Mathematics Scholarly Works: Recent submissions
Now showing items 81-100 of 283
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Traveling Waves Solutions for Bistable Differential-Difference Equations with Periodic Diffusion
(Society for Industrial and Applied Mathematics, 2001-10-05)We consider traveling wave solutions to spatially discrete reaction-diffusion equations with nonlocal variable diffusion and bistable nonlinearities. To find the traveling wave solutions we introduce an ansatz in which the ... -
Lyapunov Spectral Intervals: Theory and Computation
(Society for Industrial and Applied Mathematics, 2002-05-05)Different definitions of spectra have been proposed over the years to characterize the asymptotic behavior of nonautonomous linear systems. Here, we consider the spectrum based on exponential dichotomy of Sacker and Sell ... -
Spatially Discrete FitzHugh-Nagumo Equations
(Society for Industrial and Applied Mathematics, 2005-04-05)We consider pulse and front solutions to a spatially discrete FitzHugh--Nagumo equation that contains terms to represent both depolarization and hyperpolarization of the nerve axon. We demonstrate a technique for deriving ... -
Computation of Mixed Type Functional Differential Boundary Value Problems
(Society for Industrial and Applied Mathematics, 2005-09-05)We study boundary value differential-difference equations where the difference terms may contain both advances and delays. Special attention is paid to connecting orbits, in particular to the modeling of the tails after ... -
Traveling Wave Solutions to a Coupled System of Spatially Discrete Nagumo Equations
(Society for Industrial and Applied Mathematics, 2006-07-31)We consider a coupled system of discrete Nagumo equations and derive traveling wave solutions to this system using McKean's caricature of the cubic. A certain form of this system is used to model ephaptic coupling between ... -
On the Error in QR Integration
(Society for Industrial and Applied Mathematics, 2008-03-07)An important change of variables for a linear time varying system $\dot x=A(t)x, t\ge 0$, is that induced by the QR-factorization of the underlying fundamental matrix solution: $X=QR$, with Q orthogonal and R upper triangular ... -
On the Error in the Product QR Decomposition
(Society for Industrial and Applied Mathematics, 2010-03-17)We develop both a normwise and a componentwise error analysis for the QR factorization of long products of invertible matrices. We obtain global error bounds for both the orthogonal and upper triangular factors that depend ... -
Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion
(Society for Industrial and Applied Mathematics, 2011-08-09)We consider a bistable differential-difference equation with inhomogeneous diffusion. Employing a piecewise linear nonlinearity, often referred to as McKean's caricature of the cubic, we construct front solutions which ... -
Traveling Wavefronts in an Antidiffusion Lattice Nagumo Model
(Society for Industrial and Applied Mathematics, 2011-06-06)We consider a system of lattice Nagumo equations with cubic nonlinearity, but with a negative discrete diffusion coefficient. We are interested in the existence, uniqueness, stability, and nonexistence of the traveling ... -
Singular function mortar finite element methods
(De Gruyter Open, 2003-01-05)We consider the Poisson equation with Dirichlet boundary conditions on a polygonal domain with one reentrant corner. We introduce new nonconforming finite element discretizations based on mortar techniques and singular ... -
Three-level BDDC in three dimensions
(Society for Industrial and Applied Mathematics, 2007-10-05)Balancing domain decomposition by constraints (BDDC) methods are nonoverlapping iterative substructuring domain decomposition methods for the solution of large sparse linear algebraic systems arising from the discretization ... -
A three-level BDDC algorithm for mortar discretizations
(Society for Industrial and Applied Mathematics, 2009-03-05)In this paper, a three-level balancing domain decomposition by constraints (BDDC) algorithm is developed for the solutions of large sparse algebraic linear systems arising from the mortar discretization of elliptic boundary ... -
An iterative implementation of the implicit nonlinear filter
(EDP Sciences, 2012-03-02)Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration ... -
A Transmission Problem in the Scattering of Electromagnetic Waves by a Penetrable Object
(Society for Industrial and Applied Mathematics, 1996-10-05)Layer-potential techniques are used to study a transmission problem arising in the scattering of electromagnetic waves by a penetrable object. The method proposed does not involve the use of the calculus of pseudodifferential ... -
Discrete decompositions for bilinear operators and almost diagonal conditions
(American Mathematical Societ, 2002-10-23)Using discrete decomposition techniques, bilinear operators are naturally associated with trilinear tensors. An intrinsic size condition on the entries of such tensors is introduced and is used to prove boundedness for the ... -
Coherent light scattering of ultraviolet light by avian feather barbs
(University of California Press, 2003-04-05)Ultraviolet (UV) structural colors of avian feathers are produced by the spongy medullary keratin of feather barbs, but various physical mechanisms have been hypothesized to produce those colors, including Rayleigh scattering, ... -
Consistent estimation of the basic neighborhood of Markov random fields
(Institute of Mathematical Statistics, 2006-10-05)For Markov random fields on ℤd with finite state space, we address the statistical estimation of the basic neighborhood, the smallest region that determines the conditional distribution at a site on the condition that the ... -
On the rate of approximation in finite-alphabet longest increasing subsequence problems
(Institute of Mathematical Statistics, 2012-09-05)The rate of convergence of the distribution of the length of the longest increasing subsequence, toward the maximal eigenvalue of certain matrix ensembles, is investigated. For finite-alphabet uniform and nonuniform i.i.d. ... -
Divergence Rates of Markov Order Estimators and Their Application to Statistical Estimation of Stationary Ergodic Processes
(Bernoulli Society for Mathematical Statistics and Probability, 2013-09-05)Stationary ergodic processes with finite alphabets are estimated by finite memory processes from a sample, an n-length realization of the process, where the memory depth of the estimator process is also estimated from the ... -
On quadratic derivative Schrödinger equations in one space dimension
(American Mathematical Society, 2007-02-23)We consider the Schrödinger equation with derivative perturbation terms in one space dimension. For the linear equation, we show that the standard Strichartz estimates hold under specific smallness requirements on the ...
