Browsing School of Mathematics Faculty Publications by Title
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A KAM Theorem for Hamiltonian Networks with Long Ranged Couplings
(Georgia Institute of Technology, 2006)We consider Hamiltonian networks of long ranged and weakly coupled oscillators with variable frequencies. 
LargestFit Selection of Random Sizes under a Sum Constraint: Comparisons by Weak Convergence
(Georgia Institute of Technology, 199505) 
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 ... 
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 ... 
Lévy Processes in Cones of Banach Spaces
(Georgia Institute of Technology, 200311)Subordinators in Banach spaces are studied. The existence of the special LévyKhintchine representation is related to the geometry of the space and a Pettis integral with respect to the underlying Lévy measure. Rates of ... 
A Local Variational Principle of Pressure and Its Applications to Equilibrium States
(Georgia Institute of Technology, 2004) 
Malaria Epidemics and the SickleCell Gene Dynamics
(Georgia Institute of Technology, 2002)A mathematical model incorporating both malaria epidemics and human population genetics of the sicklecell gene is studied. The dynamics of the model can be separated into two timescales with a faster timescale for the ... 
Metapopulation Dynamics with Migration and Local Competition
(Georgia Institute of Technology, 2002)Many patchbased metapopulation models assume that the local population within each patch is at its equilibrium and independent of changes in patch occupancy. We study a metapopulation model which explicitly incorporates ... 
A Metapopulation Model with Explicit Local Population Dynamics
(Georgia Institute of Technology, 20030719)Many patchbased metapopulation models assume that the local population within each patch is at its equilibrium and independent of changes in patch occupancy. We studied a metapopulation model that explicitly incorporates ... 
Morse Theory on Spaces of Braids and Lagrangian Dynamics
(Georgia Institute of Technology, 2001)In the first half of the paper we construct a Morsetype theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of ... 
Nekhoroshev and Kam Stabilities in Generalized Hamiltonian Systems
(Georgia Institute of Technology, 2003)We present some Nekhoroshev stability results for nearly integrable, generalized Hamiltonian systems which can be odd dimensional and admit a distinct number of action and angle variables. Using a simultaneous approximation ... 
New Ramsey Bounds from Cyclic Graphs of Prime Order
(Georgia Institute of Technology, 199509)We present new explicit lower bounds for some Ramsey numbers. All the graphs are cyclic, and are on a prime number of vertices. We give a partial probabilistic analysis which suggests that the cyclic Ramsey numbers grow ... 
NonOscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes
(Georgia Institute of Technology, 20061030)This is the continuation of the paper "central discontinuous Galerkin methods on overlapping cells with a nonoscillatory hierarchical reconstruction" by the same authors. The hierarchical reconstruction introduced therein ... 
Nonlinear Oscillations and Multiscale Dynamics in a Closed Chemical Reaction System
(Georgia Institute of Technology, 2009)We investigate the oscillatory chemical dynamics in a closed isothermal reaction system described by the reversible LotkaVolterra model. This is a threedimensional, dissipative, singular perturbation to the conservative ... 
Nonparametric estimation for Levy processes with a view towards mathematical finance
(Georgia Institute of Technology, 200411)Nonparametric methods for the estimation of the Levy density of a Levy process X are developed. Estimators that can be written in terms of the "jumps" of X are introduced, and so are discretedata based approximations. A ... 
The Number of Independent Sets in a Grid Graph
(Georgia Institute of Technology, 199507) 
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. 
On a transformation of Bohl and its discrete analogue
(Georgia Institute of TechnologyAmerican Mathematical Society, 2013)Fritz Gesztesy’s varied and prolific career has produced many transformational contributions to the spectral theory of onedimensional Schrödinger equations. He has often done this by revisiting the insights of great ... 
On Almost Automorphic Dynamics in Symbolic Lattices
(Georgia Institute of Technology, 2002)We study the existence, structure, and topological entropy of almost automorphic arrays in symbolic lattice dynamical systems. In particular we show that almost automorphic arrays with arbitrarily large entropy are typical ... 
On Almost Automorphic Oscillations
(Georgia Institute of Technology, 2003)Almost automorphic dynamics have been given a notable amount of attention in recent years with respect to the study of almost periodically forced monotone systems. There are solid evidences that these types of dynamics ...