Browsing School of Mathematics Faculty Publications by Title
Now showing items 2140 of 119

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 ... 
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 ... 
Conventional Multipliers for Homoclinic Orbits
(Georgia Institute of Technology, 19950130)In this work we introduce and describe conventional multipliers, a new characteristic of homoclinic orbits of saddlenode type periodic trajectories. We prove existence and smooth dependence of conventional multipliers on ... 
Convergence in Almost Periodic Fisher and Kolmogorov Models
(Georgia Institute of Technology, 1996)We study convergence of positive solutions for almost periodic reaction diffusion equations of Fisher or Kolmogorov type. It is proved that under suitable conditions every positive solution is asymptotically almost periodic. ... 
Converse Poincaré Type Inequalities for Convex Functions
(Georgia Institute of Technology, 20091207)Converse Poincaré type inequalities are obtained within the class of smooth convex functions. This is, in particular, applied to the double exponential distribution. 
Counting Sets of Integers, No k of Which Sum to Another
(Georgia Institute of Technology, 199507)We show that for every k greater or equal than 3 the number of subsets of {1,2,...,n} containing no solution to x_1 + x_2 + ... + x_k = y, where the x_i need not be distinct, is at most c2^{\alpha n}, where \alpha = (k1)/k. 
A Curious Binomial Identity
(Georgia Institute of Technology, 20091207)In this note we shall prove the following curious identity of sums of powers of the partial sum of binomial coefficients. 
The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian System with Elliptic Segment
(Georgia Institute of Technology, 2000)We study the cyclicity of period annuli (or annulus) for general degenerate quadratic Hamiltonian systems with an elliptic segment or a saddle loop, under quadratic perturbations. By using geometrical arguments and studying ... 
Degenerate Lower Dimensional Tori in Hamiltonian Systems
(Georgia Institute of Technology, 2005) 
Dependent Sets of Constant Weight Binary Vectors
(Georgia Institute of Technology, 199507)We determine lower bounds for the number of random binary vectors, chosen uniformly from vectors of weight k, needed to obtain a dependent set. 
Dimension Free Weak Concentration of Measure Phenomenon
(Georgia Institute of Technology, 19950724)For product probability measures \mu^n, we obtain necessary and sufficient conditions (in terms of \mu) for dimension free isoperimetric inequalities of the form \mu^n (A + h[1,1]^n)\ge R_h(\mu^n(A)) to hold; for a ... 
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. 
Dynamics of Almost Periodic Scalar Parabolic Equations
(Georgia Institute of Technology, 20091207) 
Dynamics of Cyclic Feedback Systems
(Georgia Institute of Technology, 19940707)The dynamics of cyclic feedback systems are described. The emphasis is both in showing the diversity of possible dynamics in these systems and in showing that there is a underlying dynamic structure possessed by all these ... 
Eigenvalues and Perturbed Domains
(Georgia Institute of Technology, 2002) 
Epidemic Waves: A Diffusion Model for Fox Rabies
(Georgia Institute of Technology, 19940629)In this paper we formulate a model for the spread of vulpine rabies based on fox ecology. This model is also an approximation to the one introduced by J. D. Murray et al [MSB]. We prove that a heteroclinic spiral connection ... 
Ergodicity of Minimal Sets in Scalar Parabolic Equations
(Georgia Institute of Technology, 1995) 
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 ... 
An Explanation to the Phenomenon of Coupled First Order Shift of Conservative Quantities during the Interaction of Captured Discontinuities
(Georgia Institute of Technology, 2003)High resolution capturing schemes generally speaking can take advantage of the piecewise smooth property of the weak solutions of conservation laws and achieve high order accuracy wherever the solution is smooth. Thus ... 
Exponential Inequalities for Counting Processes
(Georgia Institute of Technology, 200211)We derive for counting processes some equivalents of classical exponential inequalities existing in the nsample framework. The supremum of centered integrals is our principal interest: we prove an inequality which resembles ...