Asymptotic Properties Of Stochastic Partial Differential Equations In Hilbert Spaces Driven By Non-Gaussian Noise, 2011 Louisiana State University

#### Asymptotic Properties Of Stochastic Partial Differential Equations In Hilbert Spaces Driven By Non-Gaussian Noise, V Mandrekar, Li Wang

*Communications on Stochastic Analysis*

No abstract provided.

An Extension Of Bifractional Brownian Motion, 2011 Louisiana State University

#### An Extension Of Bifractional Brownian Motion, Xavier Bardina, Khalifa Es-Sebaiy

*Communications on Stochastic Analysis*

No abstract provided.

Cdo Tranche Sensitivities In The Gaussian Copula Model, 2011 Louisiana State University

#### Cdo Tranche Sensitivities In The Gaussian Copula Model, Chao Meng, Ambar N Sengupta

*Communications on Stochastic Analysis*

No abstract provided.

Integration By Parts Formula And The Stein Lemma On Abstract Wiener Space, 2011 Louisiana State University

#### Integration By Parts Formula And The Stein Lemma On Abstract Wiener Space, Hui-Hsiung Kuo, Yuh-Jia Lee

*Communications on Stochastic Analysis*

No abstract provided.

Stochastic Jacobians In Affine Term-Structure Models: A Local Property, 2011 Louisiana State University

#### Stochastic Jacobians In Affine Term-Structure Models: A Local Property, Cody Blaine Hyndman

*Communications on Stochastic Analysis*

No abstract provided.

A General Theorem For Portfolio Generating Functions, 2011 Louisiana State University

#### A General Theorem For Portfolio Generating Functions, Olivier Menoukeu Pamen

*Communications on Stochastic Analysis*

No abstract provided.

On The Value Of Stochastic Differential Games, 2011 Louisiana State University

#### On The Value Of Stochastic Differential Games, Wendell H Fleming, Daniel Hernández-Hernández

*Communications on Stochastic Analysis*

No abstract provided.

Evolution Systems Of Measures For Non-Autonomous Ornstein-Uhlenbeck Processes With Lévy Noise, 2011 Louisiana State University

#### Evolution Systems Of Measures For Non-Autonomous Ornstein-Uhlenbeck Processes With Lévy Noise, Robert Wooster

*Communications on Stochastic Analysis*

No abstract provided.

Budding Yeast, Branching Processes, And Generalized Fibonacci Numbers, 2011 Trinity University

#### Budding Yeast, Branching Processes, And Generalized Fibonacci Numbers, Peter Olofsson, Ryan C. Daileda

*Mathematics Faculty Research*

A real-world application of branching processes to a problem in cell biology where the generalized Fibonacci numbers known as *k*-nacci numbers play a crucial role is described. The *k*-nacci sequence is used to obtain asymptotics, computational formulas, and to justify certain practical simplifications. Along the way, an explicit formula for the sum of *k*-nacci numbers is established.

Asymptotic And Numerical Analysis Of Time-Dependent Wave Propagation In Dispersive Dielectric Media That Exhibit Fractional Relaxation, 2011 New Jersey Institute of Technology

#### Asymptotic And Numerical Analysis Of Time-Dependent Wave Propagation In Dispersive Dielectric Media That Exhibit Fractional Relaxation, Matthew Frank Causley

*Dissertations*

This dissertation addresses electromagnetic pulse propagation through anomalously dispersive dielectric media. The Havriliak-Negami (H-N) and Cole-Cole (C-C) models capture the non-exponential nature of such dielectric relaxation phenomena, which is manifest in a variety of dispersive dielectric media. In the C-C model, the dielectric polarization is coupled to the time-dependent Maxwell's equations by a fractional differential equation involving the electric field. In the H-N case, a more general pseudo-fractional differential operator describes the polarization.

The development and analysis of a robust method for implementing such models is presented, with an emphasis on algorithmic efficiency. Separate numerical schemes are presented for ...

