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.

The implantable cardioverter defibrillator (lCD) is the most effective treatment available for terminating potentially life-threatening ventricular fibrillation and ventricular tachycardia. The lCD detects and attempts to correct these arrhythmias by pacing, cardioversion, and defibrillation thereby providing lifesaving therapy to patients at risk for sudden cardiac death. Currently, 150,000 Americans receive ICDs each year. Although most lCD recipients are men, more women are now qualifying for insertion (Stutts, Cross, Conti, & Sears, 2007). Despite its established health benefits, lCD implantation is accompanied by psychological factors which merit research attention. This study investigated the experiences of women who live an lCD. The homogenous, purposeful sample consisted of 15 women who had an lCD that was implanted within the last three years and were receiving follow-up treatment at the same north Florida clinic. Data collection was accomplished through a semi-structured interview specific to the areas of pre-implantation, immediate post-implantation, and discharge home. Results were transcribed verbatim and then analyzed. Five core themes emerged from the transcripts along with multiple subcategories. The main themes included: Psychological Reactions, Physical Comfort, Procedural Issues, Body Image, and Feelings Regarding a Shock. Information obtained from this research is beneficial to nurses providing care to women with ICDs and to primary care advanced nurse practitioners in order to improve the overall health outcome and ongoing care of these women.

Many samples in the real world are very small in size and often do not follow a normal distribution. Existing tests for correlation have restrictions on the distribution of data and sample sizes, therefore the current tests cannot be used in some real world situations. In this thesis, two tests are considered to test hypotheses about the population correlation coefficient. The tests are based on statistics transformed by a saddlepoint approximation and by Fisher's Z-transformation. The tests are conducted on small samples of bivariate nonnormal data and found to perfom well. Simulations were run in order to compare the type I error rates and power of the new test with other commonly used tests. The new tests controlled type I error rates well, and have reasonable power performance.

Many distributions of multivariate data in the real world follow a non-normal model with distributions being skewed and/or heavy tailed. In studies in which multivariate non-normal distributions are needed, it is important for simulations of those variables to provide data that is close to the desired parameters while also being fast and easy to perform. Three algorithms for generating multivariate non-normal distributions are reviewed for accuracy, speed and simplicity. They are the Fleishman Power Method, the Fifth-Order Polynomial Transformation Method, and the Generalized Lambda Distribution Method. Simulations were run in order to compare the three methods by how well they generate bivariate distributions with the desired means, variances, skewness, kurtoses, and correlation, simplicity of the algorithms, and how quickly the desired distributions were calculated.

In this paper, we present and implement a method to assess the mathematical synergy of two-drug combinations based on a stochastic model. The drugs in question are two isomers that are applied to the human eye via a liquid eye drop. Techniques applied to the data in this paper can be applied to other two-drug combination studies. We derive the mean and the variance terms of the drug combination "effects" in closed form using Ito's method of stochastic differential equations. The model fit of the data to the individual subject is examined by both statistical and graphical methods. Two estimation methods in SAS, PROC NUN and PROC NLMIXED, are used to estimate model parameters. We perform simulation and power studies using R software to show the strengths of the proposed approach in estimating the model parameters. From this research, we find that the combination of drugs under study is synergistic in nature. We also confirm that the proposed stochastic model is appropriate.