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Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS) approximations of th ...
The Poisson summation formula (PSF) describes the equivalence between the sampling of an analog signal and the periodization of its frequency spectrum. In engineering textbooks, the PSF is usually stated formally without explicit conditions on the signal f ...
In this thesis we study a number of problems in Discrete Combinatorial Geometry in finite spaces. The contents in this thesis are structured as follows: In Chapter 1 we will state the main results and the notations which will be used throughout the thesis. ...
A new method of phase unwrapping is proposed for the absolute phase estimation based on the first-order polynomial phase approximation within a symmetric window generated around each pixel. The accurate estimation of polynomial coefficients is performed by ...
We study the basic allocation problem of assigning resources to players to maximize fairness. This is one of the few natural problems that enjoys the intriguing status of having a better estimation algorithm than approximation algorithm. Indeed, a certain ...
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...
The interface control domain decomposition (ICDD) method of Discacciati, Gervasio, and Quarteroni [SIAM J. Control Optim., 51 (2013), pp. 3434-3458, doi:10.1137/120890764; J. Coupled Syst. Multiscale Dyn., 1 (2013), pp. 372-392, doi:10.1166/jcsmd.2013.1026 ...
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of \mathds1{p≤0} to the image plane, where \mathds1 denotes the indicator function and p is some r ...