Physical Sciences and Mathematics Commons^™

Spatiotemporal Two-Dimensional Solitons In The Complex Ginzburg-Landau Equation, Florent Berard, S.C. Mancas

Publications

We introduce spatiotemporal solitons of the two-dimensional complex Ginzburg-Landau equation (2D CCQGLE) with cubic and quintic nonlinearities in which asymmetry between space-time variables is included. The 2D CCQGLE is solved by a powerful Fourier spectral method, i.e., a Fourier spatial discretization and an explicit scheme for time differencing. Varying the system's parameters, and using different initial conditions, numerical simulations reveal 2D solitons in the form of stationary, pulsating and exploding solitons which possess very distinctive properties. For certain regions of parameters, we have also found stable coherent structures in the form of spinning (vortex) solitons which exist as a result …

Sharp Weighted Estimates For Classical Operators [Post-Print], David Cruz-Uribe Sfo, José María Martell, Carlos Perez

Faculty Scholarship

See abstract at: http://www.sciencedirect.com/science/article/pii/S0001870811003136

Economic Optimization Of Offshore Wind Farms Using The Geometric Algorithm, Mahidhar Nandigam

Electrical & Computer Engineering Theses & Dissertations

The research project related to this thesis focuses on the optimization of electrical systems for offshore wind farms for a given capacity. The optimal design and planning is a critical issue for developing cost effectively Offshore Wind Farms in energy systems. The Geometric Optimization Algorithms approach has been adopted to develop an optimization program, where the main components of the electrical system of an offshore wind farm and key technical specifications are used as parameters to be optimized for a minimum cost with necessary constraints. The effectiveness of the optimization program can be evaluated with real-time comparison between offshore wind …

A Class Of Discontinuous Petrov–Galerkin Methods. Part Iv: The Optimal Test Norm And Time-Harmonic Wave Propagation In 1d., Jeffrey Zitelli, Leszek Demkowicz, Jay Gopalakrishnan, D. Pardo, V. M. Calo

Mathematics and Statistics Faculty Publications and Presentations

The phase error, or the pollution effect in the finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems in the high-frequency range. This paper presents a new method with no phase errors for one-dimensional (1D) time-harmonic wave propagation problems using new ideas that hold promise for the multidimensional case. The method is constructed within the framework of the discontinuous Petrov–Galerkin (DPG) method with optimal test functions. We have previously shown that such methods select solutions that are the best possible approximations in an energy norm dual to any selected test …

The Geometry Of The Snail Ball, Stan Wagon

Stan Wagon, Retired

No abstract provided.

Characterizing Preservice Teachers’ Mathematical Understanding Of Algebraic Relationships, Leah A. Nillas

Leah A. Nillas

The Hamiltonian Index Of Graphs, Yi Hong, Jian-Liang Lin, Zhi-Sui Tao, Zhi-Hong Chen

Zhi-Hong Chen

The Hamiltonian index of a graph G is defined as h ( G ) = min { m : L m ( G ) is Hamiltonian } . In this paper, using the reduction method of Catlin [P.A. Catlin, A reduction method to find spanning Eulerian subgraphs, J. Graph Theory 12 (1988) 29–44], we constructed a graph H ̃ ( m ) ( G ) from G and prove that if h ( G ) ≥ 2 , then h ( G ) = min{ m : H ̃ ( m ) ( G ) has a spanning Eulerian subgraph …

Estimation Of Quality Adjusted Lifetime (Qal) Distribution., Biswabrata Pradhan Dr.

Doctoral Theses

Quality Adjusted Lifetime (QAL)Normally, overall survival time is considered as the end point for many clinical trials to study the effectiveness of different treatments. If the survival time passes through different health states, which differ in their quality of life, then other endpoints are also considered for treatment comparison, which incorporates both quality and duration of life. It is, therefore, necessary to provide a composite measure for comparison of different treatment choices, specially in the context of clinical trials, after taking into account both quality and duration of life. This issue has been first addressed by Gelber and coauthors in …

Teaching Calculus With Wolfram Alpha, Andrew Lang

College of Science and Engineering Faculty Research and Scholarship

This article describes the benefits and drawbacks of using Wolfram|Alpha as the platform for teaching calculus concepts in the lab setting. It is a result of our experiences designing and creating an entirely new set of labs using Wolfram|Alpha. We present the reasoning behind our transition from using a standard computer algebra system (CAS) to Wolfram|Alpha in our differential and integral calculus labs, together with the positive results from our experience. We also discuss the current limitations of Wolfram|Alpha, including a discussion on why we still use a CAS for our multivariate calculus labs.

Empirical Likelihood Confidence Intervals For Roc Curves Under Right Censorship, Hanfang Yang

Mathematics Theses

In this thesis, we apply smoothed empirical likelihood method to investigate confidence intervals for the receiver operating characteristic (ROC) curve with right censoring. As a particular application of comparison of distributions from two populations, the ROC curve is constructed by the combination of cumulative distribution function and quantile function. Under mild conditions, the smoothed empirical likelihood ratio converges to chi-square distribution, which is the well-known Wilks's theorem. Furthermore, the performances of the empirical likelihood method are also illustrated by simulation studies in terms of coverage probability and average length of confidence intervals. Finally, a primary biliary cirrhosis data is used …

Wavelet-Based Bayesian Estimation Of Partially Linear Regression Models With Long Memory Errors, Kyungduk Ko, Leming Qu, Marina Vannucci

Kyungduk Ko

In this paper we focus on partially linear regression models with long memory errors, and propose a wavelet-based Bayesian procedure that allows the simultaneous estimation of the model parameters and the nonparametric part of the model. Employing discrete wavelet transforms is crucial in order to simplify the dense variance-covariance matrix of the long memory error. We achieve a fully Bayesian inference by adopting a Metropolis algorithm within a Gibbs sampler. We evaluate the performances of the proposed method on simulated data. In addition, we present an application to Northern hemisphere temperature data, a benchmark in the long memory literature.

