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Full-Text Articles in Physical Sciences and Mathematics

Using The Ti-Nspire To Teach Real Applications In College Mathematics, Lisa Yocco Mar 2010

Using The Ti-Nspire To Teach Real Applications In College Mathematics, Lisa Yocco

Lisa S. Yocco

No abstract provided.


Reconstructability Analysis Of Elementary Cellular Automata, Martin Zwick, Hui Shi Mar 2010

Reconstructability Analysis Of Elementary Cellular Automata, Martin Zwick, Hui Shi

Systems Science Friday Noon Seminar Series

Reconstructability analysis is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss (reduction in constraint) into lower ordinality relations. Set-theoretic reconstructability analysis (SRA) is used to characterize the mappings of elementary cellular automata. The degree of lossless decomposition possible for each mapping is more effective than the λ parameter (Walker & Ashby, Langton) as a predictor of chaotic dynamics.

Complete SRA yields not only the simplest lossless structure but also a vector of losses of all decomposed structures, indexed by parameter, τ. This vector subsumes λ, Wuensche’s Z parameter, and Walker …


An Algorithm For Wavelet–Based Elemental Spectrum Analysis, Bruce Kessler Mar 2010

An Algorithm For Wavelet–Based Elemental Spectrum Analysis, Bruce Kessler

Bruce Kessler

At the previous Approximation Theory XII meeting, I discussed some preliminary work with the Applied Physics Institute at Western Kentucky University in using multiwavelets to provide an objective analysis of gamma-ray spectrum generated from fast neutron bombardment of objects, for the purpose of identifying the elemental composition of the object. The method discussed at the time worked moderately well with the limited amount of data provided, but subsequent use with data sets of different compounds and with different detectors brought to light serious flaws with its implementation.

This talk will illustrate those issues and will address how they have been …


Planar Cat(K) Subspaces, Russell M. Ricks Mar 2010

Planar Cat(K) Subspaces, Russell M. Ricks

Theses and Dissertations

Let M_k^2 be the complete, simply connected, Riemannian 2-manifold of constant curvature k ± 0. Let E be a closed, simply connected subspace of M_k^2 with the property that every two points in E are connected by a rectifi able path in E. We show that E is CAT(k) under the induced path metric.


Numerical Investigation Of Pre-Detonator Geometries For Pde Applications, Robert T. Fievisohn Mar 2010

Numerical Investigation Of Pre-Detonator Geometries For Pde Applications, Robert T. Fievisohn

Theses and Dissertations

A parametric study was performed to determine optimal geometries to allow the successful transition of a detonation from a pre-detonator into the thrust tube of a pulse detonation engine. The study was performed using a two-dimensional Euler solver with progress variables to model the chemistry. The geometrical configurations for the simulations look at the effect of shock reflections, flow obstructions, and detonation diffraction to determine successful geometries. It was observed that there are success and failure rates associated with pre-detonators. These success rates appear to be determined by the transverse wave structure of a stably propagating detonation wave and must …


Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher Mar 2010

Verification Of Kam Theory On Earth Orbiting Satellites, Christian L. Bisher

Theses and Dissertations

This paper uses KAM torus theory and Simplified General Perturbations 4 (SGP4) orbit prediction techniques compiled by Dr. William Wiesel and compares it to Analytical Graphics ® Incorporated (AGI) Satellite Toolkit ® (STK) orbit data. The goal of this paper is to verify KAM torus theory can be used to describe and propagate an Earth satellite orbit with similar accuracy to existing general perturbation techniques. Using SGP4 code including only truncated geopotential effects, KAM torus generating code, and other utilities were used to describe a particular satellite orbit as a torus and then propagate the satellite using traditional and KAM …


Simulation Of A Diode Pumped Alkali Laser, A Three Level Numerical Approach, Shawn W. Hackett Mar 2010

Simulation Of A Diode Pumped Alkali Laser, A Three Level Numerical Approach, Shawn W. Hackett

