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Applied Mathematics Commons™

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2005

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Articles 121 - 129 of 129

Full-Text Articles in Applied Mathematics

Multiscale Strain Analysis, Timothy Donald Breitzman Jan 2005

Multiscale Strain Analysis, Timothy Donald Breitzman

LSU Doctoral Dissertations

The mathematical homogenization and corrector theory relevant to prestressed heterogeneous materials in the linear-elastic regime is discussed. A suitable corrector theory is derived to reconstruct the local strain field inside the composite. Based on this theory, we develop an inexpensive numerical method for multi scale strain analysis within a prestressed heterogeneous material. The theory also provides a characterization of the macroscopic strength domain. The strength domain places constraints on the homogenized strain field which guarantee that the actual strain in the heterogeneous material lies inside the strength domain of each material participating in the structure.

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Laguerre Functions Associated To Euclidean Jordan Algebras, Michael Aristidou Jan 2005

Laguerre Functions Associated To Euclidean Jordan Algebras, Michael Aristidou

LSU Doctoral Dissertations

Certain differential recursion relations for the Laguerre functions, defined on a symmetric cone Ω, can be derived from the representations of a specific Lie algebra on L2(Ω,dμv). This Lie algebra is the corresponding Lie algebra of the Lie group G that acts on the tube domain T(Ω)=Ω+iV, where V is the associated Euclidean Jordan algebra of Ω. The representations involved are the highest weight representations of G on L2(Ω,dμv). To obtain these representations, we start from the highest weight representations of G on Hv(T(Ω)), the Hilbert space of holomorphic functions …

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Virtual Strings For Closed Curves With Multiple Components And Filamentations For Virtual Links, William Schellhorn Jan 2005

Virtual Strings For Closed Curves With Multiple Components And Filamentations For Virtual Links, William Schellhorn

LSU Doctoral Dissertations

The theory of filaments on oriented chord diagrams can be used to detect some non-classical virtual knots. We extend existing filament techniques to virtual links with more than one component and give examples of virtual links that these techniques can detect as non-classical. Given a signed Gauss word underlying an oriented chord diagram, we describe how to construct a finite sequence of integers that encodes all of the filament information for the diagram. We also introduce a square array of integers called a MIN-square that summarizes the filament information about all of the signed Gauss words having a given Gauss …

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Dynamical Systems With Time Delay, Norma Ortiz Jan 2005

Dynamical Systems With Time Delay, Norma Ortiz

LSU Doctoral Dissertations

In this dissertation, we study necessary conditions and weak invariance properties of dynamical systems with time delay. A number of results have been obtained recently that refine necessary conditions of optimal solutions for nonsmooth dynamical systems without time delay. In this dissertation, we examine the extension of some of these results to problems with time delay. In particular, we study the generalized problem of Bolza with the addition of delay in the state and velocity variables and refer to this problem as the Neutral Problem of Bolza. We consider the relationship between the generalized problem of Bolza with time delay …

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Transient Non-Linear Heat Conduction Solution By A Dual Reciprocity Boundary Element Method With An Effective Posteriori Error Estimator, Eduardo Divo, Alain J. Kassab Jan 2005

Transient Non-Linear Heat Conduction Solution By A Dual Reciprocity Boundary Element Method With An Effective Posteriori Error Estimator, Eduardo Divo, Alain J. Kassab

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A Dual Reciprocity Boundary Element Method is formulated to solve non-linear heat conduction problems. The approach is based on using the Kirchhoff transform along with lagging of the effective non-linear thermal diffusivity. A posteriori error estimate is used to provide effective estimates of the temporal and spatial error. A numerical example is used to demonstrate the approach.

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Stability In Dynamical Polysystems, George Cazacu Jan 2005

Stability In Dynamical Polysystems, George Cazacu

LSU Doctoral Dissertations

A dynamical polysystem consists of a family of continuous dynamical systems, all acting on a given metric space. The first chapter of the present thesis shows a generalization of control systems via dynamical polysystems and establishes the equivalence of the two notions under certain lipschitz condition on the function defining the dynamics. The remaining chapters are focused on a basic theory of dynamical polysystems. Some topological properties of limit sets are described in Chapter 2. Chapters 3 and 4 provide characterizations for various notions of strong stability. Chapter 5 makes use of the theory of closed relations to study Lyapunov …

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Dissipative Lipschitz Dynamics, Vinicio Rafael Rios Jan 2005

Dissipative Lipschitz Dynamics, Vinicio Rafael Rios

LSU Doctoral Dissertations

In this dissertation we study two related important issues in control theory: invariance of dynamical systems and Hamilton-Jacobi theory associated with optimal control theory. Given a control system modelled as a differential inclusion, we provide necessary and sufficient conditions for the strong invariance property of the system when the dynamic satisfies a dissipative Lipschitz condition. We show that when the dynamic is almost upper semicontinuous and satisfies the dissipative Lipschitz property, these conditions can be expressed in terms of approximate Hamilton-Jacobi inequalities, which subsumes the classic infinitesimal characterization of strongly invariant systems given under the Lipschitz assumtion. In the important …

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Error Estimates For Stabilized Approximation Methods For Semigroups, Sarah Campbell Mcallister Jan 2005

Error Estimates For Stabilized Approximation Methods For Semigroups, Sarah Campbell Mcallister

LSU Doctoral Dissertations

In this work we analyze error estimates for rational approximation methods, and their stabilizations, for strongly continuous semigroups. Chapter 1 consists of a brief survey of time discretization methods for semigroups. In Chapter 2, we demonstrate a new method for obtaining convergent approximations in the absence of stability for strongly continuous semigroups with arbitrary initial data. In Section 2.2, we state the stabilization result in more general form and show that this method can be used to improve known error estimates by a magnitude of up to one half for smooth initial data. In Section 2.3, we give concrete examples …

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Wavelet Sets With And Without Groups And Multiresolution Analysis, Mihaela Dobrescu Jan 2005

Wavelet Sets With And Without Groups And Multiresolution Analysis, Mihaela Dobrescu

LSU Doctoral Dissertations

In this dissertation we study a special kind of wavelets, the so-called minimally supported frequency wavelets and the associated wavelet sets. Most of the examples of wavelet sets are for dilation sets which are groups. In this work we construct wavelet sets for which the dilation set, D, is of the form D=MN, where the product is direct, and so D is not necessarily group. In the second part of this dissertation we construct multiwavelets associated with MRA's and we generalize the rotations in the dilation sets to Coxeter groups.

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