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Ordinary Differential Equations and Applied Dynamics Commons™

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2005

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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics

Multivalued Logic, Neutrosophy And Schrodinger Equation, Florentin Smarandache, Victor Christianto Dec 2005

Multivalued Logic, Neutrosophy And Schrodinger Equation, Florentin Smarandache, Victor Christianto

Branch Mathematics and Statistics Faculty and Staff Publications

This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given. Neutrosophy itself was developed in attempt to generalize Fuzzy-Logic introduced by L. Zadeh. While some aspects of theoretical foundations of logic are discussed, this book is not intended solely for pure mathematicians, but instead for physicists in the hope that some of ideas presented herein will be found useful. The book is motivated by …

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A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu Apr 2005

A Mathematical Model For Treatment-Resistant Mutations Of Hiv, Helen Moore, Weiqing Gu

All HMC Faculty Publications and Research

In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wild-type virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to …

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A Sampling And Transformation Approach To Solving Random Differential Equations, Roger A. Erich Mar 2005

A Sampling And Transformation Approach To Solving Random Differential Equations, Roger A. Erich

Theses and Dissertations

This research explores an innovative sampling method used to conduct uncertainty analysis on a system with one random input. Given the distribution of the random input, X, we seek to find the distribution of the output random variable Y. When the functional form of the transformation Y=g(X) is not explicitly known, complicated procedures, such as stochastic projection or Monte Carlo simulation must be employed. The main focus of this research is determining the distribution of the random variable Y=g(X) where g(X) is the solution to an ordinary differential equation and X is a random parameter. Here, y=g(X) is approximated by …

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Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N- Dimensions, Kurt Bryan, Lester Caudill Feb 2005

Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N- Dimensions, Kurt Bryan, Lester Caudill

Department of Math & Statistics Faculty Publications

We consider the inverse problem of determining the shape of some inaccessible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivatives, develop methods for regularizing the process, and provide computational examples.

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