In this paper, we consider periodic linear systems driven by T0-periodic signals that we desire to reconstruct. The systems under consideration are of the form ẋ=A(t)x+A0(t)w(t), y=C(t)x, x ∈ Rn, w ∈ Rm, y ∈ Rp , (m p n) where A(t), A0(t), and C(t) are T0-periodic matrices. The period T0 is known. The T0-periodic input signal w(t) is unknown but is assumed to admit a finite dimensional Fourier ...

We prove L(w) bounds for the Carleson operator C, its lacunary version Clac, and its analogue for the Walsh series W in terms of the Aq constants [w]Aq for 1 q p. In particular, we show that, exactly as for the Hilbert transform, ‖C‖Lp(w) is bounded linearly by [w]Aq for 1 q < p. We also obtain L(w) bounds in terms of [w]Ap , whose sharpness is related to certain conjectures (for instance, of K...

We consider multigrid methods for symmetric positive definite linear systems. We present a new algebraic convergence analysis of two-grid schemes with inexact solution of the coarse grid system. This analysis allows us to bound the convergence factor of such perturbed two-grid schemes, assuming only a certain bound on the convergence factor for the unperturbed scheme (with exact solution of the...

We study the continuity, smoothing, and convergence properties of Steiner symmetrization in higher space dimensions. Our main result is that Steiner symmetrization is continuous in W 1;p (1 p < 1) in all dimensions. This implies that spherical symmetrization cannot be approximated in W 1;p by sequences of Steiner symmetrizations. We also give a quantitative version of the standard energy inequa...

10.1128/JVI.79.21.13561-13571.2005. 2005, 79(21):13561. DOI: J. Virol. Warr Chapman, Paul S. Gross, Craig L. Browdy and Gregory W. Prior, Guillermo Jaramillo, Edward Scura, Robert W. Javier Robalino, Thomas Bartlett, Eleanor Shepard, Sarah Invertebrate Antiviral Response? Interference and Innate Immunity in the Marine Shrimp: Convergence of RNA Addition to Nonspecific Immunity in a Sequence-Spe...

We develop new multigrid methods for a class of saddle point problems that include the Stokes system in fluid flow and the Lamé system in linear elasticity as special cases. The new smoothers in the multigrid methods involve optimal preconditioners for the discrete Laplace operator. We prove uniform convergence of the W -cycle algorithm in the energy norm and present numerical results for W -cy...

We consider the Cahn-Hilliard equation in one space dimension with scaling parameter ε, i.e. ut = (W ′(u) − εuxx)xx, where W is a nonconvex potential. In the limit ε ↓ 0, under the assumption that the initial data are energetically well-prepared, we show the convergence to a Stefan problem. The proof is based on variational methods and exploits the gradient flow structure of the Cahn-Hilliard e...

In a Freud-type weighted (w) space, introducing another weight (v) with infinitely many roots, we give a complete and minimal system with respect to vw, by deleting infinitely many elements from the original orthonormal system with respect to w. The construction of the conjugate system implies an interpolation problem at infinitely many nodes. Besides the existence, we give some convergence pro...

I n this paper, we present a new snake-based method to delineate contours where the m e r has to specify only the two distant end points without having to supply an almost complete polygonal approximation. W e achieve much better convergence properties than those of traditional snakes by propagating the image information along the curve from both end points towards its center. W e use our new m...

Let F (uε) + ε(uε − w) = 0 (1) where F is a nonlinear operator in a Hilbert space H, w ∈ H is an element, and ε > 0 is a parameter. Assume that F (y) = 0, and F ′(y) is not a boundedly invertible operator. Sufficient conditions are given for the existence of the solution to (1) and for the convergence limε→0 ‖uε−y‖ = 0. An example of applications is considered. In this example F is a nonlinear ...