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Articles 6271 - 6300 of 7997

Full-Text Articles in Physical Sciences and Mathematics

Trace Forms Of Abelian Extensions Of Number Fields, Karli Smith Jan 2008

Trace Forms Of Abelian Extensions Of Number Fields, Karli Smith

LSU Doctoral Dissertations

This dissertation is concerned with providing a description of certain symmetric bilinear forms, called trace forms, associated with finite normal extensions N/K of an algebraic number field K, with abelian Galois group Gal(N/K). These abelian trace forms are described up to Witt equivalence, that is, they are described as elements in the Witt ring W(K). Complete descriptions are obtained when the base field K has exactly one dyadic prime and either no real embeddings or one real embedding. For these fields K, the set of abelian trace forms is closed under multiplication in the Witt ring W(K).

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Multiscale Analysis Of Heterogeneous Media For Local And Nonlocal Continuum Theories, Bacim Alali Jan 2008

Multiscale Analysis Of Heterogeneous Media For Local And Nonlocal Continuum Theories, Bacim Alali

LSU Doctoral Dissertations

The dissertation provides new multiscale methods for the analysis of heterogeneous media. The first part of the dissertation treats heterogeneous media using the theory of linear elasticity. In this context, a methodology is presented for bounding the higher order moments of the local stress and strain fields inside random elastic media. Optimal lower bounds that are given in terms of the applied loading and the volume (area) fractions for random two-phase composites are presented. These bounds provide a means to measure load transfer across length scales relating the excursions of the local fields to applied loads. The second part of …

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Rational Approximation Schemes For Solutions Of Abstract Cauchy Problems And Evolution Equations, Patricio Gabriel Jara Jan 2008

Rational Approximation Schemes For Solutions Of Abstract Cauchy Problems And Evolution Equations, Patricio Gabriel Jara

LSU Doctoral Dissertations

In this dissertation we study time and space discretization methods for approximating solutions of abstract Cauchy problems and evolution equations in a Banach space setting. Two extensions of the Hille-Phillips functional calculus are developed. The first result is the Hille-Phillips functional calculus for generators of bi-continuous semigroups, and the second is a C-regularized version of the Hille-Phillips functional calculus for generators of C-regularized semigroups. These results are used in order to study time discretization schemes for abstract Cauchy problems associated with generators of bi-continuous semigroups as well as C-regularized semigoups. Stability, convergence results, and error estimates for rational approximation schemes …

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Stochastic And Copula Models For Credit Derivatives, Chao Meng Jan 2008

Stochastic And Copula Models For Credit Derivatives, Chao Meng

LSU Doctoral Dissertations

We prove results relating to the exit time of a stochastic process from a region in N-dimensional space. We compute certain stochastic integrals involving the exit time. Taking a Gaussian copula model for the hitting time behavior, we prove several results on the sensitivity of quantities connected with the hitting times to parameters of the model, as well as the large-N behavior. We discuss the relationship of these results to certain credit derivative instruments. Relevant simulations are presented.

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Blow-Up Behavior Of Solutions For Some Ordinary And Partial Differential Equations, Sarah Y. Bahk Jan 2008

Blow-Up Behavior Of Solutions For Some Ordinary And Partial Differential Equations, Sarah Y. Bahk

Theses Digitization Project

There are two parts in this project. Part 1 the Riccati initial-value problem is looked at. Part 2 considers blow-up property solutions for the degenerate semilinear parabolic initial-boundary value problem.

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Symmetric Presentations Of Finite Groups, Joshua Anthony Roche Jan 2008

Symmetric Presentations Of Finite Groups, Joshua Anthony Roche

Theses Digitization Project

Symmetric presentations of groups allow us to represent, and manipulate, group elements in a manner that is typically more convenient than conventional techniques; in this sense, symmetric presentations are particularly useful in the study of large finite groups.

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Quenching For Degenerate Semilinear Parabolic Problems With Insulated Boundary Conditions, Bernard Iyawe Jan 2008

Quenching For Degenerate Semilinear Parabolic Problems With Insulated Boundary Conditions, Bernard Iyawe

Theses Digitization Project

This thesis studied the existence, uniqueness, and quenching behavior of the solution to a degenerate equation subject to the initial condition and the second boundary conditions.

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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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Padé Spline Functions, Tian-Xiao He Jan 2008

Padé Spline Functions, Tian-Xiao He

Scholarship

We present here the definition of Pad´e spline functions, their expressions, and the estimate of the remainders of pad´e spline expansions. Some algorithms are also given.

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On Kuiper's Question Whether Taut Submanifolds Are Algebraic, Thomas E. Cecil, Quo-Shin Chi, Gary Jensen Jan 2008

On Kuiper's Question Whether Taut Submanifolds Are Algebraic, Thomas E. Cecil, Quo-Shin Chi, Gary Jensen

Mathematics and Computer Science Department Faculty Scholarship

We prove that any connected proper Dupin hypersurface in Rn is analytic algebraic and is an open subset of a connected component of an irreducible algebraic set. From this we also prove that every taut submanifold of dimension m ≤ 4 is algebraic by exploring a finiteness condition.