Sequential Bayesian Filtering For Spatial Arrival Time Estimation, 2011 New Jersey Institute of Technology

#### Sequential Bayesian Filtering For Spatial Arrival Time Estimation, Rashi Jain

*Dissertations*

Locating and tracking a source in an ocean environment as well as estimating environmental parameters of a sound propagation medium is of utmost importance in underwater acoustics. Matched field processing is often the method of choice for the estimation of such parameters. This approach, based on full field calculations, is computationally intensive and sensitive to assumptions on the structure of the environment. As an alternative, methods that use only select features of the acoustic field for source localization and environmental inversion have been proposed. The focus here is on inversion using arrival times of identified paths within recorded time-series. After ...

Some Contributions To Modeling Usage Sensitive Warranty Servicing Strategies And Their Analyses, 2011 New Jersey Institute of Technology

#### Some Contributions To Modeling Usage Sensitive Warranty Servicing Strategies And Their Analyses, Rudrani Banerjee

*Dissertations*

Providing a warranty as a part of a product's sale is a common practice in industry. Parameters of such warranties (e.g., its duration limits, intensity of use) must be carefully specified to ensure their financial viability. A great deal of effort has been accordingly devoted in attempts to reduce the costs of warranties via appropriately designed strategies to service them. many such strategies, that aim to reduce the total expected costs of the warrantor or / and are appealing in other ways such as being more pragmatic to implement - have been suggested in the literature. Design, analysis and optimization ...

The Weak Cayley Table And The Relative Weak Cayley Table, 2011 Brigham Young University - Provo

#### The Weak Cayley Table And The Relative Weak Cayley Table, Melissa Anne Mitchell

*Theses and Dissertations*

In 1896, Frobenius began the study of character theory while factoring the group determinant. Later in 1963, Brauer pointed out that the relationship between characters and their groups was still not fully understood. He published a series of questions that he felt would be important to resolve. In response to these questions, Johnson, Mattarei, and Sehgal developed the idea of a weak Cayley table map between groups. The set of all weak Cayley table maps from one group to itself also has a group structure, which we will call the weak Cayley table group. We will examine the weak Cayley ...

Numerical And Asymptotic Modeling Of Evolving Nonlinear Ocean Surface Wave Fields, 2011 New Jersey Institute of Technology

#### Numerical And Asymptotic Modeling Of Evolving Nonlinear Ocean Surface Wave Fields, Matt Malej

*Dissertations*

The main focus of this dissertation is the asymptotic and numerical modeling of nonlinear ocean surface wave fields. In particular, a development of an accurate numerical model for the evolution of nonlinear ocean waves, including extreme waves known as Rogue/Freak waves. Due to their elusive and destructive nature, the media often portrays Rogue waves as unimaginatively huge and unpredictable monsters of the sea. To address these concerns, derivations of asymptotically reduced models, based on the small wave steepness assumption, are presented and their corresponding numerical simulations via a Fourier pseudo-spectral method are discussed. The simulations are initialized with a ...

Using Feed-Forward Networks To Infer The Activity Of Feedback Neuronal Networks, 2011 New Jersey Institute of Technology

#### Using Feed-Forward Networks To Infer The Activity Of Feedback Neuronal Networks, Xinxian Huang

*Dissertations*

The nervous system is one of the most important organ systems in a multicellular body. Animals, including human beings perceive, learn, think and deliver motion instructions through their nervous system. The basic structural units of the nervous system are individual neurons which constitute different neuronal networks with distinct functions. In each network, constituent neurons are coupled with different connection patterns, for example, some neurons send feed-forward information to the coupling neurons while others are mutually coupled. Because it is often difficult to analyze large interconnected feedback neuronal networks, it is important to derive techniques to reduce the complexity of the ...

