Inverse Stochastic Transfer Principle, 2010 Louisiana State University

#### Inverse Stochastic Transfer Principle, Matthew Linn, Anna Amirdjanova

*Communications on Stochastic Analysis*

No abstract provided.

Uniqueness Of Solution To The Kolmogorov Forward Equation: Applications To White Noise Theory Of Filtering, 2010 Louisiana State University

#### Uniqueness Of Solution To The Kolmogorov Forward Equation: Applications To White Noise Theory Of Filtering, Abhay G Bhatt, Rajeeva L Karandikar

*Communications on Stochastic Analysis*

No abstract provided.

Some Asymptotic Results For Near Critical Branching Processes, 2010 Louisiana State University

#### Some Asymptotic Results For Near Critical Branching Processes, Amarjit Budhiraja, Dominik Reinhold

*Communications on Stochastic Analysis*

No abstract provided.

Quasi-Exact Approximation Of Hidden Markov Chain Filters, 2010 Louisiana State University

#### Quasi-Exact Approximation Of Hidden Markov Chain Filters, Eckhard Platen, Renata Rendek

*Communications on Stochastic Analysis*

No abstract provided.

Preface, 2010 Louisiana State University

On The Existence Of Weak Variational Solutions To Stochastic Differential Equations, 2010 Louisiana State University

#### On The Existence Of Weak Variational Solutions To Stochastic Differential Equations, L Gawarecki, V Mandrekar

*Communications on Stochastic Analysis*

No abstract provided.

Some Solvable Classes Of Filtering Problem With Ornstein-Uhlenbeck Noise, 2010 Louisiana State University

#### Some Solvable Classes Of Filtering Problem With Ornstein-Uhlenbeck Noise, Zhicheng Liu, Jie Xiong

*Communications on Stochastic Analysis*

No abstract provided.

Local Fractional Fourier’S Transform Based On The Local Fractional Calculus, 2010 Zongxin Kang, Changhe Liu

#### Local Fractional Fourier’S Transform Based On The Local Fractional Calculus, Yang Xiao-Jun

*Xiao-Jun Yang*

A new modeling for the local fractional Fourier’s transform containing the local fractional calculus is investigated in fractional space. The properties of the local fractional Fourier’s transform are obtained and two examples for the local fractional systems are investigated in detail.

Gauge Equivalence In Stationary Radiative Transport Through Media With Varying Index Of Refraction, 2010 Western Washington University

#### Gauge Equivalence In Stationary Radiative Transport Through Media With Varying Index Of Refraction, Stephen R. Mcdowall, Plamen Stefanov, Alexandru Tamasan

*Mathematics*

Three dimensional anisotropic attenuating and scattering media sharing the same albedo operator have been shown to be related via a gauge transformation. Such transformations define an equivalence relation. We show that the gauge equivalence is also valid in media with non-constant index of refraction, modeled by a Riemannian metric. The two dimensional model is also investigated.

Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, 2010 CUNY Kingsborough Community College

#### Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, 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.In previous work [11,12] we described a numerical procedure for overcoming the Gibbs phenomenon called the Inverse Wavelet Reconstruction method (IWR). 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. However, we only described the method standard wavelet ...

Mathematics In Motion: Linear Systems Of Differential Equations On The Differential Analyzer, 2010 Marshall University

#### Mathematics In Motion: Linear Systems Of Differential Equations On The Differential Analyzer, Devon A. Tivener

*Theses, Dissertations and Capstones*

In this work, I will provide an introduction to the dierential analyzer, a machine designed to solve dierential equations through a process called mechanical integration. I will give a brief historical account of dierential analyzers of the past, and discuss the Marshall University Dierential Analyzer Project. The goal of this work is to provide an analysis of solutions of systems of dierential equations using a dierential analyzer. In particular, we are interested in the points at which these systems are in equilibrium and the behavior of solutions that start away from equilibrium. After giving a description of linear systems of ...

Some New Classes Of Complex Symmetric Operators, 2010 Pomona College

#### Some New Classes Of Complex Symmetric Operators, Stephan Ramon Garcia, Warren R. Wogen

*Pomona Faculty Publications and Research*

We say that an operator $T \in B(H)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:H\to H$ so that $T = CT^*C$. We prove that binormal operators, operators that are algebraic of degree two (including all idempotents), and large classes of rank-one perturbations of normal operators are complex symmetric. From an abstract viewpoint, these results explain why the compressed shift and Volterra integration operator are complex symmetric. Finally, we attempt to describe all complex symmetric partial isometries, obtaining the sharpest possible statement given only the data $(\dim \ker T, \dim \ker T^*)$.

Regular Functions On The Space Of Cayley Numbers, 2010 University of Florence

#### Regular Functions On The Space Of Cayley Numbers, Graziano Gentili, Daniele C. Struppa

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

In this paper we present a new definition of regularity on the space Ç of Cayley numbers (often referred to as octonions), based on a Gateaux-like notion of derivative. We study the main properties of regular functions, and we develop the basic elements of a function theory on Ç. Particular attention is given to the structure of the zero sets of such functions.

Properties Of The Generalized Laplace Transform And Transport Partial Dynamic Equation On Time Scales, 2010 University of Nebraska at Lincoln

#### Properties Of The Generalized Laplace Transform And Transport Partial Dynamic Equation On Time Scales, Chris R. Ahrendt

*Dissertations, Theses, and Student Research Papers in Mathematics*

In this dissertation, we first focus on the generalized Laplace transform on time scales. We prove several properties of the generalized exponential function which will allow us to explore some of the fundamental properties of the Laplace transform. We then give a description of the region in the complex plane for which the improper integral in the definition of the Laplace transform converges, and how this region is affected by the time scale in question. Conditions under which the Laplace transform of a power series can be computed term-by-term are given. We develop a formula for the Laplace transform for ...

The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, 2009 DePaul University and Columbia College Chicago

#### The 1905 Einstein Equation In A General Mathematical Analysis Model Of Quasars, Byron E. Bell

*Byron E. Bell*

No abstract provided.