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Super Fuzzy Matrices And Super Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal Jan 2008

Super Fuzzy Matrices And Super Fuzzy Models For Social Scientists, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Amal

Branch Mathematics and Statistics Faculty and Staff Publications

The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. He wanted them to be equipped in a branch of mathematics that was increasingly valuable for the analysis of scientific data. This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. We do not indulge in labourious use of suffixes or …

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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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Ldpc Codes From Voltage Graphs, Christine A. Kelley, Judy L. Walker Jan 2008

Ldpc Codes From Voltage Graphs, Christine A. Kelley, Judy L. Walker

Department of Mathematics: Faculty Publications

Several well-known structure-based constructions of LDPC codes, for example codes based on permutation and circulant matrices and in particular, quasi-cyclic LDPC codes, can be interpreted via algebraic voltage assignments. We explain this connection and show how this idea from topological graph theory can be used to give simple proofs of many known properties of these codes. In addition, the notion of abelianinevitable cycle is introduced and the subgraphs giving rise to these cycles are classified. We also indicate how, by using more sophisticated voltage assignments, new classes of good LDPC codes may be obtained.

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On Existence And Uniqueness Results For The Bbm Equation With Arbitrary Forcing Terms, Timothy A. Smith Jan 2008

On Existence And Uniqueness Results For The Bbm Equation With Arbitrary Forcing Terms, Timothy A. Smith

Publications

The problem of classical solutions for the regularized long-wave equation is considered where various additional forcing terms are introduced which are often required for physical modifications in the wave theory. Sufficient conditions of solvability and existence are established and then these conditions are related to the structure of the forcing terms under consideration.

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Models Of Phototransduction In Rod Photoreceptors, Harihar Khanal, Vasilios Alexiades Jan 2008

Models Of Phototransduction In Rod Photoreceptors, Harihar Khanal, Vasilios Alexiades

Publications

Phototransduction is the process by which photons of light generate an electrical response in retinal rod and cone photoreceptors, thereby initiating vision. We compare the electrical response in salamander rods from increasingly more (spacialy) detailed models of phototransduction: 0-dimensional (bulk), 1-dimensional (longitudinal), 2-dimensional (axisymmetric), and 3-dimensional (with incisures). We discuss issues of finding physical parameters for simulation and validation of models, and also present some computational experiments for rods with geometry of mouse and human photoreceptors.

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Eigenvalue Comparisons For Boundary Value Problems Of The Discrete Elliptic Equation, Jun Ji, Bo Yang Jan 2008

Eigenvalue Comparisons For Boundary Value Problems Of The Discrete Elliptic Equation, Jun Ji, Bo Yang

Faculty Articles

In this paper we study a boundary value problem for a discrete elliptic equation. The focus will be on the structure of the spectrum of this problem and the existence of a positive eigenvector corresponding to the smallest eigenvalue. Comparison results for the eigenvalues are also established as the coefficients of the problem changes.

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Estimates Of Positive Solutions For Higher Order Right Focal Boundary Value Problem, Bo Yang Jan 2008

Estimates Of Positive Solutions For Higher Order Right Focal Boundary Value Problem, Bo Yang

Faculty Articles

We consider the (p;n - p) right focal boundary value problem. A new set of upper and lower estimates of positive solutions for the boundary value problem are obtained. These estimates implement and improve the ones in the literature.

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Encapsulation Of The Anticancer Drug Cisplatin Into Nanotubes, T. A. Hilder, James M. Hill Jan 2008

Encapsulation Of The Anticancer Drug Cisplatin Into Nanotubes, T. A. Hilder, James M. Hill

Faculty of Informatics - Papers (Archive)

One important application of nanotechnology is that of drug delivery, and in particular the targeted delivery of drugs using nanotubes. A proper understanding of the encapsulation behavior of drug molecules into nanotubes is vital for the development of nanoscale drug delivery vehicles. Furthermore, there are many other materials which may form single-walled nanotubes, such as carbon, boron carbide, boron nitride and silicon, and it is also important to understand their advantages and disadvantages. This paper presents a synopsis of the recent work in which boron nitride, boron carbide and silicon nanotubes are examined as drug delivery vehicles, and their encapsulation …

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Formulas For The Fourier Series Of Orthogonal Polynomials In Terms Of Special Functions, Nataniel Greene Jan 2008

Formulas For The Fourier Series Of Orthogonal Polynomials In Terms Of Special Functions, Nataniel Greene

Publications and Research

An explicit formula for the Fourier coefficient of the Legendre polynomials can be found in the Bateman Manuscript Project. However, formulas for more general classes of orthogonal polynomials do not appear to have been worked out. Here we derive explicit formulas for the Fourier series of Gegenbauer, Jacobi, Laguerre and Hermite polynomials. The methods described here apply in principle to a class of polynomials, including non-orthogonal polynomials.

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Inverse Wavelet Reconstruction For Resolving The Gibbs Phenomenon, Nataniel Greene Jan 2008

Inverse Wavelet Reconstruction For Resolving The Gibbs Phenomenon, Nataniel Greene

Publications and Research

The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities. Here we describe a numerical procedure for overcoming the Gibbs phenomenon called the inverse wavelet reconstruction method. The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series.

