Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

Applied Mathematics

Institution
Keyword
Publication Year
Publication
Publication Type
File Type

Articles 7051 - 7080 of 7991

Full-Text Articles in Physical Sciences and Mathematics

Exotic Integral Witt Equivalence Of Algebraic Number Fields, Changheon Kang Jan 2002

Exotic Integral Witt Equivalence Of Algebraic Number Fields, Changheon Kang

LSU Doctoral Dissertations

Two algebraic number fields K and L are said to be exotically integrally Witt equivalent if there is a ring isomorphism W(OK) ~ W(OL) between the Witt rings of the number rings OK and OL of K and L, respectively. This dissertation studies exotic integral Witt equivalence for totally complex number fields and gives necessary and sufficient conditions for exotic integral equivalence in two special classes of totally complex number fields.

Go to article

On Properties Of Linear Control Systems On Lie Groups, Fabiana Cardetti Jan 2002

On Properties Of Linear Control Systems On Lie Groups, Fabiana Cardetti

LSU Doctoral Dissertations

In this work we study controllability properties of linear control systems on Lie groups as introduced by Ayala and Tirao in [AT99]. A linear control system _x0006_Σ Lie group G is defined by x' = X(x) + Σkj=1 ujYj(x), where the drift vector field X is an infinitesimal automorphism, uj are piecewise constant functions, and the control vectors Yj are left-invariant vector fields. Properties for the flow of the infinitesimal automorphism X and for the reachable set defined by _x0006_Σ are presented in Chapter 3. Under a condition similar to the Kalman …

Go to article

On The Stabilization And Regularization Of Rational Approximation Schemes For Semigroups, Simone Flory Jan 2002

On The Stabilization And Regularization Of Rational Approximation Schemes For Semigroups, Simone Flory

LSU Doctoral Dissertations

In this work we discuss consistency, stability and convergence of rational approximation methods for strongly continuous semigroups on Banach spaces. The Lax-Chernoff theorem shows that in this setting consistency and stability assumptions are necessary to obtain strong uniform convergence of approximation methods. We investigate rational approximation methods for strongly continuous semigroups and their consistency properties, with special emphasis on A-stable methods and Padé-type approximations. In particular, we discuss the stability and convergence properties of these schemes, including the stability of the well-known and widely used Backward-Euler and Crank-Nicolson Schemes. Furthermore, we modify stabilization techniques developed by Hansbo, Larsson, Luskin, Rannacher, …

Go to article

Dynamics Of A Granular Particle On A Rough Surface With A Staircase Profile, J. J. P. Veerman, F. V. Cunha Jr., G. L. Vasconcelos Jan 2002

Dynamics Of A Granular Particle On A Rough Surface With A Staircase Profile, J. J. P. Veerman, F. V. Cunha Jr., G. L. Vasconcelos

Mathematics and Statistics Faculty Publications and Presentations

A simple model is presented for the motion of a grain down a rough inclined surface with a staircase profile. The model is an extension of an earlier model of ours where we now allow for bouncing, i.e., we consider a non-vanishing normal coefficient of restitution. It is shown that in parameter space there are three regions of interest: (i) a region of smaller inclinations where the orbits are always bounded (and we argue that the particle always stops); (ii) a transition region where halting, periodic and unbounded orbits co-exist; and (iii) a region of large inclinations where no halting …

Go to article

Racks, Quandles And Virtual Knots, Victor Samuel Nelson Jan 2002

Racks, Quandles And Virtual Knots, Victor Samuel Nelson

LSU Doctoral Dissertations

We begin with a brief survey of the theory of virtual knots, which was announced in 1996 by Kauffman. This leads naturally to the subject of quandles and quandle homology, which we also briefly introduce. Chapter 2 contains a proof in terms of Gauss diagrams that the forbidden moves unknot virtual knots. This chapter includes material which has appeared in the Journal of Knot Theory and its Ramifications and is reprinted here by permission of World Scientific Publishing. In chapter 3 (cowritten with my advisor R.A.Litherland) we confirm a conjecture of J.S.Carter et.al. that the long exact sequence in rack …

