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Applied Mathematics Commons™

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2008

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Articles 151 - 158 of 158

Full-Text Articles in Applied Mathematics

Stochastic Dynamic Equations, Suman Sanyal Jan 2008

Stochastic Dynamic Equations, Suman Sanyal

Doctoral Dissertations

"We propose a new area of mathematics, namely stochastic dynamic equations, which unifies and extends the theories of stochastic differential equations and stochastic difference equations. After giving a brief introduction to the theory of dynamic equations on time scales, we construct Brownian motion on isolated time scales and prove some of its properties. Then we define stochastic integrals on isolated time scales. The main contribution of this dissertation is to give explicit solutions of linear stochastic dynamic equations on isolated time scales. We illustrate the theoretical results for dynamic stock prices and Ornstein-Uhlenbeck dynamic equations. Finally we study almost sure …

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Methods In Industrial Biotechnology For Chemical Engineers, Florentin Smarandache, W.B. Vasantha Kandasamy Jan 2008

Methods In Industrial Biotechnology For Chemical Engineers, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Industrial Biotechnology is an interdisciplinary topic to which tools of modern biotechnology are applied for finding proper proportion of raw mix of chemicals, determination of set points, finding the flow rates etc., This study is significant as it results in better economy, quality product and control of pollution. The authors in this book have given only methods of industrial biotechnology mainly to help researchers, students and chemical engineers. Since biotechnology concerns practical and diverse applications including production of new drugs, clearing up pollution etc. we have in this book given methods to control pollution in chemical industries as it has …

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Generalization Of The Hybrid Logistic Model For More Than One Rare Risk Factor, Mamunur Rashid Jan 2008

Generalization Of The Hybrid Logistic Model For More Than One Rare Risk Factor, Mamunur Rashid

Mathematics Faculty Publications

Logistic models are commonly used to analyze case-control data. For case-control studies, if there tends be rare disease in the control group with the risk factors, then the estimation procedure using logistic regression model for such factors becomes difficult. To overcome such situation, Chen et. al. (2003) proposed a hybrid logistic model in which they first estimate the problematic risk factor assuming that proportions having disease of such risk factor are treated equal for all permissible strata of the other risk factors, and then the residual of the risk factors are modeled by using logistic regression model. The purpose of …

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Algebraic Properties Of Edge Ideals, Rachelle R. Bouchat Jan 2008

Algebraic Properties Of Edge Ideals, Rachelle R. Bouchat

University of Kentucky Doctoral Dissertations

Given a simple graph G, the corresponding edge ideal IG is the ideal generated by the edges of G. In 2007, Ha and Van Tuyl demonstrated an inductive procedure to construct the minimal free resolution of certain classes of edge ideals. We will provide a simplified proof of this inductive method for the class of trees. Furthermore, we will provide a comprehensive description of the finely graded Betti numbers occurring in the minimal free resolution of the edge ideal of a tree. For specific subclasses of trees, we will generate more precise information including explicit formulas for …

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Multigrid Convergence For Second Order Elliptic Problems With Smooth Complex Coefficients, Jay Gopalakrishnan, Joseph E. Pasciak Jan 2008

Multigrid Convergence For Second Order Elliptic Problems With Smooth Complex Coefficients, Jay Gopalakrishnan, Joseph E. Pasciak

Mathematics and Statistics Faculty Publications and Presentations

The finite element method when applied to a second order partial differential equation in divergence form can generate operators that are neither Hermitian nor definite when the coefficient function is complex valued. For such problems, under a uniqueness assumption, we prove the continuous dependence of the exact solution and its finite element approximations on data provided that the coefficients are smooth and uniformly bounded away from zero. Then we show that a multigrid algorithm converges once the coarse mesh size is smaller than some fixed number, providing an efficient solver for computing discrete approximations. Numerical experiments, while confirming the theory, …

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Asymptotic And Numerical Techniques For Resonances Of Thin Photonic Structures, Jay Gopalakrishnan, Shari Moskow, Fadil Santosa Jan 2008

Asymptotic And Numerical Techniques For Resonances Of Thin Photonic Structures, Jay Gopalakrishnan, Shari Moskow, Fadil Santosa

Mathematics and Statistics Faculty Publications and Presentations

We consider the problem of calculating resonance frequencies and radiative losses of an optical resonator. The optical resonator is in the form of a thin membrane with variable dielectric properties. This work provides two very different approaches for doing such calculations. The first is an asymptotic method which exploits the small thickness and high index of the membrane. We derive a limiting resonance problem as the thickness goes to zero, and for the case of a simple resonance, find a first order correction. The limiting problem and the correction are in one less space dimension, which can make the approach …

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On The Spectra Of Certain Directed Paths, Carlos Martins Da Fonseca, J. J. P. Veerman Jan 2008

On The Spectra Of Certain Directed Paths, Carlos Martins Da Fonseca, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We describe the eigenpairs of special kinds of tridiagonal matrices related to problems on traffic on a one-lane road. Some numerical examples are provided.

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Differential Geometry In Cartesian Closed Categories Of Smooth Spaces, Martin Laubinger Jan 2008

Differential Geometry In Cartesian Closed Categories Of Smooth Spaces, Martin Laubinger

LSU Doctoral Dissertations

The main categories of study in this thesis are the categories of diffeological and Fr\"olicher spaces. They form concrete cartesian closed categories. In Chapter 1 we provide relevant background from category theory and differentiation theory in locally convex spaces. In Chapter 2 we define a class of categories whose objects are sets with a structure determined by functions into the set. Fr\"olicher's $M$-spaces, Chen's differentiable spaces and Souriau's diffeological spaces fall into this class of categories. We prove cartesian closedness of the two main categories, and show that they have all limits and colimits. We exhibit an adjunction between the …

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