Digital Commons Network^™

Matrix Norms, I-Hui C. Cheng

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

In many situations it is very useful to have a single nonnegative real number to be, in some sense, the measure of the size of a vector or a matrix. As a matter of fact we do a similiar thing with scalars, we let jÀj represent the familiar absolute value or modulus of À. Fora vector x e: C , one way n of assigning magnitude is the usual definition of length, Il I 1/2 2 1/2 xl= = {jxij } , which is called the euclidean norm of x. In this case, length gives an overall estimate of the …

Principal Component Factor Analysis, Kuang-Ming Chu

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

The principal-factor solution is probably the most widely used technique in factor analysis and a relatively straight forward method to determine the minimum number of independent dimensions needed to account for most of the variance in the original set of variables.

The principal components approach to parsimony was first proposed by Karl Pearson (1901) who studied the problem for the case of nonstochastic variables, and in a different context. Hotelling provided the full development of the method (1933) and Thomson (1947) was the first to apply it to the principal factor analysis.

This method was first developed to deal with …

Determining Sample Size For A Control Chart, Shu-Yang Catherine Jean

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

The essential tool in statistical quality control is the control chart. In spite of the apparent simplicity of the control chart, most engineers, production men, and inspectors find that its use calls for an entirely new point of view. The power of this technique lies in its ability to separate out assignable causes of quality variation. This makes possible the diagnosis and correction of many production troubles and often brings substantial improvements in product quality and reduction of spoilage and rework. The control chart tells when to leave a process alone and thus prevents unnecessarily frequent adjustments that tend to …

Recovering Individual Data In The Presence Of Group And Individual Effects, Gudmund R. Iversen

Mathematics & Statistics Faculty Works

The ecological fallacy of relating variables on the group level, when the individual-level relationship is desired, can only be avoided by using individual-level data. This paper gives some conditions for occasions when individual-level data can successfully be recovered from grouped data. Such a recovery is illustrated using data on urban or rural residence and participation or not in the labor force as an example. The conditions are given in terms of the distinction between individual-and group-level effects of one variable on another. Recovering individual data, on the one hand, and the study of individual and group-level effects, on the other …

A Method Of Moments Applied To An Invariant Imbedding Solution Of A Certain Class Of Fredholm Integral Equations., Grenfell Paul Boicourt

Mathematics & Statistics ETDs

This dissertation first develops a method for solving the integral equation when y(z') is a constant and then extends it to the case where y(z') is a step function. The solution of the integral equation is achieved by solving the integro differential invariant imbedding equations derived from the integral equation by varying the limits of integration. The imbedding equations are solved using a moment method which reduces the calculation to an initial value problem. Proofs of the existence and convergence of the method are given. In the case where y(z') is a constant, the solution of the integral equation is …

Line Critical Point Determining And Point Distinguishing Graphs.Geodetic Orientations Of Complete K-Partite Graphs., Larry Dean Gassman

Mathematics & Statistics ETDs

I. Sumner defined a graph to be point determining if and only if distinct points have distinct neighborhoods and he has characterized connected line-critical point determining graphs. Here a short alternate proof of his characterization is provided and arbitrary line-critical point determining graphs are then characterized. Next line-critical point distinguishing graphs are considered; a graph is point distinguishing if and only if it is the complement of a point determining graph. Finally line-critical graphs that are both point determining and point distinguishing are characterized.

