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 …

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.

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 …

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.

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 …

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.

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

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.

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

Communications on Stochastic Analysis

No abstract provided.

Sample Properties Of Random Fields Iii: Differentiability, Jürgen Potthoff

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.

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

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.

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.

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

Communications on Stochastic Analysis

No abstract provided.

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.