解与HJB方程相关的拟变分不等式的松弛法

本文对关于HJB方程的拟变分不等式提出了松弛算法，也给出了基于上述算法的区域分解方法，并建立了相应的收敛性定理。     

Least-square Solutions of Inverse Problems for Anti-symmetric and Skew-symmetric Matrices

The least-square solutions of inverse problem for anti-symmetric and skew-symmetric matrices are studied. In addition, the problem of using anti-symmetric and skew-symmetric matrices to construct the optimal approximation to a given matrix is discussed, the necessary and sufficient conditions for the problem are derived, and the expression of the solution is provided. A numerical example is given to show the effectiveness of the proposed method.     

Prediction of Decomposition Temperature for Lanthanide Complexes Involving Cyclopentadienyl and Benzohydroxamic Acid Ligand by ANNs

The decomposition temperatures of the lanthanide organic complexes(η^5-C5H5)2Ln(C6H5CONHO)involving cyclopentadienyl and benzohydroxamic acid ligands were calculated and predicted by the model based on ANNs(artificial neural netowrks)method.The comparison was carried out between results from ANNs method and traditinal regression method.It is proved that ANNs could be used more efficiently for the prediction of decomposition temperature of lanthanide organic complexes.     

正交表交互作用的广义方差分析

本文给出“正交表的多指标效应与单指标效应的交互列一致”的结论 ,并据此结合实例给出了交互作用的“广义方差分析”法     

Dynamic motion planning in low obstacle density environments

A fundamental task for an autonomous robot is to plan its own motions. Exact approaches to the solution of this motion planning problem suffer from high worst-case running times. The weak and realistic low obstacle density (L.O.D.) assumption results in linear complexity in the number of obstacles of the free space (Van der Stappen et al., 1997). In this paper we address the dynamic version of the motion planning problem in which a robot moves among polygonal obstacles which move along polylines. The obstacles are assumed to move along constant complexity polylines, and to respect the low density property at any given time. We will show that in this situation a cell decomposition of the free space of size O(n²(n) log² n) can be computed in O(n²(n) log² n) time. The dynamic motion planning problem is then solved in O(n²(n) log³ n) time. We also show that these results are close to optimal.     

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.     

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.