School of Mathematics Faculty Publications
Preprints, articles and papers by faculty members in the School of Mathematics
All materials in SMARTech are protected under U.S. Copyright Law and all rights are reserved. Such materials may be used, quoted or reproduced for educational purposes only with prior permission, provided proper attribution is given. Any redistribution, reproduction or use of the materials, in whole or in part, is prohibited without prior permission of the author.
Recent Submissions
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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 one-dimensional Schrödinger equations. He has often done this by revisiting the insights of great ... -
Asymptotic Almost Periodicity of Scalar Parabolic Equations with Almost Periodic Time Dependence
(Georgia Institute of Technology, 2009-12-07) -
Dynamics of Almost Periodic Scalar Parabolic Equations
(Georgia Institute of Technology, 2009-12-07) -
Random Restarts in Global Optimization
(Georgia Institute of Technology, 2009-12-07)In this article we study stochastic multistart methods for global optimization, which combine local search with random initialization, and their parallel implementations. It is shown that in a minimax sense the optimal ... -
A Curious Binomial Identity
(Georgia Institute of Technology, 2009-12-07)In this note we shall prove the following curious identity of sums of powers of the partial sum of binomial coefficients. -
Converse Poincaré Type Inequalities for Convex Functions
(Georgia Institute of Technology, 2009-12-07)Converse Poincaré type inequalities are obtained within the class of smooth convex functions. This is, in particular, applied to the double exponential distribution. -
Penalized Projection Estimators of the Aalen Multiplicative Intensity
(Georgia Institute of Technology, 2002-12-06)We study the problem of non parametric estimation of the intensity of counting processes satisfying the Aalen multiplicative intensity model. To do so, we use model selection techniques and more precisely penalized projection ... -
Exponential Inequalities for U-Statistics of Order Two with Constants
(Georgia Institute of Technology, 2002-12-13) -
Parallel Speed-Up of Monte Carlo Methods for Global Optimization
(Georgia Institute of Technology, 1990-08)We introduce the notion of expected hitting time to a goal as a measure of the con- vergence rate of a Monte Carlo optimization method. The techniques developed apply to Simulated Annealing, Genetic Algorithms and other ... -
On the Linear Prediction of Some L^p Random Fields
(Georgia Institute of Technology, 1995-08)This work is concerned with the prediction problem for a class of L^p-random fields. For this class of fields, we derive prediction error formulas, spectral factorizations, and orthogonal decompositions. -
Sharp Constants in Some Multiplicative Sobolev Inequalities
(Georgia Institute of Technology, 1995-09-16)The optimal constants in the multiplicative Sobolev inequalities where the gradient is estimated in the L_1-norm and the function in two different Lebesgue norms are found. With the optimal constants, these inequalities ... -
New Ramsey Bounds from Cyclic Graphs of Prime Order
(Georgia Institute of Technology, 1995-09)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 ... -
A Prophet Inequality for Independent Random Variables with Finite Variances
(Georgia Institute of Technology, 1995-09)It is demonstrated that for each n \ge 2 there exists a universal constant, c_n, such that for any sequence of independent random variables {X_r, r \ge 1} with finite variances, E[max_{1\le i\le n} X_i] - sup_T EX_T \le ... -
WKB and Turning Point Theory for Second Order Difference Equations: External Fields and Strong Asymptotics for Orthogonal Polynomials
(Georgia Institute of Technology, 2009-05)A LG-WKB and Turning point theory is developed for three term recurrence formulas associated with monotonic recurrence coefficients. This is used to find strong asymptotics for certain classical orthogonal polynomials ... -
Spectral, Criteria, SLLNS and A.S. Convergence of Series of Stationary Variables
(Georgia Institute of Technology, 1995-04)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 ... -
Approximate Speedup by Independent Identical Processing
(Georgia Institute of Technology, 1994-05)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 ... -
Largest-Fit Selection of Random Sizes under a Sum Constraint: Comparisons by Weak Convergence
(Georgia Institute of Technology, 1995-05) -
Smallest-Fit Selection of Random Sizes under a Sum Constraint: Weak Convergence and Moment Comparisons
(Georgia Institute of Technology, 1995-04-28) -
Information Advantages in Hiring under a Budget Constraint: Weak Convergence Comparisons
(Georgia Institute of Technology, 1995-10-06) -
Perturbations of Banach Frames and Atomic Decompositions
(Georgia Institute of Technology, 1994-06)Banach frames and atomic decompositions are sequences which have basis-like 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 ...
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