Convergent Algorithm Based on Progressive Regularization for Solving Pseudomonotone Variational Inequalities

In this paper, we extend the Moreau-Yosida regularization of monotone variational inequalities to the case of weakly monotone and pseudomonotone operators. With these properties, the regularized operator satisfies the pseudo-Dunn property with respect to any solution of the variational inequality problem. As a consequence, the regularized version of the auxiliary problem algorithm converges. In this case, when the operator involved in the variational inequality problem is Lipschitz continuous (a property stronger than weak monotonicity) and pseudomonotone, we prove the convergence of the progressive regularization introduced in Refs. 1, 2.     

Robust H∞ control for linear Markovian jump systems with unknown nonlinearities

This paper studies the problem of stochastic stability and disturbance attenuation for a class of linear continuous-time uncertain systems with Markovian jumping parameters. The uncertainties are assumed to be nonlinear and state, control and external disturbance dependent. A sufficient condition is provided to solve the above problem. An H_∞ controller is designed such that the resulting closed-loop system is stochastically stable and has a disturbance attenuation γ for all admissible uncertainties. It is shown that the control law is in terms of the solutions of a set of coupled Riccati inequalities. A numerical example is included to demonstrate the potential of the proposed technique.     

Short-range order and F ion diffusion inside the Pb1 − xAlxF2 + x solid solution Part II: Al NMR investigation and proposal of clustering process

A ²⁷Al nuclear magnetic resonance (NMR) investigation at room temperature of the Pb_{1 − x}Al_xF_{2 + x} (0 ≤ x ≤ 0.12) solid solution and of the ordered Pb₉Al₂F₂₄ phase is carried out. Two different types of aluminium ions are identified and their ratio is determined as a function of x. A clustering process based on the formation of column clusters, more and more extended when x increases, is proposed on the basis of results issued from the ¹⁹F (Part I) and ²⁷Al NMR investigations.     

On Subspaces and Quotients of Banach Spaces C(K, X)

 We study the relation of to the subspaces and quotients of Banach spaces of continuous vector-valued functions , where K is an arbitrary dispersed compact set. More precisely, we prove that every infinite dimensional closed subspace of totally incomparable to X contains a copy of complemented in . This is a natural continuation of results of Cembranos-Freniche and Lotz-Peck-Porta. We also improve our result when K is homeomorphic to an interval of ordinals. Next we show that complemented subspaces (resp., quotients) of which contain no copy of are isomorphic to complemented subspaces (resp., quotients) of some finite sum of X. As a consequence, we prove that every infinite dimensional quotient of which is quotient incomparable to X, contains a complemented copy of . Finally we present some more geometric properties of spaces. Received 8 November 2000; in revised form 7 December 2001     

Structural anisotropy in friction‐deposited layers of polystyrene

Friction‐deposited layers of atactic polystyrene (PS) on inert and OH‐grafted gold substrates were the subject of this study to establish a relationship between the friction process and the resulting anisotropy of the transferred polymer chains. We show, by using polarization‐modulation infrared reflection‐absorption spectroscopy that the deposited PS chains involve an anisotropy in which PS main backbone is rather perpendicular to the friction support, fact that is surprising when compared with the majority of polymers where the anisotropy is along the sliding direction. Moreover, our calculation of the orientation angles revealed that PS chains are more perpendicular in the transferred layers than in spin‐coated films. This particular anisotropy is probably due to a parallel reorientation of the phenyl ring on the friction support whatever the surface chemistry is. On the other hand, this study was useful to rectify the assignment of infrared bands unclearly reported in the literature. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3272–3281, 2006     

A new class of Ornstein transformations with singular spectrum

It is shown that for any family of probability measures in Ornstein type constructions, the corresponding transformation has almost surely a singular spectrum. This is a new generalization of Bourgain's theorem [J. Bourgain, On the spectral type of Ornstein class one transformations, Israel J. Math. 84 (1993) 53–63], same result is proved for Rudolph's construction [D. Rudolph, An example of a measure-preserving map with minimal self-joining and applications, J. Anal. Math. 35 (1979) 97–122].     

Quadratic spline interpolation on uniform meshes

The interpolation problem at uniform mesh points of a quadratic splines(x _i)=f _i,i=0, 1,...,N ands(x ₀)=f₀ is considered. It is known that s–f=O(h ³) and s–f=O(h ²), whereh is the step size, and that these orders cannot be improved. Contrary to recently published results we prove that superconvergence cannot occur for any particular point independent off other than mesh points wheres=f by assumption. Best error bounds for some compound formulae approximatingf _i andf _i ⁽³⁾ are also derived.     

Properties of RF sputtered ZnxCd1−xS thin films

Zn _x Cd_1–x S thin films (0x0.20) were prepared using rf sputtering in argon atmosphere and characterized using X-ray diffraction, optical transmission, electrical resistivity and photoconductive decay measurements. The films were found to possess hexagonal structure. The crystallite size and degree of preferential orientation were found to decrease with the increase ofx and to improve upon annealing in vacuum at 250 °C. The transmission edge shifted towards shorter wavelengths with the increase ofx in agreement with the expected shift in the energy band gap. The films were found to exhibit room temperature resistivity in the range 100–1000 cm. The obtained values of long wavelength transmission (70–80%) and minority carrier diffusion length (30 m) are high enough for the application of these films in the field of solar cells.