II. Ore defined a graph to be geodetic if and only if there is a unique …

Estimation Of Probability Functions Using Splines., Douglas Wade Hill

Mathematics & Statistics ETDs

In this paper, three classes of spline functions are applied to the problem of estimating probability distribution and density functions. In each case, it is shown that the spline function approximating the sample cumulative distribution function converges almost surely to the unknown distribution, F, given that F has at least two continuous derivatives. If F has three or more continuous derivatives, the derivative of the spline converges to the density function. For polynomial splines of sufficiently high degree if F has k continuous derivative, the rate of convergence for the j-th derivative is shown to be 0(hk-j-1/2) where h is …

A Method Of Analyzing Mandibular Movement, Richard B. Mccoy

Loma Linda University Electronic Theses, Dissertations & Projects

Mandibular movement is considered to be a fundamental factor in the study, analysis, and treatment of occlusion. For many years, dentists have realized that dental health depends upon the compatibility of mandibular movements and occlusion. This realization has led to the development of new methods and techniques for recording accurately and scientifically the movements of the mandible. In order for this data to be of scientific value, it must be stored in a usable form which is easily available for analysis.

The purpose of this research project was to develop a procedure for storing and recalling mandibular-movement information. Before such …

The Effect Of A Repressive-Inspirational Discussion Group On The Self-Esteem Of Selected Elderly Individuals, Rebecca Hollesca Gucilatar

Loma Linda University Electronic Theses, Dissertations & Projects

This study was conducted to determine if the use of a repressive-inspirational discussion group has significance in changing the level of self-esteem of institutionalized essentially normal elderly individuals.

A review of literature indicates the need for a group method that can help in developing and maintaining self-esteem in the elderly. Different studies reveal the need for self-esteem in the aged. The development of self-esteem is necessary so that elderly individuals can cope with situations in daily living and maintain physical and mental health.

An experimental method was utilized in conducting this study. A sample of twenty elderly individuals was selected …

Selected Physiological Responses To A Back Rub, Norma (Ewing) Anderson

Loma Linda University Electronic Theses, Dissertations & Projects

The back rub, which has been an established part of evening patient care for many years, is given to promote relaxation and sleep as well as to promote skin care. Yet its place in modern nursing seems questionable. Today's nurse is less willing to practice using empirically established procedures.

There have been few investigations showing the effect of massage to the back and no studies have shown that a brief back rub, as given by nurses, promotes relaxation. In cardiovascular nursing there is some controversy as to whether or not the back rub causes stimulation to the cardiovascular system that …

The Nursing Process And Its Relationship To The Quality Of Nursing Care, Arlene H. Johnson

Loma Linda University Electronic Theses, Dissertations & Projects

The purpose of this study was to determine the effect of the systematic use of the nursing process on the quality of nursing care. Quality nursing care was defined as being achieved when the patient's nursing care needs are identified and plans made to assist the patient with these needs.

It was hypothesized that the quality of nursing care would be improved by the participation of the team leaders in a series of classes on the nursing process. This improvement in quality nursing care would be evidenced by a higher correlation between the patient's needs perceived by the nurse and …

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 k^th 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.

An Investigation Of Cluster Analysis, John C. Klingel

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Three cluster analysis programs were used to group the same 64 individuals, generated so as to represent eight populations of eight individuals each. Each individual had quantitative values for seven attributes. All eight populations shared a common attribute variance-covariance matrix.

The first program, from F. J. Rohlf's MINT package, implemented single linkage. Correlation was used as the basis for similarity. The results were not satisfactory, and the further use of correlation is in question.

The second program, MDISP, bases similarity on Euclidean distance. It was found to give excellent results, in that it clustered individuals into the exact populations from …

A General Lr(K) Parser Building Algorithm, Thomas Joshua Sager

Mathematics & Statistics ETDs

The problem is to find an efficient algorithm that, given the productions of a context-free grammar G, will discover whether G is LR(k) for given k and if it is build an efficient parser for G . The algorithm is given in Section 8. It is essentially a synthesis of the best parts of Knuth's and DeRemer's algorithms. On simple LR(k) grarranars it yields a result equivalent to DeRemer's algorithm, and like Knuth's algorithm it will work on all LR(k) grammars.

