Browsing School of Mathematics Faculty Publications by Title
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Hierarchical Reconstruction with up to Second Degree Remainder for Solving Nonlinear Conservation Laws
(Georgia Institute of Technology, 20090731)The hierarchical reconstruction (HR) [Liu, Shu, Tadmor and Zhang, SINUM ’07] can effectively reduce spurious oscillations without local characteristic decomposition for numerical capturing of discontinuous solutions. ... 
Indefinite Quadratic Forms and the Invariance of the Interval in Special Relativity
(Georgia Institute of Technology, 2009)In this note, a simple theorem on proportionality of indefinite real quadratic forms is proved, and is used to clarify the proof of the invariance of the interval in special relativity from Einstein's postulate on the ... 
Information Advantages in Hiring under a Budget Constraint: Weak Convergence Comparisons
(Georgia Institute of Technology, 19951006) 
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 ... 
Invariant Tori in Hamiltonian Systems with High Order Proper Degeneracy
(Georgia Institute of Technology, 2009)We study the existence of quasiperiodic, invariant tori in a nearly integrable Hamiltonian system of high order proper degeneracy, i.e., the integrable part of the Hamiltonian involves several time scales and at each time ... 
Isoperimetric Constants for Product Probability Measures
(Georgia Institute of Technology, 19950724)A dimension free lower bound is found for isoperimetric constants of product probability measures. From this, some analytic inequalities are derived. 
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 ...