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Optimising Design Parameters Of Enzyme-Channelling Biosensors, Dana Mackey, Tony Killard Jan 2008

Optimising Design Parameters Of Enzyme-Channelling Biosensors, Dana Mackey, Tony Killard

Conference Papers

Two mathematical models for an electrochemical biosensor are proposed and compared with a view to determining the ratio of two immobilized enzymes which maximizes the amperometric signal amplitude.

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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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Algebraic Discretization Of The Camassa-Holm And Hunter-Saxton Equations, Rossen Ivanov Jan 2008

Algebraic Discretization Of The Camassa-Holm And Hunter-Saxton Equations, Rossen Ivanov

Articles

The Camassa-Holm (CH) and Hunter-Saxton (HS) equations have an interpretation as geodesic flow equations on the group of diffeomorphisms, preserving the H1 and H.1 right-invariant metrics correspondingly. There is an analogy to the Euler equations in hydrodynamics, which describe geodesic flow for a right-invariant metric on the infinitedimensional group of diffeomorphisms preserving the volume element of the domain of fluid flow and to the Euler equations of rigid body whith a fixed point, describing geodesics for a left-invariant metric on SO(3). The CH and HS equations are integrable bi-hamiltonian equations and one of their Hamiltonian structures is associated to the …

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Nearly-Hamiltonian Structure For Water Waves With Constant Vorticity, Adrian Constantin, Rossen Ivanov, Emil Prodanov Jan 2008

Nearly-Hamiltonian Structure For Water Waves With Constant Vorticity, Adrian Constantin, Rossen Ivanov, Emil Prodanov

Articles

We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.

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Algorithm-Independent Optimal Input Fluxes For Boundary Identification In Thermal Imaging, Kurt Bryan, Lester Caudill Jan 2008

Algorithm-Independent Optimal Input Fluxes For Boundary Identification In Thermal Imaging, Kurt Bryan, Lester Caudill

Department of Math & Statistics Faculty Publications

An inverse boundary determination problem for a parabolic model, arising in thermal imaging, is considered. The focus is on intelligently choosing an effective input heat flux, so as to maximize the practical effectiveness of an inversion algorithm. Three different methods, based on different interpretations of the term “effective", are presented and analyzed, then demonstrated through numerical examples. It is noteworthy that each of these flux-selection methods is independent of the particular inversion algorithm to be used.

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A Symbolic Operator Approach To Several Summation Formulas For Power Series Ii, Tian-Xiao He, Peter Shiue, L. C. Hsu Jan 2008

A Symbolic Operator Approach To Several Summation Formulas For Power Series Ii, Tian-Xiao He, Peter Shiue, L. C. Hsu

Scholarship

Here expounded is a kind of symbolic operator method that can be used to construct many transformation formulas and summation formulas for various types of power series including some old ones and more new ones.

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Laplace Transform Inversion And Time-Discretization Methods For Evolution Equations, Koray Ozer Jan 2008

Laplace Transform Inversion And Time-Discretization Methods For Evolution Equations, Koray Ozer

LSU Doctoral Dissertations

In this dissertation, we introduce Post-Widder-type inversion methods for the Laplace transform based on A-stable rational approximations of the exponential function. Since the results hold for Banach-space-valued functions, they yield efficient time-discretization methods for evolution equations of convolution type; e.g., linear first and higher order abstract Cauchy problems, inhomogeneous Cauchy problems, delay equations, Volterra and integro-differential equations, and problems that can be re-written as an abstract Cauchy problem on an appropriate state space.

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Polynomial Extension Operators. Part I, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl Jan 2008

Polynomial Extension Operators. Part I, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl

Mathematics and Statistics Faculty Publications and Presentations

In this series of papers, we construct operators that extend certain given functions on the boundary of a tetrahedron into the interior of the tetrahedron, with continuity properties in appropriate Sobolev norms. These extensions are novel in that they have certain polynomial preservation properties important in the analysis of high order finite elements. This part of the series is devoted to introducing our new technique for constructing the extensions, and its application to the case of polynomial extensions from H½(∂K) into H¹(K), for any tetrahedron K.

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A Mixed Method For Axisymmetric Div-Curl Systems, Dylan M. Copeland, Jay Gopalakrishnan, Joseph E. Pasciak Jan 2008

A Mixed Method For Axisymmetric Div-Curl Systems, Dylan M. Copeland, Jay Gopalakrishnan, Joseph E. Pasciak

Mathematics and Statistics Faculty Publications and Presentations

We present a mixed method for a three-dimensional axisymmetric div-curl system reduced to a two-dimensional computational domain via cylindrical coordinates. We show that when the meridian axisymmetric Maxwell problem is approximated by a mixed method using the lowest order Nédélec elements (for the vector variable) and linear elements (for the Lagrange multiplier), one obtains optimal error estimates in certain weighted Sobolev norms. The main ingredient of the analysis is a sequence of projectors in the weighted norms satisfying some commutativity properties.

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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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