Other Mathematics Commons^™

Positive Harris Recurrence Of The Cir Process And Its Applications, Peng Jin, Vidyadhar Mandrekar, Barbara Rüdiger, Chiraz Trabelsi

Communications on Stochastic Analysis

No abstract provided.

Itô Formula And Girsanov Theorem For Anticipating Stochastic Integrals, Hui-Hsiung Kuo, Yun Peng, Benedykt Szozda

Communications on Stochastic Analysis

No abstract provided.

A Bochner-Type Representation Of Positive Definite Mappings On The Dual Of A Compact Group, Herbert Heyer

Communications on Stochastic Analysis

No abstract provided.

On Optimal Proportional Reinsurance And Investment In A Partial Markovian Regime-Switching Economy, Xin Zhang

Communications on Stochastic Analysis

No abstract provided.

A Bayesian Model For Cluster Detection, Jonathan Wakefield, Albert Y. Kim

Statistical and Data Sciences: Faculty Publications

The detection of areas in which the risk of a particular disease is significantly elevated, leading to an excess of cases, is an important enterprise in spatial epidemiology. Various frequentist approaches have been suggested for the detection of “clusters” within a hypothesis testing framework. Unfortunately, these suffer from a number of drawbacks including the difficulty in specifying a p-value threshold at which to call significance, the inherent multiplicity problem, and the possibility of multiple clusters. In this paper, we suggest a Bayesian approach to detecting “areas of clustering” in which the study region is partitioned into, possibly multiple, “zones” …

Examples Where The Conjunctive And Dempster’S Rules Are Insensitive, Florentin Smarandache, Jean Dezert, Valeri Kroumov

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present several counter-examples to the Conjunctive rule and to Dempster rule of combinations in information fusion.

Elementary Teacher Candidates' Images Of Mathematics, Diverse Students, And Teaching: An Exploratory Study With Implications For Culturally Responsive Mathematics Education, Bernd Richard Ferner

Dissertations and Theses

Children from many culturally diverse backgrounds do not achieve in mathematics at the same rates as their counterparts from the dominant White, European-American culture (Gay, 2010). This so-called achievement gap is an artifact of an educational system that continues to fail to provide equal learning opportunities to culturally diverse children (Ladson-Billings, 2006; Nieto & Bode, 2011). Teachers who employ culturally responsive teaching (Gay, 2010) may help to close this opportunity gap and hence, the achievement gap. This study investigated, "How do elementary teacher candidates perceive teaching mathematics in a multicultural environment"; Using a critical constructivism research paradigm, this qualitative instrumental …

Field Control Of The Surface Electroclinic Effect In Liquid Crystal Displays, Dana Hipolite

Physics

Liquid crystals (LCs) are a fascinating class of materials exhibiting a range of phases intermediate between liquid and crystalline. Smectic LCs consist of elongated molecules arranged in a periodic stack (along z) of liquid like layers. In the smectic-A (Sm-A) phase, the average molecular long axis (director) points along z. In the smectic-C (Sm-C) phase, it is tilted relative to z, thus picking out a special direction within the layers. Typically, the Sm-A* to Sm- C* transition will occur as temperature is decreased. In chiral smectics (Sm-*A or Sm-C*) it is possible to induce director titling (i.e. the Sm-C* phase) …

Development And Application Of Difference And Fractional Calculus On Discrete Time Scales, Tanner J. Auch

Department of Mathematics: Dissertations, Theses, and Student Research

The purpose of this dissertation is to develop and apply results of both discrete calculus and discrete fractional calculus to further develop results on various discrete time scales. Two main goals of discrete and fractional discrete calculus are to extend results from traditional calculus and to unify results on the real line with those on a variety of subsets of the real line. Of particular interest is introducing and analyzing results related to a generalized fractional boundary value problem with Lidstone boundary conditions on a standard discrete domain N_a. We also introduce new results regarding exponential order for functions on …

A Math Therapy Exercise, Gary Stogsdill

Journal of Humanistic Mathematics

Math anxiety prevents many liberal arts undergraduates from appreciating mathematics and realizing their potential in math courses and math-related endeavors. The author describes his development and use of a "math therapy exercise" that enables students to move beyond the paralyzing grip of math anxiety and cultivate a more positive relationship with mathematics.

A Parabolic Equation Analysis Of The Underwater Noise Radiated By Impact Pile Driving, Nathan Laws

Dissertations and Theses

Impact pile driving can produce extremely high underwater sound levels, which are of increasing environmental concern due to their deleterious effects on marine wildlife. Prediction of underwater sound levels is important to the assessment and mitigation of the environmental impacts caused by pile driving. Current prediction methods are limited and do not account for the dynamic pile driving source, inhomogeneities in bathymetry and sediment, or physics-based sound wave propagation.

In this thesis, a computational model is presented that analyzes and predicts the underwater noise radiated by pile driving and is suitable for shallow, inhomogeneous environments and long propagation ranges. The …

Generalized Finite-Difference Time-Domain Schemes For Solving Nonlinear Schrödinger Equations, Frederick Ira Moxley Iii

Doctoral Dissertations

The nonlinear Schrödinger equation (NLSE) is one of the most widely applicable equations in physical science, and characterizes nonlinear dispersive waves, optics, water waves, and the dynamics of molecules. The NLSE satisfies many mathematical conservation laws. Moreover, due to the nonlinearity, the NLSE often requires a numerical solution, which also satisfies the conservation laws. Some of the more popular numerical methods for solving the NLSE include the finite difference, finite element, and spectral methods such as the pseudospectral, split-step with Fourier transform, and integrating factor coupled with a Fourier transform. With regard to the finite difference and finite element methods, …

Hilbert Space Theory And Applications In Basic Quantum Mechanics, Matthew Gagne

Mathematics

We explore the basic mathematical physics of quantum mechanics. Our primary focus will be on Hilbert space theory and applications as well as the theory of linear operators on Hilbert space. We show how Hermitian operators are used to represent quantum observables and investigate the spectrum of various linear operators. We discuss deviation and uncertainty and briefly suggest how symmetry and representations are involved in quantum theory.

Meromorphic Lévy-Khintchine Exponents With Poles Of Order Two, Guillaume Coqueret

Communications on Stochastic Analysis

No abstract provided.

A Converse Comparison Theorem For Discrete-Time Finite-State Bsdes And Risk Measures Using G-Expectation, Robert Elliott, Yin Lin, Hailiang Yang

Communications on Stochastic Analysis

No abstract provided.

A Hull And White Formula For A Stochastic Volatility Lévy Model With Infinite Activity, Hossein Jafari, Josep Vives

Communications on Stochastic Analysis

No abstract provided.

Fluctuation Properties Of Compound Poisson-Erlang Lévy Processes, Richard B Paris, Vladimir Vinogradov

Communications on Stochastic Analysis

No abstract provided.

Asymptotic Spectral Distributions Of Distance-K Graphs Of Hamming Graphs, Yuji Hibino

Communications on Stochastic Analysis

No abstract provided.

Partially Gaussian Stationary Stochastic Processes In Discrete Time, K R Parthasarathy

Communications on Stochastic Analysis

No abstract provided.

Linear Stochastic Differential Equations With Anticipating Initial Conditions, Narjess Khalifa, Hui-Hsiung Kuo, Habib Ouerdiane, Benedykt Szozda

Communications on Stochastic Analysis

No abstract provided.