Geological Survey of the U. S. Department of Interior (Plate 1). It covers 7 1/2 minutes of latitude and longitude at a scale of 1:24, 000 or 1 inch to 2, 000 feet. It is bounded by lat 41°22'30" N. and lat 41°30' N. and long 111°45' W. and long 111 °52 '30" W The quadrangle includes 56 square miles and has maximum relief of about 4, 300 feet.

The James Peak quadrangle is located in northern Utah between the Wasatch Range on the west and the …

Boolean Space, Tzeng-Hsiang Sun

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

M. H. A. Stone showed in 1937 and subsequently that many interesting and important results of general topology involve latices and Boolean rings. This type of result forms the substance of this thesis.

Theorem 4, page 11, states that for any r ≠ 0 in a Boolean ring, there exists a homomorphism h into I₂ , (the field of integers modulo 2), such that h(r) = 1.

Theorem 3, page 6, states that any subring of a characteristic ring of a Boolean space X is the whole ring if it has the two points property (that is, given x, …

Thermochemistry Of Cyclophanes, Chyi-Feng Shieh

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The syntheses and properties of various cyclophanes have been extensively investigated by Cram and others. The paracyclophanes are compounds in which benzene rings are linked to each other by two saturated chains at the para positions, as in structure I. When they are joined to the meta positions, they are called metacyclophanes.

Bear River Project First Phase Idaho And Utah (Appendix D), United States Department Of The Interior, Bureau Of Reclamation

Elusive Documents

By means of storage reservoirs, distribution works, and water exchanges, the Bear River project, first phase, would increase the usable water supply of Bear River below Bear Lake and its Cache Valley tributaries, Cub River and Mink Creek, for irrigation, municipal and industrial uses, and fish and wildlife propagation. Project reservoirs would also provide recreation and flood control benefits. The project would have main stem and East Cache segments.

National Forest Recreation In Utah, U.S. Department Of Agriculture: Forest Service

Elusive Documents

No abstract provided.

Flow Rate Measurement Of Logan Outfall Effluents, M. Leon Hyatt, J. Raymond Johnson, Joe D. England

Reports

No abstract provided.

Estimation Of Pan Evaporation From Climatological Data, Jerald Emmet Christiansen, Ashwin D. Mehta

Reports

A new formula and coefficients for climatological factors was developed for estimating pan evaporation based on an analysis of data from 23 states in the U. S. and from five other countries. This formula may be written: Ev=K R Ct Cw Ch Cs Ce Cm in which K is a dimensionless constant R is the theoretical radiation reaching the outer atmosphere, expressed as equivalent evaporation in the same units~ , as Ev. Ct, Cw, Ch,and Cs are dimensionless sub-coefficients for temperature , wind, humidity, and sunshine. Ce is a sub-coefficient for elevation, and Cm is a monthly coefficient Equations were …

Submerged Parshall Flumes Of Small Size, Gaylord V. Skogerboe, M. Leon Hyatt, J. Raymond Johnson, Joe D. England

Reports

The calibration of small Parshall flumes for measuring flows ranging in magnitude from 0.1 to 1.1 cubic feet per second (cfs) was accomplished by A. R. Robinson (1960) at Colorado State University. The purpose of Robinson’s investigation was to accurately calibrate and standardize the design of small Parshall measuring flumes. The rated flumes were constructed of galvanized sheet metal. Data was collected for Parshall flumes having throat widths of 1-, 2-, and 3- inches. Calibration tables or curves were prepared for both free and submerged flow. The dimensions of the Parshall flumes rated by Robinson are shown in Figure 1. …

Design, Calibration, And Evaluation Of A Trapezoidal Measuring Flume By Model Study, M. Leon Hyatt

Reports

SCOPE AND PURPOSE OF INVESTIGATION

The discharge occurring in an open channel can be measured by placing a constriction in the channel. Flumes are commonly used as constriction in open channels. A flume is a specially designed and calibrated section built into a channel, the physical properties of which allow the calculation of the discharge. The narrowest section of the flume is usually called the throat. The velocity of flow through the throat, for any given flow rate, increases with a decrease in the flow depth. The ideal condition for measurement of discharge is a throat sufficiently constricted to produce …

Water Vapor Measurements Using Infrared Absorption, Duard S. Woffinden

Reports

Man’s attempt to control the amount of available water has taken two approaches, i.e., weather modification and water storage through the use of man-made reservoirs. In either case, it is necessary to ascertain the water vapor content of the atmosphere. In the case of weather modification, if the water vapor content is insufficient, it is futile to attempt to start precipitation. In the case of reservoirs, it is important to know the evaporation rate since it has been demonstrated that some reservoirs provide a net negative contribution to the total water supply by increasing the normal evaporation losses. Any attempt …

Proceedings Of A Summer Institute In Water Resources: Volume 3 - Water Quality Control And Management, P. H. Mcgauhey

Reports

Foreward: Recognizing the need for training of individuals to meet the rapidly rising problems connected with water resources development, Utah State University, with National Science Foundation support, organized a Summer Institute in Water Resources for college teachers. it was hoped that participants carefully selected from all regions of the country would receive additional insight and stimulation to improve and enlarge water resources training programs at their own institutions. Thus, the accelerated dissemination of such knowledge on a national scale could be facilitated. Realizing further that the key to a successful institute of this nature lay in the excellence of its …

Submergence In A Two-Foot Parshall Flume, Gaylord V. Skogerboe, M. Leon Hyatt, Joe D. England, J. Raymond Johnson

