Browsing School of Mathematics Faculty Publications by Title
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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 ... 
Center Manifold and ExponentiallyBounded Solutions of a System of Parabolic Equations
(Georgia Institute of Technology, 20021001) 
Center Manifolds for Invariant Manifolds
(Georgia Institute of TechnologyAmerican Mathematical Society, 1997)We study dynamics of flows generated from smooth vector fields in R^n in the vicinity of an invariant and closed smooth manifold Y. By applying the Hadamard graph transform technique, we show that there exists an invariant ... 
Center Manifolds for Invariant Sets
(Georgia Institute of Technology, 1999)We derive a general center manifolds theory for a class of compact invariant sets of flows generated by a smooth vector fields in R^n. By applying the Hadamard graph transform technique, it is shown that, associated to ... 
Central Discontinuous Galerkin Methods on Overlapping Cells with a NonOscillatory Hierarchical Reconstruction
(Georgia Institute of Technology, 20060828)The central scheme of Nessyahu and Tadmor [J. Comput. Phys, 87 (1990)] solves hyperbolic conservation laws on a staggered mesh and avoids solving Riemann problems across cell boundaries. To overcome the difficulty of ... 
Central Schemes and Central Discontinuous Galerkin Methods on Overlapping Cells
(Georgia Institute of Technology, 2005)The central scheme of Nessyahu and Tadmor (J. Comput. Phys, 87(1990)) has the bene t of not having to deal with the solution within the Riemann fan for solving hyperbolic conservation laws and related equations. But the ... 
Central Schemes on Overlapping Cells
(Georgia Institute of Technology, 2004)Nessyahu and Tadmor's central scheme (J. Comput. Phys, 87(1990)) has the benefi t of not using Riemann solvers or characteristic decomposition for solving hyperbolic conservation laws and related convection diffusion ... 
A Characterization of Gaussian Measures via the Isoperimetric Property of HalfSpaces
(Georgia Institute of Technology, 19950725)If the halfspaces of the form {x\in R^n: x_1 \le c} are extremal in the isoperimetric problem for the product measure \mu^n, n\ge 2, then \mu is Gaussian. 
Commutator Bounds for Eigenvalues of Some Differential Operators
(Georgia Institute of Technology, 199403) 
Commutator Bounds for Eigenvalues, with Applications to Spectral Geometry
(Georgia Institute of Technology, 199403)We prove a purely algebraic version of an eigenvalue inequality of Hile and Protter, and derive corollaries bounding differences of eigenvalues of LaplaceBeltrami operators on manifolds. We significantly improve earlier ... 
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.