Go to article

Discrete Mathematics Topics In The Secondary School Curriculum, Aimee Beth Boyd Jan 2002

Discrete Mathematics Topics In The Secondary School Curriculum, Aimee Beth Boyd

LSU Master's Theses

This thesis discusses two topics of discrete mathematics in a manner suitable for presentation at a secondary-school level. The introduction outlines the benefits of including discrete mathematics in the secondary-school curriculum. The two chapters which follow include detailed treatment of the two selected topics: the Traveling Salesman Problem and RSA encryption. The discussion of the Traveling Salesman Problem consists of introduction to the problem through several real-life scenarios, followed by a discussion of various methods for solving the problem. We discuss exact and approximate algorithms together with their computational complexity and practical limitations. The discussion of RSA encryption begins with …

Go to article

Tuberculosis Models With Fast And Slow Dynamics: The Role Of Close And Casual Contacts, Baojun Song, Carlos Castillo-Chavez, Juan Pablo Aparicio Jan 2002

Tuberculosis Models With Fast And Slow Dynamics: The Role Of Close And Casual Contacts, Baojun Song, Carlos Castillo-Chavez, Juan Pablo Aparicio

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Models that incorporate local and individual interactions are introduced in the context of the transmission dynamics of tuberculosis (TB). The multi-level contact structure implicitly assumes that individuals are at risk of infection from close contacts in generalized household (clusters) as well as from casual (random) contacts in the general population. Epidemiological time scales are used to reduce the dimensionality of the model and singular perturbation methods are used to corroborate the results of time-scale approximations. The concept and impact of optimal average cluster or generalized household size on TB dynamics is discussed. We also discuss the potential impact of our …

Go to article

An Analysis Of The Development And Application Of Orthogonal Polynomials With An Emphasis On The Legendre Polynomials, Francis Radnoti Jan 2002

An Analysis Of The Development And Application Of Orthogonal Polynomials With An Emphasis On The Legendre Polynomials, Francis Radnoti

Capstone Research Projects

No abstract provided.

Go to article

Single-Particle Model For A Granular Ratchet, Albert J. Bae, Welles Antonio Martinez Morgado, J. J. P. Veerman, Giovani L. Vasconcelos Jan 2002

Single-Particle Model For A Granular Ratchet, Albert J. Bae, Welles Antonio Martinez Morgado, J. J. P. Veerman, Giovani L. Vasconcelos

Mathematics and Statistics Faculty Publications and Presentations

A simple model for a granular ratchet corresponding to a single grain bouncing off a vertically vibrating sawtooth-shaped base is studied. Depending on the model parameters, horizontal transport is observed in both the preferred and unfavoured directions. A phase diagram is presented indicating the regions in parameter space where the different regimes (no current, normal current, and current reversal) occur.

Go to article

Flow Patterns In A Two-Roll Mill, Christopher Hills Jan 2002

Flow Patterns In A Two-Roll Mill, Christopher Hills

Articles

The two-dimensional flow of a Newtonian fluid in a rectangular box that contains two disjoint, independently-rotating, circular boundaries is studied. The flow field for this two-roll mill is determined numerically using a finite-difference scheme over a Cartesian grid with variable horizontal and vertical spacing to accommodate satisfactorily the circular boundaries. To make the streamfunction numerically determinate we insist that the pressure field is everywhere single-valued. The physical character, streamline topology and transitions of the flow are discussed for a range of geometries, rotation rates and Reynolds numbers in the underlying seven-parameter space. An account of a preliminary experimental study of …

Go to article

Numerical Solution Of Markov Chains, Amr Lotfy Elsayad Jan 2002

Numerical Solution Of Markov Chains, Amr Lotfy Elsayad

Theses Digitization Project

This project deals with techniques to solve Markov Chains numerically.

Go to article

Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, And The Boundary Element Method, Tian-Xiao He Jan 2002

Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, And The Boundary Element Method, Tian-Xiao He

Scholarship

This paper discusses the connection between boundary quadrature formulas constructed by using solutions of partial differential equations and boundary element schemes.

