Digital Commons Network^™

On Functional Equations Related To Mielnik's Probability Spaces, C. F. Blakemore, Caslav V. Stanojevic

Mathematics and Statistics Faculty Research & Creative Works

It is shown that the method used by C. V. Stanojevic to obtain a characterization of inner product spaces in terms of a Mielnik probability space of dimension 2 does not admit a generalization to dimension n > 2. © 1975 American Mathematical Society.

The Absolute Continuity Of Phase Operators, Joanne Dombrowski, G. H. Fricke

Mathematics and Statistics Faculty Publications

This paper studies the spectral properties of a class of operators known as phase operators which originated in the study of harmonic oscillator phase. Ifantis conjectured that such operators had no point spectrum. It was later shown that certain phase operators were, in fact, absolutely continuous and that all phase operators at least had an absolutely continuous part. The present work completes the discussion by showing that all phase operators are absolutely continuous.

Stiefel-Whitney Homology Classes And Bordism, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

We develop the theory of mod 2 Stiefel-Whitney homology classes for Euler polyhedral. We then describe a simple method of obtaining pJ. bordism theories. Finally, we define the ungraded bordism theory of Euler spaces and show that it is isomorphic to ordinary total homology. © 1975 American Mathematical Society.

A Statistical Approach To The Study Of The Ecosystems Of Seven Ponds In East-Central Illinois, Gregory Lee Orr

Masters Theses

Gross primary productivity, heterotrophic bacterial numbers, and net phytoplankton densities of seven ponds in Coles County, Illinois, were studied in relation to physical, chemical, and biological habitat variables (light intensity and duration, turbidity, water temperature, pH, dissolved oxygen, sulfur, nitrogen, phosphorus, production, bacteria, and phytoplankton). Ten observations were made for each pond (except where otherwise noted) from 17 June through 25 August 1974. Stepwise multiple linear regression analyses of the data were used in order to determine those environmental factors which were important in predicting (i.e., significantly correlated with) bacterial and phytoplankton densities, and production. A multiple linear regression equation …

Program For Missing Data In The Multivariate Normal Distribution, Chi-Ping Lu

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

Missing data can often cause many problems in research work. Therefore for carrying out analysis, some procedure for obtaining estimates in the presence of missing data should be applied. Various theories and techniques have been developed for different types of problems.

Analysis of the Multivariate Normal Distribution with missing data is one of the areas studied. It has been discussed earlier by Wilkes (1932), Lord (1955), Edgett (1956) and Hartley (1958). They have established some basic concepts and an outline in the way of estimation.

In the last ten years, A. A. Afifi and R. M. Elasfoff also have contributed …

Multivariate Analysis Of Variance For Simple Designs, Yin-Yin Chen

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

The analysis of variance is a well known tool for testing how treatments change the average response of experimental units. The essence of the procedure is to compare the variation among means of groups of units subjected to the same treatment with the within treatment variation. If the variation among means is large with respect to the within group variation we are likely to conclude that the treatments caused the variation and hence we say the treatments cause some change in the group means.

The usual analysis of variance checks how far apart the group means are in a single …

Discriminant Function Analysis, Kuo Hsiung Su

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

The technique of discriminant function analysis was originated by R.A. Fisher and first applied by Barnard (1935). Two very useful summaries of the recent work in this technique can be found in Hodges (1950) and in Tosuoka and Tiedeman (1954). The techniques have been used primarily in the fields of anthropology, psychology, biology, medicine, and education, and have only begun to be applied to other fields in recent years.

