Browsing School of Mathematics Faculty Publications by Issue Date
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Approximate Speedup by Independent Identical Processing
(Georgia Institute of Technology, 199405)In this paper we prove that for algorithms which proceed to the next state based on information available from the current state, identical independent parallel processing using stochastic multistart methods always yields ... 
Perturbations of Banach Frames and Atomic Decompositions
(Georgia Institute of Technology, 199406)Banach frames and atomic decompositions are sequences which have basislike properties but which need not be bases. In particular, they allow elements of a Banach space to be written as combinations of the frame or atomic ... 
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 ... 
Least Squares Approximate Feedback Linearization
(Georgia Institute of Technology, 199407)We study the least squares approximate feedback linearization problem: given a single input nonlinear system, find a linearizable nonlinear system that is close to the given system in a least squares (L_2) sense. A ... 
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 ... 
On a Class of Aperiodic SumFree Sets
(Georgia Institute of Technology, 199410)We show that certain natural aperiodic sumfree sets are incomplete that is that there are infinitely many n not in S which are not a sum of two element of S. 
Ergodicity of Minimal Sets in Scalar Parabolic Equations
(Georgia Institute of Technology, 1995) 
Generalization of a Theorem of Malta and Palis
(Georgia Institute of Technology, 1995)We study the saddlenode bifurcation of a partially hyperbolic fixed point in a Lipschitz family of C^k diffeomorphisms on an ndimensional manifold, in the case that the stable set and unstable set of the fixed point ... 
Almost Automorphic and Almost Periodic Dynamics in SkewProduct Semiflows
(Georgia Institute of Technology, 1995)The current series of papers, which consists of three parts, are devoted to the study of almost automorphic dynamics in differential equations. By making use of techniques from abstract topological dynamics, we show that ... 
Feedback Linearization of Transverse Dynamics for Periodic Orbits
(Georgia Institute of Technology, 19950112)In this paper we give necessary and sufficient conditions for feedback linearization of the transverse dynamics (TFL) of a nonlinear affine singleinput system in a neighborhood of a periodic orbit. The TFL procedure ... 
Approximate Feedback Linearization: A Homotopy Operator Approach
(Georgia Institute of Technology, 19950112)In this paper, we present an approach for finding feedback linearizable systems that approximate a given singleinput nonlinear system on a given compact region of the state space. First, we show that if the system is ... 
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 ... 
Feedback Linearization of Transverse Dynamics for Periodic Orbits in R^3 with Points of Transverse Controllability Loss
(Georgia Institute of Technology, 199503)In this paper we show how one can linearize the transverse dynamics of a nonlinear affine singleinput system in R^3 in a neighborhood of a periodic orbit in the case when the transverse linear controllability fails in ... 
Spectral, Criteria, SLLNS and A.S. Convergence of Series of Stationary Variables
(Georgia Institute of Technology, 199504)It is shown here how to extend the spectral characterization of the strong law of large numbers for weakly stationary processes to certain singular averages. For instance, letting {X_t, t \in R^3}, be a weakly stationary ... 
SmallestFit Selection of Random Sizes under a Sum Constraint: Weak Convergence and Moment Comparisons
(Georgia Institute of Technology, 19950428) 
LargestFit Selection of Random Sizes under a Sum Constraint: Comparisons by Weak Convergence
(Georgia Institute of Technology, 199505) 
C^k Conjugacy of 1D Diffeomorphisms with Periodic Points
(Georgia Institute of Technology, 19950605)It is shown that the set of heteroclinic orbits between two periodic orbits of saddlenode type induces a functional modulus. For onedimensional C^2 diffeomorphisms with saddlenode periodic points, two such diffeomorphisms ... 
Some Conditions on Periodicity for SumFree Sets
(Georgia Institute of Technology, 199507)Cameron has introduced a natural bijection between the set of one way in nite binary sequences and the set of sumfree sets (of positive integers), and observed that a sumfree set is ultimately periodic only if the ... 
The Number of Independent Sets in a Grid Graph
(Georgia Institute of Technology, 199507) 
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.