Mathematics Commons^™

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.

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 ²S_1/2 state to the ²P_3/2 , a collisional relaxation from ²P_3/2 to ²P_{1/ 2} , and then lasing from ²P_1/2 to ²S_1/2 . The hyperfine absorption and emission cross sections for these transitions are developed in detail. Differential equations for intra-gain pump attenuation …

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 …

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

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 …

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.

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 (x_n) is Benford if the significands, i.e. the fraction parts in the floating-point representation of (x_n) 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 …

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

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.

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.

Software Internationalization: A Framework Validated Against Industry Requirements For Computer Science And Software Engineering Programs, John Huân Vũ

Master's Theses

View John Huân Vũ's thesis presentation at http://youtu.be/y3bzNmkTr-c.

In 2001, the ACM and IEEE Computing Curriculum stated that it was necessary to address "the need to develop implementation models that are international in scope and could be practiced in universities around the world." With increasing connectivity through the internet, the move towards a global economy and growing use of technology places software internationalization as a more important concern for developers. However, there has been a "clear shortage in terms of numbers of trained persons applying for entry-level positions" in this area. Eric Brechner, Director of Microsoft Development Training, suggested …

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Communications on Stochastic Analysis

No abstract provided.

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, Zhicheng Liu, Jie Xiong

Communications on Stochastic Analysis

No abstract provided.

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

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

Communications on Stochastic Analysis

No abstract provided.

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

Communications on Stochastic Analysis

No abstract provided.

Inverse Stochastic Transfer Principle, Matthew Linn, Anna Amirdjanova

Communications on Stochastic Analysis

No abstract provided.

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

Communications on Stochastic Analysis

No abstract provided.