Interior projection-like methods for monotone variational inequalities

We propose new interior projection type methods for solving monotone variational inequalities. The methods can be viewed as a natural extension of the extragradient and hyperplane projection algorithms, and are based on using non Euclidean projection-like maps. We prove global convergence results and establish rate of convergence estimates. The projection-like maps are given by analytical formulas for standard constraints such as box, simplex, and conic type constraints, and generate interior trajectories. We then demonstrate that within an appropriate primal-dual variational inequality framework, the proposed algorithms can be applied to general convex constraints resulting in methods which at each iteration entail only explicit formulas and do not require the solution of any convex optimization problem. As a consequence, the algorithms are easy to implement, with low computational cost, and naturally lead to decomposition schemes for problems with a separable structure. This is illustrated through examples for convex programming, convex-concave saddle point problems and semidefinite programming.The work of this author was partially supported by the United States–Israel Binational Science Foundation, BSF Grant No. 2002-2010.     

方差分量谱分解估计的几个性质

对于线性混合模型中方差分量的估计，虽有多种方法，但一般情况下只有方差分析估计和谱分解估计有显式解，本文就线性混合模型中含两个方差分量的情形，对方差分析估计和谱分解估计进行了比较，证明了在一些条件下两个估计的方差相等，由此推出谱分解估计也具有方差分析估计的某些优良性．文末用实例进一步说明了文中的结果．     

The effects of the spinodal microstructure on the electrical properties of TiO2-SnO2 ceramics

The electrical properties of ceramics within the TiO₂-SnO₂ system which exhibit spinodal decomposition were investigated under different annealing conditions. Changes in the lattice parameter and the phase evolution of the spinodal decomposition, measured in terms of the volume fraction transformed X(t), were examined as a function of annealing time using X-ray diffraction. The room temperature dielectric properties were measured and compared to dielectric mixing rules. Doping with pentavalent Nb was found to slow the decomposition kinetics and a high permittivity (ε_r>1000) was induced. The origin of the high permittivity is linked to the formation of an electrically heterogeneous structure which is derived from the spinodal microstructure. Lastly, it was observed that Nb-doped TiO₂-SnO₂ ceramics exhibited non-linear current-voltage behavior which can be attributed to the negative temperature coefficient of resistance effect.     

An implicit pseudo‐spectral multi‐domain method for the simulation of incompressible flows

A pseudo‐spectral method for the solution of incompressible flow problems based on an iterative solver involving an implicit treatment of linearized convective terms is presented. The method allows the treatment of moderately complex geometries by means of a multi‐domain approach and it is able to cope with non‐constant fluid properties and non‐orthogonal problem domains. In addition, the fully implicit scheme yields improved stability properties as opposed to semi‐implicit schemes commonly employed. Key components of the method are a Chebyshev collocation discretization, a special pressure–correction scheme, and a restarted GMRES method with a preconditioner derived from a fast direct solver. The performance of the proposed method is investigated by considering several numerical examples of different complexity, and also includes comparisons to alternative solution approaches based on finite‐volume discretizations. Copyright © 2003 John Wiley & Sons, Ltd.     

谱半径前六位的n阶单圈图

恰含一个圈的简单连通图称为单圈图。Cn记n个顶点的圈。△（i,j,κ）记C3的三个顶点上分别接出i,j,κ条悬挂边所得的图，其中i≥j≥κ≥0.Sl^n-l记Cl的某一顶点上接出n-l条悬挂边所得到的图。△（n-4 1,0,0)记△（n-4,0,0)的某个悬挂点上接出一条悬挂边所得到的图。本文证明了：若把所有n(n≥12）阶单圈图按其最大特征值从大到小的顺序排列，则排在前六位的依次是S3^n-3，△（n-4,1,0),△（n-4 1,0,0),S4^n-4,△（n-5,2,0),△（n-5,1,1)。     

Riemannian Foliations and Eigenvalue Comparison

Eigenvalue comparison theorems for the Laplacian on a Riemannian manifold generally give bounds for the first Dirichlet eigenvalue on balls in the manifold in terms of an eigenvalue arising from a geometrically or analytically simpler situation. Cheng's eigenvalue comparison theory assumes bounds on the curvature of the manifold and then compares this eigenvalue to the eigenvalue of a ball in a constant curvature space form. In this paper we examine the basic Laplacian – the appropriate Laplacian on functions that are constant on the leaves of the foliation. The main theorems generalize Cheng's eigenvalue comparison theorem and other eigenvalue comparison theorems to the category of Riemannian foliations by estimating the first Dirichlet eigenvalue for the basic Laplacian on a metric tubular neighborhood of a leaf closure. Several other facts about the the first eigenvalue of such foliated tubes as well as some needed facts about the tubes themselves are established. This comparison theory, like Cheng's theorem, remains valid for large tubes that are not homotopic to the middle leaf closure and that may have irregular boundaries. We apply these results to obtain upper bounds for the eigenvalues of the basic Laplacian on a closed manifold in terms of curvature bounds and the transverse diameter of the foliation.     

Electrochemical cells with multilayer functional electrodes

Microstructural and chemical changes in a NiO-YSZ electrocatalytic electrode were studied. The microstructural changes in the NiO-YSZ electrocatalytic electrode after the cell operation was compared with the electrode quenched under the applied voltage to suppress the oxidation process. The reversible reduction of NiO into Ni and the formation of intergranular Ni layers at the NiO/YSZ interface were investigated. It was shown that in a compositional range of the NiO-YSZ electrodes from 1/3 to 2/3 the value of the ambipolar conductivity increased with increasing voltage applied to the electrochemical cell. The observed reversible increase in the value of ambipolar conductivity of the electrocatalytic electrode is described in frames of the model of reversible reduction of NiO into Ni under the conditions of cell operation.     

Fe40—45Cr30—35Co20—25Mo0—4Zr0—2合金微观结构对矫顽力的影响

研究了高矫顽力型FeCrCo合金的磁性和微观结构.实验结果表明，适当的合金成分及热处理 条件可以明显提高FeCrCo合金的矫顽力.通过透射电镜、x射线衍射等手段得出结论：主体元 素含量的提高和微量元素的掺杂可以有效地控制相的组成，磁场热处理导致强磁性相和弱磁 性相的分离，回火后形成起磁硬化作用的调幅结构.该调幅结构中较大的两相成分差有利于 提高FeCrCo合金的矫顽力. 关键词： 矫顽力 调幅分解 磁场热处理 两相结构 成分差     

关于矩阵二次型极值的若干结果

本文出于统计研究的需要，系统地讨论了Ｒａｙｌｅｉｇｈ－Ｒｉｔｚ定理在矩阵形式下的推广，给出了若干新结果，完善了现有文献中这方面的研究。     

与A-调和方程有关的两个结果

给出两个与A 调和方程有关的结果 .第一个结果是一类A 调和方程的很弱解可由调和函数逼近 .另一个是变分积分弱极值的充分必要条件