Department of Mathematics and Statistics
Recent Submissions

Spatiotemporal Distributions of Migratory Birds : Patchy Models with Delay
We derive and analyze a mathematical model for the spatiotemporal distribution of a migratory bird species. The birds have specific sites for breeding and winter feeding, and usually several stopover sites along the migration ... 
Interaction of Migratory Birds and Domestic Poultry and Its Role in Sustaining Avian Influenza, The
We investigate the role of migratory birds in the spread of H5N1 avian influenza, focusing on the interaction of a migratory bird species with nonmigratory poultry. The model is of patch type and is derived with the aid ... 
Simple Proof of Fiedler's Conjecture Concerning Orthogonal Matrices, A
We give a simple proof that an n x n orthogonal matrix with n ≥ 2 which cannot be written as a direct sum has at least 4n4 nonzero entries. 
Distances in Weighted Trees and Group Inverse of Laplacian Matrices
In this paper we find formulas for group inverses of Laplacians of weighted trees. We then develop a relationship between entries of the group inverse and various distance functions on trees. In particular, we show that ... 
On Matrices with Signed Null Spaces
We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A has signed nullspace provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the nullspace of ... 
Sign Patterns That Allow a Positive or Nonnegative Left Inverse
An m by n sign pattern S is an m by n matrix with entries in {+,, 0}. Such a sign pattern allows a positive (resp., nonnegative) left inverse, provided that there exist an m by n matrix A with the sign pattern S and an n ... 
Reconstruction of a Spherically Symmetrical Speed of Sound
Consider the inverse acoustic scattering problem for a spherically symmetric inhomogeneity of compact support that arises, among other places, in nondestructive testing. Define the corresponding homogeneous and inhomogeneous ... 
Domain Decomposition Operator Splittings for the Solution of Parabolic Equations
We study domain decomposition counterparts of the classical alternating direction implicit (ADI) and fractional step (FS) methods for solving the large linear systems arising from the implicit time stepping of parabolic ... 
Particle Method and Numerical Study of a Quasilinear Partial Differential Equation, A
We present a particle method for studying a quasilinear partial differential equation (PDE) in a class proposed for the regularization of the Hopf (inviscid Burger) equation via nonlinear dispersionlike terms. These are ... 
Automatic Differentiability and Characterization of Cocycles of Holomorphic Flows
In this paper we prove that cocycles of holomorphic flows on domains in the complex plane are automatically differentiable with respect to the flow parameter, and their derivatives are holomorphic functions. We use this ... 
Set of All MXN Rectangular Real Matrices of RankR Is Connected by Analytic Regular Arcs, The
It is well known that the set of all square invertible real matrices has two connected components. The set of all m x n rectangular real matrices of rank r has only one connected component when m ≠ n or r < m = n. We show ... 
Novel Method for Solving Multiscale Elliptic Problems with Randomly Perturbed Data, A
We propose a method for efficient solution of elliptic problems with multiscale features and randomly perturbed coefficients. We use the multiscale finite element method (MsFEM) as a starting point and derive an algorithm ... 
Renormalization Group Analysis of Nonlinear Diffusion Equations with Time Dependent Coefficients : Analytical Results
We study the longtime asymptotics of a certain class of nonlinear diffusion equations with timedependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. ... 
Renormalization Group Analysis of Nonlinear Diffusion Equations with Periodic Coefficients
In this paper we present an efficient numerical approach based on the renormalization group method for the computation of selfsimilar dynamics. The latter arise, for instance, as the longtime asymptotic behavior of ... 
Scaling Analysis for the Tracer Flow Problem in SelfSimilar Permeability Fields
The spatial variations in porous media (aquifers and petroleum reservoirs) occur at all length scales (from the pore to the reservoir scale) and are incorporated into the governing equations for multiphase flow problems ... 
Large Deviation Principle and Inviscid Shell Models
A LDP is proved for the inviscid shell model of turbulence. As the viscosity coefficient v converges to 0 and the noise intensity is multiplied by root v, we prove that some shell models of turbulence with a multiplicative ... 
Evolution of a Random Vortex Filament, The
We study an evolution problem in the space of continuous loops in a threedimensional Euclidean space modeled upon the dynamics of vortex lines in 3d incompressible and inviscid fluids. We establish existence of a local ...