Theses and Dissertations

This paper develops a three level model for a continuous wave diode pumped alkali laser by creating rate equations based on a three level system. The three level system consists of an alkali metal vapor, typically Rb or Cs, pumped by a diode from the 2S1/2 state to the 2P3/2 , a collisional relaxation from 2P3/2 to 2P1/ 2 , and then lasing from 2P1/2 to 2S1/2 . The hyperfine absorption and emission cross sections for these transitions are developed in detail. Differential equations for intra-gain pump attenuation …


An Algorithm For Wavelet–Based Elemental Spectrum Analysis, Bruce Kessler Mar 2010

An Algorithm For Wavelet–Based Elemental Spectrum Analysis, Bruce Kessler

Mathematics Faculty Publications

At the previous Approximation Theory XII meeting, I discussed some preliminary work with the Applied Physics Institute at Western Kentucky University in using multiwavelets to provide an objective analysis of gamma-ray spectrum generated from fast neutron bombardment of objects, for the purpose of identifying the elemental composition of the object. The method discussed at the time worked moderately well with the limited amount of data provided, but subsequent use with data sets of different compounds and with different detectors brought to light serious flaws with its implementation.

This talk will illustrate those issues and will address how they have been …


Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge Mar 2010

Validation Of A Novel Approach To Solving Multibody Systems Using Hamilton's Weak Principle, Ashton D. Hainge

Theses and Dissertations

A novel approach for formulating and solving for the dynamic response of multibody systems has been developed using Hamilton’s Law of Varying Action as its unifying principle. In order to assure that the associated computer program is sufficiently robust when applied across a wide range of dynamic systems, the program must be verified and validated. The purpose of the research was to perform the verification and validation of the program. Results from the program were compared with closed-form and numerical solutions of simple systems, such as a simple pendulum and a rotating pendulum. The accuracy of the program for complex …


Stability Of Choice In The Honey Bee Nest-Site Selection Process, Andrew L. Nevai, Kevin M. Passino, Parthasarathy Srinivasan Mar 2010

Stability Of Choice In The Honey Bee Nest-Site Selection Process, Andrew L. Nevai, Kevin M. Passino, Parthasarathy Srinivasan

Mathematics and Statistics Faculty Publications

We introduce a pair of compartment models for the honey bee nest-site selection process that lend themselves to analytic methods. The first model represents a swarm of bees deciding whether a site is viable, and the second characterizes its ability to select between two viable sites. We find that the one-site assessment process has two equilibrium states: a disinterested equilibrium (DE) in which the bees show no interest in the site and an interested equilibrium (IE) in which bees show interest. In analogy with epidemic models, we define basic and absolute recruitment numbers (R0R0 and B0B0) as measures of the …


Using The Ti-Nspire As A Tool To Explore Real Applications In Precalculus, Lisa Yocco Mar 2010

Using The Ti-Nspire As A Tool To Explore Real Applications In Precalculus, Lisa Yocco

Lisa S. Yocco

No abstract provided.


Finite-State Markov Chains Obey Benford’S Law, Babar Kaynar, Arno Berger, Theodore P. Hill, Ad Ridder Mar 2010

Finite-State Markov Chains Obey Benford’S Law, Babar Kaynar, Arno Berger, Theodore P. Hill, Ad Ridder

Research Scholars in Residence

A sequence of real numbers (xn) is Benford if the significands, i.e. the fraction parts in the floating-point representation of (xn) are distributed logarithmically. Similarly, a discrete-time irreducible and aperiodic finite-state Markov chain with probability transition matrix P and limiting matrix P* is Benford if every component of both sequences of matrices (Pn - P*) and (Pn+1-Pn) is Benford or eventually zero. Using recent tools that established Benford behavior both for Newton's method and for finite-dimensional linear maps, via the classical theories of uniform distribution modulo 1 …


Finite Element Approximations For Stokes-Darcy Flow With Beavers-Joseph Interface Conditions, Yanzhao Cao, Max Gunzburger, Xiaolong Hu, Fei Hua, Xiaoming Wang, Weidong Zhao Mar 2010

Finite Element Approximations For Stokes-Darcy Flow With Beavers-Joseph Interface Conditions, Yanzhao Cao, Max Gunzburger, Xiaolong Hu, Fei Hua, Xiaoming Wang, Weidong Zhao

