Perturbed unstable variational inequalities with unbounded operators on approximately given sets

The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.This research was supported in part by the Ministry of Science Grant 3481-1-91 and by the Ministry of Absorption Center for Absorption in Science.     

Asymptotics for the remainder of a class of positive quadratures for integrands with an interior singularity

Summary For functions with an interior singularity, the errors of a class of positive quadrature formulae with high algebraic degree are reduced to those of the much simpler Euler-Maclaurin type formulae. Applying this method to certain classes of functions, such as, for example,f(x)=h(x)|x-u| , where >–1, with a sufficiently smooth functionh, we obtain the main term of the error expansion for quadrature rules of ultraspherical type.     

The gauge theorem for a class of additive functionals of zero energy

Summary In earlier works, the gauge theorem was proved for additive functionals of Brownian motion of the form ₀ ^t q(B _s )ds, whereq is a function in the Kato class. Subsequently, the theorem was extended to additive functionals with Revuz measures in the Kato class. We prove that the gauge theorem holds for a large class of additive functionals of zero energy which are, in general, of unbounded variation. These additive functionals may not be semi-martingales, but correspond to a collection of distributions that belong to the Kato class in a suitable sense. Our gauge theorem generalizes the earlier versions of the gauge theorem.Research supported in part by NSA grant MDA-92-H-30324     

Rigidity of harmonic maps of maximum rank

Thehomotopical rank of a mapf:M →N is, by definition, min{dimg(M) ¦g homotopic tof}. We give upper bounds for this invariant whenM is compact Kähler andN is a compact discrete quotient of a classical symmetric space, e.g., the space of positive definite matrices. In many cases the upper bound is sharp and is attained by geodesic immersions of locally hermitian symmetric spaces. An example is constructed (Section 9) to show that there do, in addition, exist harmonic maps of quite a different character. A byproduct is construction of an algebraic surface with large and interesting fundamental group. Finally, a criterion for lifting harmonic maps to holomorphic ones is given, as is a factorization theorem for representations of the fundamental group of a compact Kähler manifold. The technique for the main result is a combination of harmonic map theory, algebra, and combinatorics; it follows the path pioneered by Siu in his ridigity theorem and later extended by Sampson.     

A Systematic Evaluation of Polyurethane as a Conformal Coating for the Inhibition of Corrosion on Electronic Components

The corrosion of printed circuit boards can be effectively prevented with a polyurethane conformal coating. In this study, the protective performance of PU coating was investigated systematically through electrochemical measurements and simulated exposure/immersion tests. Some fungi tests were also included. All experimental results show that a polyurethane coating effectively inhibits corrosion on printed circuit boards. The optimal thickness of the coating film should be about 60 μm. Long-term exposure tests showed that this coating material could preserve the reliability of the investigated printed circuit boards for more than 400 days in a 90% relative humidity environment at 25°C.     

镀液中Ce^3＋离子对锡镀层结构缺陷和可焊性的影响

应用荧光分析法、X光电子能谱法(XPS)及正电子湮没寿命谱法(PALS)等研究了从含硫酸铈添加剂的酸性光亮锡镀液获得的锡镀层结构缺陷与可焊性的关系。结果表明,电镀时Ce与Sn不发生共沉积,Ce~(3+)的主要作用是阻化Sn~(2+)的水解和氧化使镀液稳定,因而使锡镀层纯度提高、结构致密、表层氧含量减少,有利于提高镀层的可焊性。当Ce~(3+)浓度控制在3.5g/L左右时,可使镀层结构缺陷较少,可焊性较佳,说明结构缺陷是影响锡镀层可焊性的直接原因。     

丙烯酸酯接枝炭黑无皂水性涂料的性能研究

旋转粘度计研究了丙烯酸酯接枝炭黑无皂水性涂料的流变性能，并考察了着色涂料的冻融及贮存稳定性。接枝炭黑争散于无皂水性涂料中形成的着色涂料具有良好的综合性能。     

Printed plastic electronics and paperlike displays

Plastic electronic materials and high‐resolution printing methods may be important technologies for new classes of consumer electronic devices that are lightweight, mechanically flexible and bendable, and that can cover large areas at low cost. This article summarizes some of our recent work in this area. It focuses on the materials and patterning techniques that we used to produce plastic active‐matrix backplane circuits for a type of paperlike display. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3327–3334, 2002     

Molecular Rectangle Formed by Head-to-tail Self-Assembly of 1-(Dipyrrin-2-yl)-1-(dipyrrin-3-yl)methane

Summary. 1-(Dipyrrin-2-yl)-1-(dipyrrin-3-yl)methane, the N-confused analog of biladiene-ac, is prepared by condensation of 2,3-dipyrromethane with two molecules of 2-formylpyrrole in dichloromethane in the presence of hydrogen bromide. Self-assembly of the ligand with Zn(II) in dichloromethane and methanol offers a dinuclear dimeric complex with a ligand:metal ratio of 2:2. X-Ray crystal structure analysis reveals two ligands bound through a head-to-tail pattern to two zinc centers to form a severely distorted helical conformation, which has the shape of a rectangle.