Convergence Lattices, Armando Rosario Gingras

Mathematics & Statistics ETDs

This study is concerned with complete lattices in which order convergence coincides with topological convergence with respect to the order topology. Such lattices are termed convergence lattices. After a brief discussion of topology on lattices (Introduction), some preliminary results concerning order convergence and the order topology are presented (Section 1). Several theorems characterizing convergence lattices are presented in Section 2. There it is shown that every neighborhood of a point of a convergence lattice contains an interval that is also a neighborhood of the point. It is also shown that each complete chain, each arbitrary product of convergence lattices, and …

Leadership Techniques In Groups With Chronic Schizophrenics, Judith L. Jensen, Leona W. Mcgrew

Loma Linda University Electronic Theses, Dissertations & Projects

The study was designed to assess the level of anxiety experienced by chronic schizophrenic patients when two different methods of leadership were used in group therapy. A search of literature revealed suggestions for modification of leadership approach due to the tenuous anxiety tolerance of chronic schizophrenics but no studies were found directly related to the amount of anxiety resulting from different leadership approaches.

A structured group in which the leader maintained a directive role was compared with a nonstructured group in which the leader maintained a nondirective role in the group process. The randomized sample included five male and five …

The Effect Of A Training Program On Job Satisfaction Among Hospital Dietary Supportive Personnel, Alice E. Calkins

Loma Linda University Electronic Theses, Dissertations & Projects

Steadily rising labor costs are forcing health-care institutions to give increased attention to meeting manpower needs. Dietary service management is recognizing the need for employees to be satisfied with their work, as well as the difficulty of providing adequate training for each employee. A study of the effect of a training program on job satisfaction should provide information relevant to more effective planning for the training and development of human resources within the hospital dietary service.

The purpose of this research was to determine the level of job satisfaction among hospital dietary supportive personnel; relate it to such factors as …

Backward And Forward Equations For Random Evolutions., Manuel Keepler

Mathematics & Statistics ETDs

Let V= [v(t),t>=0] be a separable right continuous Markov hain with state space [1,…,N], stationary transition probabilities Pij(t) and infinitesimal matrix Q=(Qij). Let [Ti(t),t>=0, i=1,…,N] be a family of strongly continuous uniformly bounded semigroups of bounded linear operators on a Banach space B. Ai is the infinitesimal generator of T1.

Quasi-Unmixed Local Rings And Quasi-Subspaces, Peter G. Sawtelle

Mathematics and Statistics Faculty Research & Creative Works

The concept of a quasi-subspace is defined so that it plays a role relative to quasi-unmixedness analogous to that of subspace to unmixedness. This definition is used to characterize quasi-unmixed local rings. © 1973 American Mathematical Society.

A First Order Method For Differential Equations Of Neutral Type, R. N. Castleton, L. J. Grimm

Mathematics and Statistics Faculty Research & Creative Works

A first order method is presented for solution of the initial-value problem for a differential equation of neutral type with implicit delay in the critical case where the time-lag is zero and the method of stepwise integration does not apply. A convergence theorem is proved, and numerical examples are given. © 1973, American Mathematical Society.

Computer Programs Supporting The Teaching Of Statistics, Chien-Hwa Liu

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

During the past few years there has been an increasing interest in developing computer packages to enhance the teaching of elementary statistics. The conventional ways of teaching statistics have used such devices as desk calculators, tables of functions, short-cut calculating formulas and electronic calculators, etc. to manipulate the involved computations. Electronic computers, in the past decade, have been broadly used in universities and colleges in many ways. It is only natural to extend the use of computers to the teaching function. Remote terminals can now be installed in any classroom and bring the computer to the students.

The Evaluation Of Glasser's Maximum Likelihood Method On Missing Data In Regression, Gayle M. Yamasaki

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

Missing data in regression is often a problem to research workers because standard regression methods are applicable only to complete data sets. At present there are three general methods for solving the problem of missing data.

At first, the reduced data method, reduces the incomplete data set to a complete data set before analyzing. Although this method is very simple to apply, substantial amounts of information are sometimes lost when data is eliminated. This results in less precise estimates of the regression parameters.