Classification and discriminant function analyses are two phases in the attempt to predict which of several populations an observation might be a member of, on the basis of multivariate measurements. Both …

An Evaluation Of Bartlett's Chi-Square Approximation For The Determinant Of A Matrix Of Sample Zero-Order Correlation Coefficients, Stephen M. Hattori

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

The single equation least-squares regression model has been extensively studied by economists and statisticians alike in order to determine the problems which arise when particular assumptions are violated. Much literature is available in terms of the properties and limitations of the model. However, on the multicollinearity problem, there has been little research, and consequently, limited literature is available when the problem is encountered. Farrar & Glauber (1967) present a collection of techniques to use in order to detect or diagnose the occurrence of multicollinearity within a regression analysis. They attempt to define multicollinearity in terms of departures from a hypothesized …

The Computation Of Eigenvalues And Eigenvectors Of An Nxn Real General Matrix, Yeh-Hao Ma

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

The eigenvalues of the matrix eigenproblem Ax = λx are computed by the QR double-step method and the eigenvectors by inverse power method.

The matrix A is preliminarily scaled by the equilibration and normalization procedure. The scaled matrix is then reduced to an upper-Hessenberg form by Householder's method. The QR double-step iteration is performed on the upper-Hessenberg matrix. After all the eigenvalues are found, the inverse power method is performed on the upper-Hessenberg matrix to obtain the corresponding eigenvectors.

The program consists of five subroutines which is able to find real and/or complex eigen value/vector of an nxn real matrix.

Models For Estimating Psychiatric Bed Needs, Patricia A. Brenneman

Loma Linda University Electronic Theses, Dissertations & Projects

Inland Counties Comprehensive Health Planning Council wished to estimate the psychiatric bed needs by type (such as state hospitals, board and care homes, etc.) in San Bernardino County from the distributions of patient arrivals and of lengths of stay. A statistical description of the system during 1973 was considered the first step toward estimating future bed needs. A computer simulation model using IBM's programming language General Purpose Simulation System (GPSS) was developed and was found to be unsatisfactory.

Theorems were then developed for a statistical model, seeking to predict future bed needs. The most convenient of these theorems states that …

Concerns Of Postnatal Mothers About Sexuality, Sheela A. Gideon

Loma Linda University Electronic Theses, Dissertations & Projects

An exploratory study was designed to find out what questions mothers had about postnatal sexuality. A questionnaire was prepared by the nurse researcher to find out answers to the following questions.

1. What specific questions do mothers have about sexual relations following delivery?
2. Do mothers feel free to initiate discussion about resumption of intercourse following delivery?
3. Do mothers like their husbands to be included in the discussion?
4. When do mothers prefer to receive information regarding sexual relationships following delivery?

The questionnaire was mailed to fifty primipara mothers between three and four weeks after delivery. Mothers with pronounced anemia, heart and lung …

Exploration Of The Incidence Of Identified Emotional Disorders In Selected General Hospitals Of Nebraska, Arlene M. Van Horn

Loma Linda University Electronic Theses, Dissertations & Projects

A descriptive-comparative survey using content analysis of medical records has been done to determine the frequency with which emotional disorders are identified by medical personnel in the population hospitalized in small general hospitals in north-central Nebraska.

A systematic, random sample of medical records was taken from two hospitals arbitrarily included in the study on the basis of bed capacity and distance from mental health facilities.

Each medical record that was reviewed has been placed in a category based on whether an emotional disorder was identified in it by the medical personnel, or whether it contained recorded behaviors that could indicate …

Prenatal Instruction Of Breast Feeding Mothers, Anita Berry

Loma Linda University Electronic Theses, Dissertations & Projects

This experimental study tested the effect of prenatal instruction on the success of a group of mothers who desired to breast feed their infants. It was hypothesized that mothers receiving information on how to nurse their infants, how to prevent complications and how to cope with common problems of breast feeding would have a higher success rate than those not so instructed.

Criteria for success was that the mothers would have an adequate supply of milk to meet the nutritional demands of their infant without supplementation, would have fewer and less severe complications, and would express a higher degree of …

The Extended Tukey Procedure Compared To The Scheffe And Bonferroni Procedures, Wilber B. Emmert

Masters Theses

No abstract provided.