Go to article

On A Conjecture Of Furstenberg, Grzegorz Świçatek, J. J. P. Veerman Jan 2002

On A Conjecture Of Furstenberg, Grzegorz Świçatek, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

The Hausdorff dimension of the set of numbers which can be written using digits 0, 1,t in base 3 is estimated. For everyt irrational a lower bound 0.767 … is found.

Go to article

Semicontinuity Of Dimension And Measure For Locally Scaling Fractals, L. B. Jonker, J. J. P. Veerman Jan 2002

Semicontinuity Of Dimension And Measure For Locally Scaling Fractals, L. B. Jonker, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

The basic question of this paper is: If you consider two iterated function systems close to one another in an appropriate topology, are the dimensions of their respective invariant sets close to one another? It is well-known that the Hausdorff dimension (and Lebesgue measure) of the invariant set do not depend continuously on the iterated function system. Our main result is that (with a restriction on the ‘non-conformality’ of the transformations) the Hausdorff dimension is a lower semi-continuous function in the C1- topology of the transformations of the iterated function system. The same question is raised of the …

Go to article

Proceedings Of The First International Conference On Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability And Statistics, Florentin Smarandache Jan 2002

Proceedings Of The First International Conference On Neutrosophy, Neutrosophic Logic, Neutrosophic Set, Neutrosophic Probability And Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In 1960s Abraham Robinson has developed the non-standard analysis, a formalization of analysis and a branch of mathematical logic, that rigorously defines the infinitesimals. Informally, an infinitesimal is an infinitely small number. Formally, x is said to be infinitesimal if and only if for all positive integers n one has xxx < 1/n. Let &>0 be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers. Let’s consider the non-standard finite numbers 1+ = 1+&, where “1” is its standard part and “&” its non-standard part, …

Go to article

A Monotone Follower Control Problem With A Nonconvex Functional And Some Related Problems, Jamiiru Luttamaguzi Jan 2002

A Monotone Follower Control Problem With A Nonconvex Functional And Some Related Problems, Jamiiru Luttamaguzi

LSU Doctoral Dissertations

A generalized one-dimensional monotone follower control problem with a nonconvex functional is considered. The controls are assumed to be nonnegative progressively measurable processes. The verification theorem for this problem is presented. A specific monotone follower control problem with a nonconvex functional is then considered in which the diffusion term is constant. The optimal control for this problem, which is explicitly given, can be viewed as tracking a standard Wiener process by a non anticipating process starting at 0. For some parameters values, the value function for this monotone follower control problem is shown to be C2 and for other …

Go to article

The Effect Of Surface Curvature On Wound Healing In Bone, J. A. Adam Jan 2002

The Effect Of Surface Curvature On Wound Healing In Bone, J. A. Adam

Mathematics & Statistics Faculty Publications

The time-independent nonhomogeneous diffusion equation is solved for the equilibrium distribution of wound-induced growth factor over a hemispherical surface. The growth factor is produced at the inner edge of a circular wound and stimulates healing in regions where the concentration exceeds a certain threshold value. An implicit analytic criterion is derived for complete healing of the wound. (C) 2001 Elsevier Science Ltd. All rights reserved.

Go to article

Advances In Space Radiation Shielding Codes, John W. Wilson, Ram K. Tripathi, Garry D. Qualls, Francis A. Cucinotta, Richard E. Prael, John W. Norbury, John H. Heinbockel, John Tweed, Giovanni De Angelis Jan 2002

Advances In Space Radiation Shielding Codes, John W. Wilson, Ram K. Tripathi, Garry D. Qualls, Francis A. Cucinotta, Richard E. Prael, John W. Norbury, John H. Heinbockel, John Tweed, Giovanni De Angelis

Mathematics & Statistics Faculty Publications

Early space radiation shield code development relied on Monte Carlo methods and made important contributions to the space program. Monte Carlo methods have resorted to restricted one-dimensional problems leading to imperfect representation of appropriate boundary conditions. Even so, intensive computational requirements resulted and shield evaluation was made near the end of the design process. Resolving shielding issues usually had a negative impact on the design. Improved spacecraft shield design requires early entry of radiation constraints into the design process to maximize performance and minimize costs. As a result, we have been investigating high-speed computational procedures to allow shield analysis from …

