Hepatitis B virus (HBV) is one of many viruses transmitted through the blood or body fluids. This paper concentrates on a mathematical study of the survival rate of HBV. Using data which includes the survival time for individuals who were diagnosed as being affected by HBV and those who died from HBV, we fit non-linear models to study the survival time for people affected by the virus. Survival probabilities suggest an exponential curve for the survival time. We also consider a pure death process which is a stochastic model for the survival time of the individuals affected. Our results show that individuals who have been diagnosed as having HBV have an estimated life expectancy of approximately 625 days.

Many methods have been developed to determine the "appropriate" subset of independent variables in a multiple variable problem. Some of the methods are application specific while others have a wide range of uses. This study compares two such methods, Regression Trees and Stepwise Regression. A simulation using a known distribution is used for the comparison. In 699 out of 742 cases the Regression Tree method gave better predictors than the Stepwise Regression procedure.

Identifying non-tracking individuals in a population of longitudinal data has many applications as well as complications. The analysis of longitudinal data is a special study in itself. There are several accepted methods, of those we chose a two-stage random effects model coupled with the Estimation Maximization Algorithm (E-M Algorithm) . Our project consisted of first estimating population parameters using the previously mentioned methods. The Mahalanobis distance was then used to sequentially identify and eliminate non-trackers from the population. Computer simulations were run in order to measure the algorithm's effectiveness. Our results show that the average specificity for the repetitions for each simulation remained at the 99% level. The sensitivity was best when only a single non-tracker was present with a very different parameter a. The sensitivity of the program decreased when more than one tracker was present, indicating our method of identifying a non-tracker is not effective when the estimates of the population parameters are contaminated.

A method is described for finding the least squares solution of the overdetermined linear system that arises in the photogrammetric problem of bundle adjustment of aerial photographs. Because of the sparse, blocked structure of the coefficient matrix of the linear system, the proposed method is based on sparse QR factorization using Givens rotations. A reordering of the rows and columns of the matrix greatly reduces the fill-in during the factorization. Rules which predict the fill-in for this ordering are proven based upon the block structure of the matrix. These rules eliminate the need for the usual symbolic factorization in most cases. A subroutine library that implements the proposed method is listed. Timings and populations of a range of test problems are given.

Infant mortality is a public health concern in the United states. We concentrate on neonatal mortality for its high accountability of infant mortality. In this paper we study the neonatal mortality of Florida's 1989 live birth cohort. The data has been analyzed for two major causes of deaths: perinatal conditions and congenital anomalies. We use the KAPLAN-MEIER method to estimate the survival probabilities. For each cause, data were fit to the Weibull models and Extreme Value models to estimate the parameters of the survival curves. The results indicate that primary factors for each cause of neonatal deaths are very low birth weight, prior pregnancies of the mother, and late initiation of prenatal care when the variables are considered separately. The conclusion still remains the same for perinatal conditions when the interaction effects of the factors are considered, but we do not conclude similarly for the congenital anomalies at the same interaction level.

Let A = {an}∞n = 1 be a sequence of positive integers. There are two related sequences Pn and Qn obtained from A by taking partial convergents out of the number [0; a1, a2, ..., an, ...], where Pn and Qn are the numerators and denominators of the finite continued fraction [0; a1, a2, ...,an]. Let P(n) be the largest positive integer k , such that Pk ≤ n. The sequence Q(n) is defined similarly. • A known result of Barnes' Theorem states that P ( n ) = o ( n ) and Q ( n ) = o ( n ). • In this paper we improve this result as P ( n ) = O (log n) and Q ( n ) = O (log n), where it follows that P ( n )= o ( nε ) and Q ( n ) = o ( nε ) for any ε >0.

A meta-analysis is the combination of results from several similar studies, conducted by different scientists, in order to arrive at a single, overall conclusion. Unlike common experimental procedures, the data used in a meta-analysis happen to be the descriptive statistics from the distinct individual studies. In this thesis, we will consider two regression studies performed by two scientists. These studies have one common dependent variable, Y, and one or more independent common variables, X. A regression of Y on X with other independent variables is carried out on both studies. We will estimate the regression coefficients of X meta-analytically. After combining the two studies, we will derive a single regression model. There will be observations that one scientist witnesses and the other does not. The missing observations are considered parameters and are estimated using a method called Gibbs sampling.

In this thesis, the geometry of curved surfaces is studied using the methods of differential geometry. The introduction of manifolds assists in the study of classical two-dimensional surfaces. To study the geometry of a surface a metric, or way to measure, is needed. By changing the metric on a surface, a new geometric surface can be obtained. On any surface, curves called geodesics play the role of "straight lines" in Euclidean space. These curves minimize distance locally but not necessarily globally. The curvature of a surface at each point p affects the behavior of geodesics and the construction of geometric objects such as circles and triangles. These fundamental ideas of manifolds, geodesics, and curvature are developed and applied to classical surfaces in Euclidean space as well as models of non-Euclidean geometry, specifically, two-dimensional hyperbolic space.

The Fibonacci sequence and Cantor's ternary set are two objects of study in mathematics. There is much theory published about these two objects, individually. This paper provides a fascinating relationship between the Fibonacci sequence and Cantor's ternary set. It is a fact that every natural number can be expressed as the sum of distinct Fibonacci numbers. This expression is unique if and only if no two consecutive Fibonacci numbers are used in the expression--this is known as Zekendorf's representation of natural numbers. By Zekendorf's representation, a function F from the natural numbers into [0,0.603] will be defined which has the property that the closure of F(N) is homeomorphic to Cantor's ternary set. To accomplish this, it is shown that the closure of F(N) is a perfect, compact, totally disconnected metric space. This then shows that the closure of F(N) is homeomorphic to Cantor's ternary set and thereby establishing a relationship between the Fibonacci sequence and Cantor's ternary set.

Confidence Bands for Nonlinear Regression Functions can be found analytically for a very limited range of functions with a restrictive parameter space. A computer intensive technique, the Monte Carlo Method will be used to develop an algorithm to find confidence bands for any given nonlinear regression functions with a broader parameter space. The logistic regression function with one independent variable and two parameters will be used to test the validity and efficiency of the algorithm. The confidence bands for this particular function have been solved for analytically by Khorasani and Milliken (1982). Their derivations will be used to test the Monte Carlo algorithm.