Generalized Vector Quasi-Variational Inequality Problems Over Product Sets

In this paper we consider vector quasi-variational inequality problems over product sets (in short, VQVIP). Moreover we study generalizations of this model, namely problems of a system of vector quasi-variational inequalities (in short, SVQVIP), generalized vector quasi-variational inequality problems over product sets (in short, GVQVIP) and problems of a system of generalized vector quasi-variational inequalities (in short, SGVQVIP). We show that every solution of (VQVIP) (respectively, (GVQVIP)) is a solution of (SVQVIP) (respectively, (SGVQVIP)). By defining relatively pseudomonotone and relatively maximal pseudomonotone maps and by employing a known fixed point theorem, we establish the existence of a solution of (VQVIP) and (SVQVIP). These existence results are then used to derive the existence of a solution of (GVQVIP) and (SGVQVIP), respectively, The results of this paper extend recent results in the literature. They are obtained in a more general setting.     

New Bell-type inequalities forN > 4 necessary for existence of a hidden variable

The purpose of this paper is to extend Bell's inequalities to obtain some general necessary conditions for the existence of a joint probability distribution for any finite collection of Bell-type random variables. Our results show that forN > 4 many new elementary inequalities beyond those of Bell must be satisfied by any hidden variable theory.     

A self-adaptive method for solving general mixed variational inequalities

The general mixed variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method cannot be applied to solve this problem due to the presence of the nonlinear term. To overcome this disadvantage, Noor [M.A. Noor, Pseudomonotone general mixed variational inequalities, Appl. Math. Comput. 141 (2003) 529-540] used the resolvent equations technique to suggest and analyze an iterative method for solving general mixed variational inequalities. In this paper, we present a new self-adaptive iterative method which can be viewed as a refinement and improvement of the method of Noor. Global convergence of the new method is proved under the same assumptions as Noor's method. Some preliminary computational results are given.     

Hilbert不等式的各种精化与拓广综述

在本文中,我们较全面的概述了1990年至2002年间有关Hilbert级数型与积分型不等式的种种精化与拓广工作.涉及发表于海内外的文献资料40余篇,其中我国学者的工作成果占有重要份量.文末还列举了一些有待进一步研究的公开问题.     

PPLN waveguide for quantum communication

We report on energy-time and time-bin entangled photon-pair sources based on a periodically poled lithium niobate (PPLN) waveguide. Degenerate twin photons at 1 314 nm wavelength are created by spontaneous parametric down-conversion and coupled into standard telecom fibers. Our PPLN waveguide features a very high conversion efficiency of about 10^-6, roughly 4 orders of magnitude more than that obtained employing bulk crystals [#!Tanzilli01a!#]. Even if using low power laser diodes, this engenders a significant probability for creating two pairs at a time - an important advantage for some quantum communication protocols. We point out a simple means to characterize the pair creation probability in case of a pulsed pump. To investigate the quality of the entangled states, we perform photon-pair interference experiments, leading to visibilities of 97% for the case of energy-time entanglement and of 84% for the case of time-bin entanglement. Although the last figure must still be improved, these tests demonstrate the high potential of PPLN waveguide based sources to become a key element for future quantum communication schemes. Received 13 July 2001     

广义双拟变分不等式和广义拟变分不等式解的存在性

本文研究一类抽象广义双拟变分不等式和广义拟变分不等式问题，获得了解的存在性定理，改进推广了相关文献的一些主要结果．     

Infinite divisibility of a bethe lattice ising model

It is shown that the probability distribution for the infinite-volume, free-boundary-condition Ising ferromagnet on the Bethe lattice under zero external field is infinitely divisible with respect to the group operation of pointwise multiplication of spin variables.     

Proximal Methods for Mixed Quasivariational Inequalities

A proximal method for solving mixed quasivariational inequalities is suggested and analyzed by using the auxiliary principle technique. We show that the convergence of the proposed method requires only the pseudomonotonicity, which is a weaker condition than monotonicity. Since mixed quasivariational inequalities include variational and complementarity problems as special cases, the result proved in this paper continues to hold for these problems.     

Inequalities for the Extremal Coefficients of Multivariate Extreme Value Distributions

The extremal coefficients are the natural dependence measures for multivariate extreme value distributions. For an m-variate distribution 2^m distinct extremal coefficients of different orders exist; they are closely linked and therefore a complete set of 2^m coefficients cannot take any arbitrary values. We give a full characterization of all the sets of extremal coefficients. To this end, we introduce a simple class of extreme value distributions that allows for a 1-1 mapping to the complete sets of extremal coefficients. We construct bounds that higher order extremal coefficients need to satisfy to be consistent with lower order extremal coefficients. These bounds are useful as lower order extremal coefficients are the most easily inferred from data.     

Two-weight norm inequalities for the Cesàro means of Hermite expansions

An accurate estimate is obtained of the Cesàro kernel for Hermite expansions. This is used to prove two-weight norm inequalities for Cesàro means of Hermite polynomial series and for the supremum of these means. These extend known norm inequalities, even in the single power weight and ``unweighted' cases. An almost everywhere convergence result is obtained as a corollary. It is also shown that the conditions used to prove norm boundedness of the means and most of the conditions used to prove the boundedness of the Cesàro supremum of the means are necessary.