Reports

The primary objective in this study was to ascertain the validity of the method of analyzing submergence developed by Hyatt (1965) in a standard 2-foot Parshall flume. The method of analyzing submergence was first developed for a trapezoidal flume (Hyatt, 1965), was later verified for a rectangular flume (Skogerboe, walker and Robinson, 1965), and has been shown by the authors to be valid for small Parshall flumes (Skogerboe, Hyatt, Johnson, and England, 1965). In view of previous findings, it was felt the method would also be valid for large Parshall flumes, and for this purpose the 2-foot flume was selected. …

Proceedings Of A Summer Institute In Water Resources: Volume Ii - The Economics Of Water Resource Development And Conservation, B. Delworth Gardner, Allen Lebaron

Reports

Foreward: Recognizing the need for training of individuals to meet the rapidly rising problems connected with water resources development, Utah State University, with National Science Foundation support, organized a Summer Institute in Water Resources for college teachers. it was hoped that participants carefully selected from all regions of the country would receive additional insight and stimulation to improve and enlarge water resources training programs at their own institutions. Thus, the accelerated dissemination of such knowledge on a national scale could be facilitated. Realizing further that the key to a successful institute of this nature lay in the excellence of its …

Design, Operation, And Calibration Of The Canal "A" Submerged Rectangular Measuring Flume, Gaylord V. Skogerboe, W. Roger Walker, Lawrence R. Robinson

Reports

The D.M.A.D. dam and reservoir are located on the Servier River northeast of Delta, utah, and serve as a stroage reservoir for the winter and spring flows of the Sevier River below Sevier Bridge Reservoir. The D.M.A.D. dam has been constructed with two outlet works, one for feeding Canal "A", which serves the Delta and Melville Irrigation Companies, while the other canal serves the Abraham and Desert Irrigation Companies.

A gaging station located along Canal"A" has been used for many years to obtain flow measurements. The gaging station measurements appeared to be very inconsistent, and consequently, in 1963 a study …

Construction, Instrumentation, And Preliminary Verification Of A Physical Hydrologic Model, Donald L. Chery Jr.

Reports

From theoretical consideration involving a rationalized dimensional analysis of the rainfall-runoff phenomena, dimensionless products of the pertinent variables are derived. These dimensionless products guided the design and construction of a rainstorm simulator and topographic model. The design and construction of these two basic elements of the physical hydrologic model are described. A description of the instrumentation and several relevant calibration tests is followed by a discussion of two preliminary verification test sets. The tests indicated that some necessary refinements in equipment and instrumentation were needed before more precise experimental data could be obtained. Further, the tests produced results which encouraged …

Equipment And Techniques For Aerial Application Of Evaporation-Reducing Monlayer-Forming Materials To Lakes And Reservoirs, Vaughn E. Hansen, Gaylord V. Skogerboe

Reports

The authors wish to express their gratitude and sincere appreciation to the many organizations and individual who assisted in this research effort. The U. S. Bureau of Reclamation has sponsored the investigation of aerial application equipment and techniques. U.S. Bureau of Reclamation personnel concerned with the evaporation reduction research program have b en most cooperative in supporting the efforts at Utah State University. The Reeder Flying Service has worked with Utah State University in the developn1 pilot of aerial application equipment since the inception of the project in 1961. Mr. Charles Reeder ha been very cooperative throughout the research program. …

Water Yields In Utah Developing A State Water Plan, Jay M. Bagley, Roland W. Jeppson, Cleve H. Milligan

Reports

Need and Importance of Study

Utah's problems of water use and water supply are becoming increasingly important. They are also becoming increasingly complex as competition for our water resources becomes more keen among various types of uses. In the formulation of plans for sound and efficient use of water it is essential to know the characteristics of occurrence and use of water supplies so that requirements can be balanced most effectively and economically against supply. This ordinarily requires basic hydrologic data to determine relations among climate, water losses, and water yield from watersheds.

Such data are often unavailable - especially …

Geomorphic Features And History Of The Lower Part Of Logan Canyon, Utah, Edmund J. Williams

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Logan Canyon is located east of Logan, Utah, in the Bear River Range. The lower part of Logan Canyon is considered that section of the canyon from its mouth upstream to Tony Grove Canyon, a distance of 22 miles¹, Figure 1. Some tributary canyons of the lower part of Logan Canyon have been included in this investigation because of their relationship to Logan Canyon. Grassy Flat Canyon, a south tributary of Logan Canyon 4.4 miles from Logan, exhibits several geomorphic features related to the geology of Logan Canyon. Because of its extensive use and close association with Logan …

Influence Of Fertilizer Treatment On The Response Of Sugar Beet Yield To Moisture, Samad Farzanfar

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many factors that influence the growth and quality of sugar beets behave in one way under one set of conditions and in quite another under other conditions. Consequently, these factors should be considered together under a dynamic situation to find their interrelations and their influence on sugar beet yield.

This study is a statistical analysis of the interaction of fertilizer and soil moisture potential with the yield of sugar beets grown in a crop rotation under different regimes of irrigation conducted over a period of seven years.

The data are available for the years 1949 through 1956, from an intensive …

Geology Of The Southwestern Part Of The Randolph Quadrangle, Utah-Wyoming, Steven C. Hansen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A detailed study of the southwestern part of the Randolph quadrangle was undertaken in view of the fact that Richardson (1941) mapped a large area of undifferentiated Ordovician rock. Therefore, the purposes of this investigation are: (1) to prepare a more detailed geologic map of the south­western part of the Randolph quadrangle (Plate 1), (2) to describe the struc­ture, stratigraphy, and geologic history of the area, and (3) to relate the geology to adjacent areas.