In this paper we propose a new nonparametric regression algorithm based on Fuzzy systems with overlapping concepts. We analyze its consistency properties, showing that it is capable to reconstruct an infinite-dimensional class of function when the size of the (noisy) dataset grows to infinity. Moreover convergence to the target function is guaranteed in Sobolev norms so ensuring uniform converg...

The three bilinearities uv, uv, uv for functions u, v : R2×[0, T ] 7−→ C are sharply estimated in function spaces Xs,b associated to the Schrödinger operator i∂t+∆. These bilinear estimates imply local wellposedness results for Schrödinger equations with quadratic nonlinearity. Improved bounds on the growth of spatial Sobolev norms of finite energy global-in-time and blow-up solutions of the cu...

We study properties of spherical Bernstein-Bézier splines. Algorithms for practical implementation of the global splines are presented for a homogeneous case as well as a non-homogeneous. Error bounds are derived for the global splines in terms of Sobolev type spherical semi-norms. Multiple star technique is studied for the minimal energy interpolation problem. Numerical summary supporting theo...

In this paper we will establish two different classes of ellipticity criteria, called the L criteria and the L-L criteria respectively, for planar linear Hamiltonian systems with periodic coefficients. The criteria are explicitly expressed using the L and L norms of coefficients and some known Sobolev constants. These results can be considered as the extensions of the famous Lyapunov stability ...

We compute the length of geodesics on a Riemannian manifold by regular polynomial interpolation of the global solution of the eikonal equation related to the line element ds = gijdx dx of the manifold. Our algorithm approximates the length functional in arbitrarily strong Sobolev norms. Error estimates are obtained where the geometric information is used. It is pointed out how the algorithm can...

The paper formulates and proves a second order interpolation result for square-integrable functions by means of locally nite series of Daubechies' wavelets. Sample values of a suuciently smooth function can be used as coeecients of a wavelet expansion at a ne scale, and the corresponding wavelet interpolation function converges in Sobolev norms of rst order to the original function. This has ap...

1. Overview 2 2. Electromagnetic waves 3 2.1. Approximate cloaking via change of variables 3 2.1.1. Cloaking for the Helmholtz equation 3 2.1.2. Full range estimates for the degree of invisibility 4 2.1.3. Perfect cloaking for the Helmholtz equation 4 2.2. Electrical impedance tomography 5 2.3. Generalized impedance boundary conditions 5 2.3.1. The Helmholtz equation 6 2.3.1. The time harmonic ...

The paper addresses a problem of sampling discretization integral norms elements finite-dimensional subspaces satisfying some conditions. We prove results under standard assumption formulated in terms the Nikol'skii-type inequality. In particular, we obtain upper bounds on number sample points sufficient for good Lp norms, 1≤p<2, functions from continuous functions. Our new improve upon known t...