Browsing School of Mathematics Faculty Publications by Issue Date
Now showing items 1-20 of 119
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Parallel Speed-Up of Monte Carlo Methods for Global Optimization
(Georgia Institute of Technology, 1990-08)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, 1993-10)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) Laplace-Beltrami operator on a closed manifold of the topological type of the two-sphere S^2 and q is a symmetric non-negative quadratic form in the principal ... -
Partially Hyperbolic Sets from a Co-Dimension One Bifurcation
(Georgia Institute of Technology, 1994)We study the saddle-node 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 Competition-Diffusion Equations
(Georgia Institute of Technology, 1994)In this paper, we shall consider the competition-diffusion equation with Lotka-Volterra 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 Kaplan-Yorke'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 Kaplan-Yorke 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 Kaplan-Yorke type of differential delay equations. Some new sufficient conditions for the existence of Kaplan-Yorke 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 δ-trajectories (pseudotrajectories) near an attractor of a finite-dimensional 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 Competition-Diffusion Systems
(Georgia Institute of Technology, 1994)In this paper, we consider monotone travelling waves for the generic competition-diffusion system which satisfies the following property: The system has a finite number of equilibrium points in the first quadrant, and each ... -
Fisher-Type Property of Travelling Waves for Competition-Diffusion 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 ... -
Slowly-Migrating Transition Layers for the Discrete Allen-Cahn and Cahn-Hilliard Equations
(Georgia Institute of Technology, 1994)It has recently been proposed that spatially discretized versions of the Allen-Cahn and Cahn-Hilliard equations for modeling phase transitions have certain theoretical and phenomenological advantages over their continuous ... -
Instability of Stationary Solutions for Lotka-Volterra Competition Model with Diffusion
(Georgia Institute of Technology, 1994)We consider the Lotka-Volterra 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 N-Cubes by Hyperplanes and its Application to Artificial Neural Networks
(Georgia Institute of Technology, 1994-02)We obtain a new sufficient condition that a region be classifiable by a 2-layer feed-forward 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, 1994-03) -
On the Inverse Fractal Problem for Two Dimensional Disjoint Polyhulled Attractors
(Georgia Institute of Technology, 1994-03) -
Commutator Bounds for Eigenvalues, with Applications to Spectral Geometry
(Georgia Institute of Technology, 1994-03)We prove a purely algebraic version of an eigenvalue inequality of Hile and Protter, and derive corollaries bounding differences of eigenvalues of Laplace-Beltrami operators on manifolds. We significantly improve earlier ...