Markovian And Stochastic Differential Equation Based Approaches To Computer Virus Propagation Dynamics And Some Models For Survival Distributions, 2011 New Jersey Institute of Technology

#### Markovian And Stochastic Differential Equation Based Approaches To Computer Virus Propagation Dynamics And Some Models For Survival Distributions, Lianzhe Xu

*Dissertations*

This dissertation is divided in two Parts. The first Part explores probabilistic modeling of propagation of computer `malware' (generally referred to as `virus') across a network of computers, and investigates modeling improvements achieved by introducing a random latency period during which an infected computer in the network is unable to infect others. In the second Part, two approaches for modeling life distributions in univariate and bivariate setups are developed.

In Part I, homogeneous and non-homogeneous stochastic susceptible-exposedinfectious- recovered (SEIR) models are specifically explored for the propagation of computer virus over the Internet by borrowing ideas from mathematical epidemiology. Large computer ...

High-Order Adaptive Methods For Computing Invariant Manifolds Of Maps, 2011 New Jersey Institute of Technology

#### High-Order Adaptive Methods For Computing Invariant Manifolds Of Maps, Jacek K. Wrobel

*Dissertations*

The author presents efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given curve/surface, he proposes using higher-order interpolation/approximation techniques from geometric modeling. He uses B´ezier curves/triangles, fundamental objects in curve/surface design, to create adaptive methods. The methods are based on tolerance conditions derived from properties of B´ezier curves/triangles. The author develops and tests the methods for an ordinary parametric curve; then he adapts these methods to invariant manifolds of planar ...

Confidence Bands For Survival Functions Under Semiparametric Random Censorship Models, 2011 New Jersey Institute of Technology

#### Confidence Bands For Survival Functions Under Semiparametric Random Censorship Models, Peixin Zhang

*Dissertations*

In medical reports point estimates and pointwise confidence intervals of parameters are usually displayed. When the parameter is a survival function, however, the approach of joining the upper end points of individual interval estimates obtained at several points and likewise for the lower end points would not produce bands that include the entire survival curve with a given confidence. Simultaneous confidence bands, which allow confidence statements to be valid for the entire survival curve,would be more meaningful

This dissertation focuses on a novel method of developing one-sample confidence bands for survival functions from right censored data. The approach is ...

Uniform Heating Of Thin Ceramic Slabs In A Multimode Microwave Cavity, 2011 New Jersey Institute of Technology

#### Uniform Heating Of Thin Ceramic Slabs In A Multimode Microwave Cavity, Shuchi Agrawal

*Dissertations*

Two-dimensional reaction diffusion equations, which contain a functional and an inhomogeneous source term, are good models for describing microwave heating of thin ceramic slabs and cylinders in a multi mode, highly resonant cavity. A thin ceramic slab situated in a TEN03 rectangular cavity modeled in the small Biot number limit and a thin silicon wafer situated in a TM101 cylindrical cavity modeled in the small fineness ratio limit are studied to gain insight into the dynamics of the heating process. The evolution of temperature is governed by a two-dimensional reaction diffusion equation and a spatially non-homogeneous reaction term. Numerical methods ...

Boundary Quasi-Orthogonality And Sharp Inclusion Bounds For Large Dirichlet Eigenvalues, 2011 Dartmouth College

#### Boundary Quasi-Orthogonality And Sharp Inclusion Bounds For Large Dirichlet Eigenvalues, A. H. Barnett, A. Hassell

*Open Dartmouth: Faculty Open Access Scholarship*

We study eigenfunctions $\phi_j$ and eigenvalues $E_j$ of the Dirichlet Laplacian on a bounded domain $\Omega\subset\mathbb{R}^n$ with piecewise smooth boundary. We bound the distance between an arbitrary parameter $E>0$ and the spectrum $\{E_j\}$ in terms of the boundary $L^2$-norm of a normalized trial solution *u* of the Helmholtz equation $(\Delta+E)u=0$. We also bound the $L^2$-norm of the error of this trial solution from an eigenfunction. Both of these results are sharp up to constants, hold for all *E* greater than a small constant, and improve upon the best-known ...