Consistency Properties For Growth Model Parameters Under An Infill Asymptotics Domain, David T. Mills

Theses and Dissertations

Growth curves are used to model various processes, and are often seen in biological and agricultural studies. Underlying assumptions of many studies are that the process may be sampled forever, and that samples are statistically independent. We instead consider the case where sampling occurs in a finite domain, so that increased sampling forces samples closer together, and also assume a distance-based covariance function. We first prove that, under certain conditions, the mean parameter of a fixed-mean model cannot be estimated within a finite domain. We then numerically consider more complex growth curves, examining sample sizes, sample spacing, and quality of …

Compactons In Nonlinear Schrödinger Lattices With Strong Nonlinearity Management, F. Kh. Abdullaev, Panos Kevrekidis, M. Salerno

Panos Kevrekidis

The existence of compactons in the discrete nonlinear Schr\"odinger equation in the presence of fast periodic time modulations of the nonlinearity is demonstrated. In the averaged DNLS equation the resulting effective inter-well tunneling depends on modulation parameters {\it and} on the field amplitude. This introduces nonlinear dispersion in the system and can lead to a prototypical realization of single- or multi-site stable discrete compactons in nonlinear optical waveguide and BEC arrays. These structures can dynamically arise out of Gaussian or compactly supported initial data.

Schrödinger Dispersive Dstimates For A Dcaling-Critical Class Of Potentials, Marius Beceanu, Michael Goldberg

Mathematics and Statistics Faculty Scholarship

Consider the focussing cubic nonlinear Schr\"odinger equation in R 3 :

iψ t +Δψ=−|ψ| 2 ψ.

It admits special solutions of the form e itα ϕ , whereϕ is a Schwartz function and a positive (ϕ>0 ) solution of

−Δϕ+αϕ=ϕ 3 .

The space of all such solutions, together with those obtained from them by rescaling and applying phase and Galilean coordinate changes, called standing waves, is the eight-dimensional manifold that consists of functions of the form e i(v⋅+Γ) ϕ(⋅−y,α) . We prove that any solution starting sufficiently close to a standing wave in the Σ=W 1,2 (R 3 …

Bioinformatics Across The Sciences, Nigel Yarlett

Cornerstone 3 Reports : Interdisciplinary Informatics

No abstract provided.

Covariance Identities And Mixing Of Random Transformations On The Wiener Space, Nicolas Privault

Communications on Stochastic Analysis

No abstract provided.

A Finite Element Method For Martingale-Driven Stochastic Partial Differential Equations, Andrea Barth

Communications on Stochastic Analysis

No abstract provided.

Sample Properties Of Random Fields Iii: Differentiability, Jürgen Potthoff

Communications on Stochastic Analysis

No abstract provided.

The Itô Integral For A Certain Class Of Lévy Processes And Its Application To Stochastic Partial Differential Equations, Erika Hausenblas

Communications on Stochastic Analysis

No abstract provided.

Sufficient Conditions Of Optimality For Backward Stochastic Evolution Equations, Abdulrahman Al-Hussein

Communications on Stochastic Analysis

No abstract provided.

Upper Bounds On Rubinstein Distances On Configuration Spaces And Applications, Laurent Decreusefond, Aldéric Joulin, Nicolas Savy

Communications on Stochastic Analysis

No abstract provided.

Convergence Of Particle Filtering Method For Nonlinear Estimation Of Vortex Dynamics, Sivaguru S Sritharan, Meng Xu

Communications on Stochastic Analysis

No abstract provided.

Zeons, Lattices Of Partitions, And Free Probability, René Schott, G Stacey Staples

Communications on Stochastic Analysis

No abstract provided.

Surface Measures On The Dual Space Of The Schwartz Space, S Chaari, F Cipriano, H.-H. Kuo, H Ouerdiane

Communications on Stochastic Analysis

No abstract provided.

Solutions Of Semilinear Wave Equation Via Stochastic Cascades, Yuri Bakhtin, Carl Mueller

Communications on Stochastic Analysis

No abstract provided.

Roger Temam On The Occasion Of His 70th Birthday, Claude Michel Brauner, Danielle Hilhorst, Alain Miranville, Shouhong Wang, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Energetyka Niskoemisyjna, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

An Explicit Super‐Time‐Stepping Scheme For Non‐Symmetric Parabolic Problems, Stephen O'Sullivan, Katharine Gurski

Conference papers

Explicit numerical methods for the solution of a system of differential equations may suffer from a time step size that approaches zero in order to satisfy stability conditions. When the differential equations are dominated by a skew-symmetric component, the problem is that the real eigenvalues are dominated by imaginary eigenvalues. We compare results for stable time step limits for the super-time-stepping method of Alexiades, Amiez, and Gremaud (super-time-stepping methods belong to the Runge-Kutta-Chebyshev class) and a new method modeled on a predictor-corrector scheme with multiplicative operator splitting. This new explicit method increases stability of the original super-time-stepping whenever the skew-symmetric …

Diffeomorphic Approximation Of Sobolev Homeomorphisms, Tadeusz Iwaniec, Leonid V. Kovalev, Jani Onninen

Mathematics - All Scholarship

Every homeomorphism h: X -> Y between planar open sets that belongs to the Sobolev class W^1;p(X;Y), 1 < p < 1, can be approximated in the Sobolev norm by C^infinity -smooth dieomorphisms.

Coarser Connected Metrizable Topologies, Lynne Yengulalp

Mathematics Faculty Publications

We show that every metric space, X, with w(⩾) c has a coarser connected metrizable topology.