Mathematics and Statistics Faculty Research & Creative Works

Numerical solutions using finite element methods are considered for transient flow in a porous medium coupled to free flow in embedded conduits. Such situations arise, for example, for groundwater flows in karst aquifers. the coupled flow is modeled by the Darcy equation in a porous medium and the Stokes equations in the conduit domain. on the interface between the matrix and conduit, Beavers-Joseph interface conditions, instead of the simplified Beavers-Joseph-Saffman conditions, are imposed. Convergence and error estimates for finite element approximations are obtained. Numerical experiments illustrate the validity of the theoretical results. © 2010 Society for Industrial and Applied Mathematics.


On The Existence Of Weak Variational Solutions To Stochastic Differential Equations, L Gawarecki, V Mandrekar Mar 2010

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

Communications on Stochastic Analysis

No abstract provided.


Uniqueness Of Solution To The Kolmogorov Forward Equation: Applications To White Noise Theory Of Filtering, Abhay G Bhatt, Rajeeva L Karandikar Mar 2010

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.


Preface Mar 2010

Preface

Communications on Stochastic Analysis

No abstract provided.


Some Solvable Classes Of Filtering Problem With Ornstein-Uhlenbeck Noise, Zhicheng Liu, Jie Xiong Mar 2010

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

Communications on Stochastic Analysis

No abstract provided.


Risk-Based Indifference Pricing Under A Stochastic Volatility Model, Robert J Elliott, Tak Kuen Siu Mar 2010

Risk-Based Indifference Pricing Under A Stochastic Volatility Model, Robert J Elliott, Tak Kuen Siu

Communications on Stochastic Analysis

No abstract provided.


Inverse Stochastic Transfer Principle, Matthew Linn, Anna Amirdjanova Mar 2010

Inverse Stochastic Transfer Principle, Matthew Linn, Anna Amirdjanova

Communications on Stochastic Analysis

No abstract provided.


Commutativity Properties Of Conditional Distributions And Palm Measures, Olav Kallenberg Mar 2010

Commutativity Properties Of Conditional Distributions And Palm Measures, Olav Kallenberg

Communications on Stochastic Analysis

No abstract provided.


Some Asymptotic Results For Near Critical Branching Processes, Amarjit Budhiraja, Dominik Reinhold Mar 2010

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, Eckhard Platen, Renata Rendek Mar 2010

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

Communications on Stochastic Analysis

No abstract provided.


Dynamical Laws Of The Coupled Gross-Pitaevskii Equations For Spin-1 Bose-Einstein Condensates, Weizhu Bao, Yanzhi Zhang Mar 2010

Dynamical Laws Of The Coupled Gross-Pitaevskii Equations For Spin-1 Bose-Einstein Condensates, Weizhu Bao, Yanzhi Zhang

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we derive analytically the dynamical laws of the coupled Gross- Pitaevskii equations (CGPEs) without/with an angular momentum rotation term and an external magnetic field for modelling nonrotating/rotating spin-1 Bose-Eintein condensates. We prove the conservation of the angular momentum expectation when the external trapping potential is radially symmetric in two dimensions and cylindrically symmetric in three dimensions; obtain a system of first order ordinary differential equations (ODEs) governing the dynamics of the density of each component and solve the ODEs analytically in a few cases; derive a second order ODE for the dynamics of the condensate width and …


First-Order And Second-Order Optimality Conditions For Nonsmooth Constrained Problems Via Convolution Smoothing, Andrew C. Eberhard, Boris S. Mordukhovich Mar 2010

First-Order And Second-Order Optimality Conditions For Nonsmooth Constrained Problems Via Convolution Smoothing, Andrew C. Eberhard, Boris S. Mordukhovich

Mathematics Research Reports

This paper mainly concerns deriving first-order and second-order necessary (and partly sufficient) optimality conditions for a general class of constrained optimization problems via smoothing regularization procedures based on infimal-like convolutions/envelopes. In this way we obtain first-order optimality conditions of both lower subdifferential and upper subdifferential types and then second-order conditions of three kinds involving, respectively, generalized second-order directional derivatives, graphical derivatives of first-order subdifferentials, and secondorder subdifferentials defined via coderivatives of first-order constructions.


