for some fixed large N0; we shall call such weights admissible. Rubio de Francia [11] showed that for every w ∈ L(R) there is a nonnegative W ∈ L(R) such that ‖W‖2 ≤ Cλ‖w‖2, Cλ < ∞ if λ > 0, and the analogous weighted norm inequality for S t holds uniformly in t. He used methods related to factorization theory of operators and the proof gave no information on how to construct w from W . In [3] ...

amalgam space W (C,L2(R, T 1 1 )) which is locally continuous and globally L2. We show that the sampling or discretization operator R from S to l2(Z, T 1 1 ) is a bounded linear operator. We introduce the dilated spaces S∆ = D∆ S parametrized by the coarseness ∆, and show that the discretization operator is also bounded with a bounded inverse for any ∆ ∈ Zn. This allows us to represent discrete...

Let ε > 0 and consider ε2u′′(t; ε) + u′(t; ε) = Au(t; ε) + ∫ t 0 K(t− s)Au(s; ε)ds+ f(t; ε), t ≥ 0, u(0; ε) = u0(ε), u ′(0; ε) = u1(ε), and w′(t) = Aw(t) + ∫ t 0 K(t− s)Aw(s)ds+ f(t), t ≥ 0, w(0) = w0, in a Banach space X when ε → 0. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and K(t) is a bounded linear operator for t ≥ 0. With some conv...

For a class of high-gain stabilizable multivariable linear innnite-dimensional systems we present an adaptive control law which achieves approximate asymptotic tracking in the sense that the tracking error tends asymptotically to a ball centred at 0 and of arbitrary prescribed radius > 0. This control strategy, called-tracking, combines proportional error feedback with a simple nonlinear adapta...

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...

We consider Perron solutions to the Dirichlet problem for quasilinear elliptic equation divA(x,∇u)=0 in a bounded open set Ω⊂Rn. The vector-valued function A satisfies standard ellipticity assumptions with 1<p<∞ and p-admissible weight w. show that arbitrary perturbations on sets of (p,w)-capacity zero continuous (and certain quasicontinuous) boundary data f are resolutive such coincide. As con...

an experimental study of the phase inversion behavior of liquid-liquid dispersion has been conducted in a spray extraction column for systems of toluene / water, n-hexane/water, ccl4/water, toluene /water + glycerol (25 % wt), toluene + ccl4 (25 % wt) / water and toluene / acetic acid (5 % wt)/water. the effects of physical properties, mass transfer and column geometry on phase inversion have b...

This paper investigates the role of topological methods in the analysis of canardtype periodic and chaotic trajectories. In Sections 1 – 5 we apply topological degree [1, 2] to the analysis of multi-dimensional canards. This part of the paper was written mainly by the first and the last authors. Sections 6 – 7 are devoted to an application of a special corollary of the Poincaré–Bendixson theore...

where ε > 0 is very small and Σ ⊂ R is Lipschitz, open and bounded. A point of Σε is denoted by (x, x3) with x ∈ Σ and x3 ∈]− ε 2 , ε 2 [. Let W : M 3×3 → [0,+∞] be the stored-energy function supposed to be continuous and coercive, i.e., W (F ) ≥ C|F | for all F ∈ M and some C > 0. In order to take into account the important physical properties that the interpenetration of matter does not occur...