Go to article

Healing Times For Circular Wounds On Plane And Spherical Bone Surfaces, J. A. Adam Jan 2002

Healing Times For Circular Wounds On Plane And Spherical Bone Surfaces, J. A. Adam

Mathematics & Statistics Faculty Publications

A mathematical model is developed for the rate of healing of a circular wound in a spherical "skull". The motivation for this model is based on experimental studies of the "'critical size defect" (CSD) in animal models; this has been defined as the smallest intraosseous wound that does not heal by bone formation during the lifetime of the animal [1]. For practical purposes, this timescale can usually be taken as one year. In [2], the definition was further extended to a defect which has less than ton percent bony regeneration during the lifetime of the animal. CSDS can "heal" by …

Go to article

Stable Refinable Generators Of Shift Invariant Spaces With Certain Regularities And Vanishing Moments, Tian-Xiao He Dec 2001

Stable Refinable Generators Of Shift Invariant Spaces With Certain Regularities And Vanishing Moments, Tian-Xiao He

Tian-Xiao He

In this paper, we discuss the stable refinable functions that generate shift in variant (SI) spaces and possess the largest possible regularities and required vanishing moments. The stability of the corresponding complementary spaces is also discussed.

Go to article

High-Order Interaction Of Solitary Waves On Shallow Water, Prof. Tim Marchant Dec 2001

High-Order Interaction Of Solitary Waves On Shallow Water, Prof. Tim Marchant

Tim Marchant

The interaction of solitary waves on shallow water is examined to fourth order. At first order the interaction is governed by the Korteweg-de Vries (KdV) equation, and it is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at third order. To resolve this, a mass conserving system of KdV equations, involving both right- and left-moving waves, is derived to third order. A fourth-order interaction term, in which the right- and left-moving waves are coupled, is also derived as this term is crucial in determining the fourth-order change in solitary wave amplitude. The form of …

Go to article

The Occurrence Of Limit-Cycles During Feedback Control Of Microwave Heating, Prof. Tim Marchant Dec 2001

The Occurrence Of Limit-Cycles During Feedback Control Of Microwave Heating, Prof. Tim Marchant

Tim Marchant

The microwave heating of one- and two-dimensional slabs, subject to linear feedback control, is examined. A semianalytical model of the microwave heating is developed using the Galerkin method. A local stability analysis of the model indicates that Hopf bifurcations occur; the regions of parameter space in which limit-cycles exist are identified. An efficient numerical scheme for the solution of the governing equations, which consist of the forced heat equation and a Helmholtz equation describing the electric-field amplitude, is also developed. An excellent comparison between numerical solutions of the semianalytical model and the governing equations is obtained for the temporal evolution …

Go to article

Cubic Autocatalytic Reaction-Diffusion Equations: Semi-Analytical Solutions, Prof. Tim Marchant Dec 2001

Cubic Autocatalytic Reaction-Diffusion Equations: Semi-Analytical Solutions, Prof. Tim Marchant

Tim Marchant

The Gray-Scott model of cubic-autocatalysis with linear decay is coupled with diffusion and considered in a one-dimensional reactor (a reaction-diffusion cell). The boundaries of the reactor are permeable, so diffusion occurs from external reservoirs that contain fixed concentrations of the reactant and catalyst. The Galerkin method is used to approximate the spatial structure of the reactant and autocatalyst concentrations in the reactor. Ordinary differential equations are then obtained as an approximation to the governing partial differential equations. The ordinary differential equations are then analysed to obtain semi-analytical results for the reaction-diffusion cell. Steady-state concentration profiles and bifurcation diagrams are obtained …

Go to article

Semi-Analytical Solutions For Continuous-Flow Microwave Reactors, Prof. Tim Marchant Dec 2001

Semi-Analytical Solutions For Continuous-Flow Microwave Reactors, Prof. Tim Marchant