Probability Driven Heuristic Nets, Lynn Robert Carter

Dissertations and Theses

Let a probability driven switch be defined as a switch of three input paths and three output paths. The status of the input paths defines a probability for each output path (as to whether it will generate a signal or not.) One output path is linked to one input path, so the results of the switch at time t can affect the switch at time t+1. A switch so constructed can be defined (by the probabilities) to take on the function of the standard logic gates (AND, OR, …) A net constructed of these switches can be “taught” by …

Levi Structures For Polynomial Ideals., Richard Michael Grassl

Mathematics & Statistics ETDs

Let R be the ring of polynomials in a denumerable set of independent indeterminates over a field F and let I be an ideal (Xo,x1,x2, ... ) in R. A Levi structure for I provides bases for I and R as vector spaces over F and an associated algorithm for determining whether an element of R is in I.

Such structures have been developed previously for certain principal differential ideals [i.e., ideals (Xc),x1 , ... ) with xj the j-th derivative of Xol in which the generator is homogeneous and isobaric and for a family of related ordinary ideals. The …

Branching Processes With Cataclysmic Environmental Changes., Juan F. Corona-BurgueñO

Mathematics & Statistics ETDs

In this dissertation we consider a continuous time branching process with a random environment in which the environment changes according to a continuous time Markov chain. The extinction problem for this model is posed and solved by two distinct methods: by the method of random evolutions of Griego and Hersh and by the results of Athreya and Karlin on branching processes with random environments. Limit theorems for the population size as well as a system of partial differential equations for the expected number of particles (as functions of time) are obtained.

A Prior Distribution For Smooth Regression, Leonard W. Deaton

Statistics

No abstract provided.

A Cephalometric Study Of Mandibulo-Facial Disostosis In Monozygotic Twins Using Computerized Methods, Lyn M. Lamberton

Loma Linda University Electronic Theses, Dissertations & Projects

An investigation using computerized cephalometrics has been conducted to consider the cephalometric factors responsible for the characteristic appearance evident in individuals afflicted with Mandibulo-Facial Dysostosis. A pair of Negro monozygotic affected twins were studied using the other 10 non-affected members of the family as a control to minimize the environmental and hereditary factors. The Rocky Mountain Data System was utilized to analyze the lateral and frontal cephalometric radiographs of each individual using Ricketts Analysis and the data were subjected to statistical tests to determine the factors contributory to the syndrome. Age and size were considered and adjustments were made to …

The Numerical Solution Of The Generalized Eigenvalue Problem For Rectangular Matrices, Charles Henry Burris Jr.

Mathematics & Statistics ETDs

This paper studies the Generalized Eigenvalue Problem Ax=λBx for real, rectangular matrices A and B. Several current algorithms for solving this problem are examined, most of which involve a determination of the rank of B, or one of its submatrices. An example is given in which such a decision cannot be made without introducing unnecessary error into the problem. The QZR Algorithm is then introduced as an algorithm which uses unitary transformations to reduce the matrices to a prescribed canonical form. This canonical form provides the information necessary for making decisions about rank. Since A and B can be non …

Independence, Essential Independence And Zero Correlation Of Two Random Variables Conditioned On A Third., Chester Raymond Crain Jr.

Mathematics & Statistics ETDs

In a recent paper Stoughton Bell and William J. Zimmer defined three distinct types of conditional independence; which they call pointwise, intervalwise and strong; of two random variables given a third. They considered these and four closely related independence properties, and they examined the relationships among the 128 (=23+4) Boolean combinations. Bell and Zimmer also considered the kinds of assumptions in applied research that would give rise to each type of conditional independence.

I have searched published texts and papers in probabil­ity and statistics for the three types of conditional inde­pendence. The type considered by Alfred Renyi [Foundations of Probability …

Cephalometric Norms For The Mexican Population Using The Ricketts, Steinar, And Tweed Analyses, Eduardo A. Velarde

Loma Linda University Electronic Theses, Dissertations & Projects

In order to investigate the characteristics of the facial complex of the Mexican and to compare them with the Caucasian, a sample of 40 subjects, 31 males and nine females, of Latin American origin from Chihuahua, Chihuahua, Mexico, with a mean age of 16.6 years, were selected for this study. The criteria for selection were visual and only individuals with clinical normal, Angle Class I occlusion were chosen.