Interaction Of Excited States In Two-Species Bose-Einstein Condensates: A Case Study, T Kapitula, Kjh Law, Pg Kevrekidis Mar 2010

Interaction Of Excited States In Two-Species Bose-Einstein Condensates: A Case Study, T Kapitula, Kjh Law, Pg Kevrekidis

Panos Kevrekidis

In this paper we consider the existence and spectral stability of excited states in two-species Bose–Einstein condensates in the case of a pancake magnetic trap. Each new excited state found in this paper is to leading order a linear combination of two one-species dipoles, each of which is a spectrally stable excited state for one-species condensates. The analysis is done via a Lyapunov–Schmidt reduction and is valid in the limit of weak nonlinear interactions. Some conclusions, however, can be made at this limit which remain true even when the interactions are large.


A Rigorous Analysis Using Optimal Transport Theory For A Two-Reflector Design Problem With A Point Source, Tilmann Glimm Mar 2010

A Rigorous Analysis Using Optimal Transport Theory For A Two-Reflector Design Problem With A Point Source, Tilmann Glimm

Mathematics Faculty Publications

We consider the following geometric optics problem: construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We give a rigorous analysis of this problem. The reflectors we construct are (parts of) the boundaries of convex sets. We prove existence of solutions for a large class of input data and give a uniqueness result. To the author’s knowledge, this is the first time that a rigorous mathematical analysis of this problem is given. The approach is based on optimal transportation theory. …


On Sumudu Transform And System Of Differential Equations, Adem Kiliçman, Hassan Eltayeb, Ravi P. Agarwal Mar 2010

On Sumudu Transform And System Of Differential Equations, Adem Kiliçman, Hassan Eltayeb, Ravi P. Agarwal

Mathematics and System Engineering Faculty Publications

The regular system of differential equations with convolution terms solved by Sumudu transform.


Incompressibility And Global Inversion, Eduardo C. Balreira Mar 2010

Incompressibility And Global Inversion, Eduardo C. Balreira

Mathematics Faculty Research

Given a local diffeomorphism ƒ : ℝn → ℝn, we consider certain in- compressibility conditions on the parallelepiped Dƒ(x) ([0, 1]n) which imply that the pre-image of an affine subspace is non-empty and has trivial homotopy groups. These conditions are then used to establish criteria for ƒ to be globally invertible, generalizing in all dimensions the previous results of M. Sabatini.


When Is The Numerical Range Of A Nilpotent Matrix Circular?, Valentin Matache, Mihaela Teodora Matache Mar 2010

When Is The Numerical Range Of A Nilpotent Matrix Circular?, Valentin Matache, Mihaela Teodora Matache

Mathematics Faculty Publications

The problem formulated in the title is investigated. The case of nilpotent matrices of size at most 4 allows a unitary treatment. The numerical range of a nilpotent matrix M of size at most 4 is circular if and only if the traces tr MM2 and tr MM3 are null. The situation becomes more complicated as soon as the size is 5. The conditions under which a 5×5nilpotent matrix has circular numerical range are thoroughly discussed.


A Sharp Diameter Bound For Unipotent Groups Of Classical Type Overℤ /Pℤ, Jordan S. Ellenberg, Julianna Tymoczko Mar 2010

A Sharp Diameter Bound For Unipotent Groups Of Classical Type Overℤ /Pℤ, Jordan S. Ellenberg, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

The unipotent subgroup of a finite group of Lie type over a prime field Fp comes equipped with a natural set of generators; the properties of the Cayley graph associated to this set of generators have been much studied. In the present paper, we show that the diameter of this Cayley graph is bounded above and below by constant multiples of np + n2 log p, where n is the rank of the associated Lie group. This generalizes the result of Ellenberg, A sharp diameter bound for an upper triangular matrix group, Harvard University, 1993, which treated the case of …