Tim Marchant

A prototype chemical reaction is examined in both one and two-dimensional continuous-flow microwave reactors, which are unstirred so the effects of diffusion are important. The reaction rate obeys the Arrhenius law and the thermal absorptivity of the reactor contents is assumed to be both temperature- and concentration-dependent. The governing equations consist of coupled reaction-diffusion equations for the temperature and reactant concentration, plus a Helmholtz equation describing the electric-field amplitude in the reactor. The Galerkin method is used to develop a semi-analytical microwave reactor model, which consists of ordinary differential equations. A stability analysis is performed on the semi-analytical model. This …

Go to article

The Initial Boundary Problem For The Korteweg-De Vries Equation On The Negative Quarter-Plane, Prof. Tim Marchant Dec 2001

The Initial Boundary Problem For The Korteweg-De Vries Equation On The Negative Quarter-Plane, Prof. Tim Marchant

Tim Marchant

The initial boundary-value problem for the Korteweg-de Vries (KdV) equation on the negative quarter-plane, x < 0 and t > 0, is considered. The formulation of this problem is different to the usual initial boundary-value problem on the positive quarter-plane, for which x > 0 and t > 0. Two boundary conditions are required at x = 0 for the negative quarter-plane problem, in contrast to the one boundary condition needed at x = 0 for the positive quarter-plane problem. Solutions of the KdV equation on the infinite line, such as the soliton, cnoidal wave, mean height variation and undular bore solution, are used to find approximate …

Go to article

The Microwave Heating Of Three-Dimensional Blocks: Semi-Analytical Solutions, Prof. Tim Marchant Dec 2001

The Microwave Heating Of Three-Dimensional Blocks: Semi-Analytical Solutions, Prof. Tim Marchant

Tim Marchant

The microwave heating of three-dimensional blocks, by the transverse magnetic waveguide mode TM11, is considered in a long rectangular waveguide. The governing equations are the forced heat equation and a steady-state version of Maxwell's equations, while the boundary conditions take into account both convective and radiative heat loss. Semi-analytical solutions, valid for small thermal absorptivity, are found using the Galerkin method. The electrical conductivity and the thermal absorptivity are assumed to be temperature dependent, while both the electrical permittivity and magnetic permeability are taken to be constant. Both a quadratic relation and an Arrhenius-type law are used for the temperature …

Go to article

Numerical Solitary Wave Interaction: The Order Of The Inelastic Effect, Prof. Tim Marchant Dec 2001

Numerical Solitary Wave Interaction: The Order Of The Inelastic Effect, Prof. Tim Marchant

Tim Marchant

Solitary wave interaction is examined using an extended Benjamin-Bona-Mahony (eBBM) equation. This equation includes higher-order nonlinear and dispersive effects and is is asymptotically equivalent to the extended Korteweg-de Vries (eKdV) equation. The eBBM formulation is preferable to the eKdV equation for the numerical modelling of solitary wave collisions, due to the stability of its finite-difference scheme. In particular, it allows the interaction of steep waves to be modelled, which due to numerical instability, is not possible using the eKdV equation. Numerical simulations of a number of solitary wave collisions of varying nonlinearity are performed for two special cases corresponding to …

Go to article

Mathematical Models In Biology, Borbala Mazzag Dec 2001

Mathematical Models In Biology, Borbala Mazzag

Borbala Mazzag

No abstract provided.

Go to article

Analysis And Classification Of Nonlinear Dispersive Evolution Equations In The Potential Representation, Andrei Ludu Dec 2001

Analysis And Classification Of Nonlinear Dispersive Evolution Equations In The Potential Representation, Andrei Ludu

Andrei Ludu

No abstract provided.

Go to article

Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, And The Boundary Element Method, Tian-Xiao He Dec 2001

Dimensionality-Reducing Expansion, Boundary Type Quadrature Formulas, And The Boundary Element Method, Tian-Xiao He

Tian-Xiao He

This paper discusses the connection between boundary quadrature formulas constructed by using solutions of partial differential equations and boundary element schemes.

Go to article

First Prev Next Last