The second method, generalized least squares, estimates the missing values through least squares techniques, thus obtaining a …

Objective Measurement Of Wool : Criteria, Methods And Materials, A Ingleton

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

An outline of some of the technical aspects of the objective measurement of wool—processes that will mean major cost savings to the wool industry.

A Monte Carlo Comparison Of Nonparametric Reliability Estimators, Jia-Jinn Yueh

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

It is very difficult to construct a reliability model for a complex system. However, the reliability model for a series configuration is relatively simple. In the simplest case in which the components are mutually independent, the system reliability can be represented as follows:

R_s(x) = ∑ⁿ_i=1R_i(x),

where R_i is the reliability for the i^th component. It is also known that for moderate levels of system reliability for large systems, the component reliability must be high.

Extreme Value Theory indicates that under very general conditions, the initial form of the distribution function …

Integer Programming By Cutting Planes Methods, Sung-Yen Wu

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

Linear programming is a relatively new, very important branch of modern mathematics and is about twenty five years old.

In this day and age, most planners and decision makers will acknowledge that some linear optimization problems are worth the expense and trouble to solve. Using linear programming technique as a tool to make decision plannes are able to greatly redice cost or increase profit for any project under consideration.

Since Dr. George B. Dantzig published his first paper on the simplex method in 1947, progress in that field has been rapid. Although the first applications were military in nature, it …

A Nonparametric Solution For Finding The Optimum Useful Life Of Equipment, Barry T. Stoll

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

It is often the case that equipment used by industry must be replaced with new equipment from time to time either because frequent malfunctions make it too costly to repair, or because the equipment has simply worn out. The new equipment often has the nature of either malfunctioning soon after installation due to manufacturing defects, or functioning for an extended period of time because it is free of these defects. For this reason, equipment is often given a preliminary running called the burn-in which gives no useful output but merely tests for manufacturing defects. Also, after a given amount of …

Canonical Analysis Of Several Sets Of Variables, Chong S. Kim

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

Many procedures have been proposed for analyzing and describing multivariate dependence structure.

Partial correlation, multiple correlation, canonical correlation, principal component and factor analysis are used to analyze the dependence structures of a multinormal population.

For a partial correlation analysis it is necessary to decide which variables are to be correlated and which of the remaining variables must be held constant.

Multiple correlation demands that one variable be dependent upon some or all of the remaining variates.

For a canonical correlation, the variables must be collected into two or more sets. The factor analysis technique is for explaining the covariances of …

Stochastic Integro-Differential Equations Of Volterra Type, William J. Padgett, Chris P. Tsokos

Faculty Publications

No abstract provided.

Adaptive Prediction Of Stationary Time Series By Modified Conjugate Direction Methods, James Otto Friel

Mathematics & Statistics ETDs

We consider the problem of obtaining finite memory linear one-step predictors for a non-deterministic weakly stationary stochastic process {u_t : t = 0, ± 1, ± 2, ± ···} which have minimum mean square error. If φ(k) = Ɛ u_t u_t+k is the (unknown) covariance function for the process this problem reduces to solving the system of linear equations φ x = φ where φ = (φ(1), φ(2), ..., φ(d)), φ = (φ(i - j)) i, j = 1, 2, ..., d. Two iterative procedures are developed for producing a sequence of estimators {x_n}_{n=1 …}

Health Status Of Emergency Department Patients, Marjean J. Horning

Loma Linda University Electronic Theses, Dissertations & Projects

The purpose of this study was to help nursing develop a comprehensive care system for patients in selected emergency departments. To develop such a system, it was necessary to know the characteristics of and the health needs of that population.

The problem of this study was to describe the characteristics and health needs of patients in selected emergency departments.

Patients were interviewed using the Kisch Health Status Proxy (KHSP) and the Health Habits Inventory (HHI) as a guide. The KHSP listed acute and chronic conditions that an individual experienced. It gave a numerical score which rated the respondent in good, …