Browsing School of Mathematics Faculty Publications by Issue Date
Now showing items 120 of 119

Parallel SpeedUp of Monte Carlo Methods for Global Optimization
(Georgia Institute of Technology, 199008)We introduce the notion of expected hitting time to a goal as a measure of the con vergence rate of a Monte Carlo optimization method. The techniques developed apply to Simulated Annealing, Genetic Algorithms and other ... 
Construction of Orthogonal Wavelets Using Fractal Interpolation Functions
(Georgia Institute of Technology, 199310)Fractal interpolation functions are used to construct a compactly supported continuous, orthogonal wavelet basis spanning L^2(IR). The wavelets share many of the properties normally associated with spline wavelets in ... 
Least Energy Solutions of Semilinear Neumann Problems and Asymptotics
(Georgia Institute of Technology, 1994)The asymptotic behavior of the least energy solutions of the semilinear Neumann problems involving critical Sobolev exponent on a bounded domain in R^4 is studied. The effect of the geometry of the boundary and the critical ... 
On the Second Eigenvalue of the Laplace Operator Penalized by Curvature
(Georgia Institute of Technology, 1994)Consider the operator  ∇^2  q(κ), where  ∇^2 is the (positive) LaplaceBeltrami operator on a closed manifold of the topological type of the twosphere S^2 and q is a symmetric nonnegative quadratic form in the principal ... 
Partially Hyperbolic Sets from a CoDimension One Bifurcation
(Georgia Institute of Technology, 1994)We study the saddlenode bifurcation of a partially hyperbolic fixed point in a Lipschitz family of C^k diffeomorphisms on a Banach manifold (possibly infinite dimensional) in the case that the fixed point is a saddle along ... 
Existence of Standing Waves for CompetitionDiffusion Equations
(Georgia Institute of Technology, 1994)In this paper, we shall consider the competitiondiffusion equation with LotkaVolterra type, and establish an existence theorem of a parameter family of standing waves which exponentially decay to a stable equilibrium ... 
Uniform Ultimate Boundedness and Synchronization for Nonautonomous Equations
(Georgia Institute of Technology, 1994)In this work we present some mathematical methods for the study of synchronization of two similar nonautonomous systems of differential equations. We give sufficient conditions to control the coupling devices in order to ... 
Proof and Generalization of KaplanYorke's Conjecture on Periodic Solution of Differential Delay Equations
(Georgia Institute of Technology, 1994)In this paper, using the theory of existence of periodic solutions of Hamiltonian systems, we show that infinitely many periodic solutions of differential delay equations can be yielded from a family of periodic solutions ... 
On the Construction of Periodic Solutions of KaplanYorke Type for Some Differential Delay Equations
(Georgia Institute of Technology, 1994)In this paper we point out the main idea to yield periodic solutions of KaplanYorke type of differential delay equations. Some new sufficient conditions for the existence of KaplanYorke type periodic solutions have been ... 
Complete Families of Pseudotrajectories and Shape of Attractors
(Georgia Institute of Technology, 1994)We study the behavior of families of δtrajectories (pseudotrajectories) near an attractor of a finitedimensional dynamical system. It is shown that for arbitrary dynamical system the boundary of any attractor can be ... 
Wave Train of Monotone Travelling Waves for Generic CompetitionDiffusion Systems
(Georgia Institute of Technology, 1994)In this paper, we consider monotone travelling waves for the generic competitiondiffusion system which satisfies the following property: The system has a finite number of equilibrium points in the first quadrant, and each ... 
FisherType Property of Travelling Waves for CompetitionDiffusion Equations
(Georgia Institute of Technology, 1994) 
Dynamics in a Discrete Nagumo Equation  Spatial Topological Chaos
(Georgia Institute of Technology, 1994)In this paper we show the existence of spatial topological chaos in a discrete Nagumo equation, and discuss the similarities and differences between the discrete Nagumao equation and the continuous one. 
Stability and Bifurcation of Traveling Wave Solutions in Coupled Map Lattices
(Georgia Institute of Technology, 1994)A class of coupled map lattices are considered. For each such coupled map lattice, the stability and bifurcation of its traveling wave solutions are studied. A stability criteria is given. It is shown that bifurcation ... 
SlowlyMigrating Transition Layers for the Discrete AllenCahn and CahnHilliard Equations
(Georgia Institute of Technology, 1994)It has recently been proposed that spatially discretized versions of the AllenCahn and CahnHilliard equations for modeling phase transitions have certain theoretical and phenomenological advantages over their continuous ... 
Instability of Stationary Solutions for LotkaVolterra Competition Model with Diffusion
(Georgia Institute of Technology, 1994)We consider the LotkaVolterra competition model with diffusion on R, and study the stability of axial symmetric positive stationary solutions relative to the space X of bounded uniformly continuous functions with the ... 
Separating the Vertices of NCubes by Hyperplanes and its Application to Artificial Neural Networks
(Georgia Institute of Technology, 199402)We obtain a new sufficient condition that a region be classifiable by a 2layer feedforward net using threshold activation functions. Briefly, it is either a convex polytope, or that minus the removal of convex polytope ... 
Commutator Bounds for Eigenvalues of Some Differential Operators
(Georgia Institute of Technology, 199403) 
On the Inverse Fractal Problem for Two Dimensional Disjoint Polyhulled Attractors
(Georgia Institute of Technology, 199403) 
Commutator Bounds for Eigenvalues, with Applications to Spectral Geometry
(Georgia Institute of Technology, 199403)We prove a purely algebraic version of an eigenvalue inequality of Hile and Protter, and derive corollaries bounding differences of eigenvalues of LaplaceBeltrami operators on manifolds. We significantly improve earlier ...