Lateral head Roentgenograms were obtained and cephalometric evaluation of the Skeletal and Dental Pattern was carried out using the Ricketts, Steiner, and Tweed Analyses.

The mean values for the Mexican were compared …

Effects Of Cocaine, Nicotine And Diet On Voluntary Alcohol Consumption In Rats, Zaida Raquel Cordero Loayza

Loma Linda University Electronic Theses, Dissertations & Projects

The consumption of alcohol is a problem not only in this country (U.S.), but also in many other places in the world. Thus we find the Indians in Peru, Bolivia and other neighboring countries (Ecuador and northern part of Argentina) consuming alcohol to the point that they become alcoholics, in addition to this they also chew coca leaves, plant from which cocaine is extracted.

In an effort to establish the cause for this behavior, we put Sprague-Dawley albino rats on either a poor or good basal diet. Once every other day the rats were injected with a solution of cocaine. …

Comparison Of Transition Matrices Between Metropolitan And Non-Metropolitan Areas In The State Of Utah Using Juvenile Court Data, Sung-Ik Song

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to use Markov Chains for the study of youths referred to the juvenile court in the metropolitan and non-metropolitan areas of the state of Utah.

Two computer programs were written for creating case histories for each person referred to the court and for testing for the significance of the difference among several transition matrices.

Another computer program, which was written by Soo Hong Uh, was used for analyzing realizations of a Markov chains up to the 4th order; a third computer program, originally written by David White, was used for interpreting Markov chains.

The …

A Comparative Analysis Of The Use Of A Markov Chain Versus A Binomial Probability Model In Estimating The Probability Of Consecutive Rainless Days, Jack Wilfred Homeyer

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Markov chain process for predicting the occurence of a sequence of rainless days, a standard technique, is critically examined in light of the basic underlying assumptions that must be made each time it is used. This is then compared to a simple binomial model wherein an event is defined to be a series of rainless days of desired length. Computer programs to perform the required calculations are then presented and compared as to complexity and operating characteristics. Finally, an example of applying both programs to real data is presented and further comparisons are drawn between the two techniques.

Multiregional Interactions Between Energy And Transportation, Karen R. Polenske

Applications

Because of the number and complexity of the issues that will determine the use of coal by the electric-generating plants, an important asset of policy makers will be the availability of a method of analysis that allows for quick studies of many different combinations of assumptions and policies. The present prototype study is designed to show how the multiregional input-output model can be used to investigate each different assumption and policy alternative. For this paper, the analysis has necessarily been restricted to two issues. First, the results of using regional rather than national technologies in the model are assessed. This …

The Order Of An Entire Function With Some Derivatives Univalent, S. M. Shah, S. Y. Trimble

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

A Note On T, Topologies, Wilson R. Crisler, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

Let t be a T. topology for a set X. The problem of representing t as the lattice product (intersection) of stronger topologies is considered. © 1974 American Mathematical Society.

Grain Moisture And The Weather : What Can The Records Tell Us?, M W. Perry, P. A. Fievez

Journal of the Department of Agriculture, Western Australia, Series 4

The expansion of cereal production in areas along the south coast has exposed harvesting problems associated with high grain moisture.

A grain delivery standard of 12 per cent moisture means that, in the absence of grain drying facilities, harvesting times in the field are restricted to those hours when grain moisture falls below this figure.

Grain moisture, however, remains the major problem and for planning purposes, producers require an estimate of the harvesting time available in a given year. This will depend on all the climatic variables which affect grain moisture. These include rainfall and dew which deposit water directly …

A Sequential Testing System For Health Services Research And Testing, Matthew B. Barkley

MUSC Theses and Dissertations

Use of the Sequential Probability Ratio Test (SPRT) can save an experimenter's time, material, and money. Written for the Wang 600 Programmable Calculator, the Sequential Testing System performs the SPRT for any of seven common one-sample tests, greatly facilitating the use of this long-neglected clinical tool.