1 1+x 2. This shows that arbitrary (not exp-ra denable) analytic functions may result in architectures with in-nite VC dimension. (Moreover, the architecture used is the simplest one that appears in neural nets practice.) Note that if we wish the x i 's to be bounded, for instance to be restricted to the interval [01; 1], one may replace the above x i 's and w j 's by xi c and cw j , where c = ...

We study homeomorphisms h : X onto −→ Y between two bounded domains in Rn having finite conformal energy E[h] = ∫ X ||Dh(x) || n dx < ∞ , h ∈ W (X,Y). We consider the behavior of such mappings, including continuous extension to the closure of X and injectivity of h : X → Y. In general, passing to the weak W 1,n-limit of a sequence of homeomorphisms hj : X → Y one loses injectivity. However, if ...

We establish in this article spreading properties for the solutions of equations of the type ∂tu − a(x)∂xxu − q(x)∂xu = f(x, u), where a, q, f are only assumed to be uniformly continuous and bounded in x, the nonlinearity f is of monostable KPP type between two steady states 0 and 1 and the initial datum is compactly supported. Using homogenization techniques, we construct two speeds w ≤ w such...

Objective(s) Theophylline, a xanthenes derivative, is still widely used as an effective bronchodilator in the management of asthmatic patients. It is used both as a prophylactic drug and to prevent acute exacerbations of asthma. The aim of study was to formulate and evaluate effect of the microencapsulation of theophylline loaded nanoparticles on the reduction of burst release. Materials and Me...

The strong∗ topology s∗(X) of a Banach space X is defined as the locally convex topology generated by the seminorms x → ‖Sx‖ for bounded linear maps S from X into Hilbert spaces. The w-right topology for X, ρ(X), is a stronger locally convex topology, which may be analogously characterized by taking reflexive Banach spaces in place of Hilbert spaces. For any Banach space Y , a linear map T : X ...

1.1 Notations and Hypotheses In the sequel, Ω is a bounded domain in R (N ≥ 2), with a Lipschitz continuous boundary. n is the unit normal to ∂Ω outward to Ω. We denote by x · y the usual Euclidean product of two vectors (x, y) ∈ R × R ; the associated Euclidean norm is written |.|. The Lebesgue measure of a measurable subset E of R is denoted by |E|; σ is the Lebesgue measure on ∂Ω (i.e. the (...

Let 1 < p ≤ q < +∞ and let v, w be weights on (0,+∞) satisfying: (?) v(x)xis equivalent to a non-decreasing function on (0,+∞) for some ρ ≥ 0; [w(x)x] ≈ [v(x)x] for all x ∈ (0,+∞). We prove that if the averaging operator (Af)(x) := 1 x R x 0 f(t) dt, x ∈ (0,+∞), is bounded from the weighted Lebesgue space Lp((0,+∞); v) into the weighted Lebesgue space Lq((0,+∞);w), then there exists ε0 ∈ (0, p−...

We establish universality type limits for Bergman orthogonal polynomials on simply connected regions in the complex plane with smooth boundary. Keywords: Universality Limits, Bergman Polynomials AMS Classi…cation: 41A55, 65D30, 65B99, 42C99 Research supported by NSF grant DMS0700427 and US-Israel BSF grant 2004353 1. Introduction and Results Let G be a bounded simply connected domain in the com...