实二次域上理想类的zeta-函数在-1处的值

用连分数给出了实二次域理想类的zeta-函数-1处值的一个具体的计算公式.     

An Improved Gradient Projection-based Decomposition Technique for Support Vector Machines

In this paper we propose some improvements to a recent decomposition technique for the large quadratic program arising in training support vector machines. As standard decomposition approaches, the technique we consider is based on the idea to optimize, at each iteration, a subset of the variables through the solution of a quadratic programming subproblem. The innovative features of this approach consist in using a very effective gradient projection method for the inner subproblems and a special rule for selecting the variables to be optimized at each step. These features allow to obtain promising performance by decomposing the problem into few large subproblems instead of many small subproblems as usually done by other decomposition schemes. We improve this technique by introducing a new inner solver and a simple strategy for reducing the computational cost of each iteration. We evaluate the effectiveness of these improvements by solving large-scale benchmark problems and by comparison with a widely used decomposition package.     

Solving Problems with Min-Type Functions by Disjunctive Programming

We consider applications of disjunctive programming to global optimization and problems with equilibrium constraints. We propose a modification of the algorithm of F. Beaumont for disjunctive programming problems and show its numerical efficiency.     

非完整系统Chetaev动力学和vakonomic动力学的等价条件

就一般非完整约束系统，从约束方程满足的变分恒等式出发，利用增广位形流形上的向量场定义三类非自由变分，即非完整变分：vakonomic变分、Hlder变分、Suslov变分，并讨论它们之间的关系以及它们成为自由变分的充要条件.利用非完整变分以及相应的积分变分原理建立两类动力学方程：vakonomic方程和Routh方程或Chaplygin方程.通过vakonomic方程分别与Routh方程和Chaplygin方程比较，得到它们具有共同解的两类充分必要条件.这些条件并不是约束的可积性条件. 关键词： 非完整约束 非完整变分 Chetaev条件 vakonomic动力学     

An applied cell mapping method for optimal control problems

From the application point of view, a series of modifications are proposed for the cell mapping method discussed in Ref. 1 for the optimal control analysis of dynamical systems. The cell order around the target set is rearranged. A set of common discriminate principles is used for the selection of the optimal one among competing control strategies of the same cost. Inequality constraints of the system are taken into account. The number of elements in the set of allowable time intervals is not prescribed, but left open. These modifications seem to make the cell mapping method more efficient for analyzing feedback systems and for obtaining their global optimal control information. The algorithms presented in this paper could broaden the application of the cell mapping approach of Ref. 1 to a wider class of engineering problems.     

Generalized quasilinearization method for reaction-diffusion equations under nonlinear and nonlocal flux conditions

In this paper we consider an initial boundary value problem for a reaction-diffusion equation under nonlinear and nonlocal Robin type boundary condition. Assuming the existence of an ordered pair of upper and lower solutions we establish a generalized quasilinearization method for the problem under consideration whose characteristic feature consists in the construction of monotone sequences converging to the unique solution within the interval of upper and lower solutions, and whose convergence rate is quadratic. Thus this method provides an efficient iteration technique that produces not only improved approximations due to the monotonicity of its iterates, but yields also a measure of the convergence rate.     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Asymptotics of estimates in constrained nonlinear regression with long-range dependent innovations

The purpose of this paper is to investigate the asymptotic properties of the least squares estimates (L ₂-estimates) and the least absolute deviation estimates (L ₁-estimates) of the parameters of a nonlinear regression model subject to a set of equality and inequality restrictions, which has a long-range dependent stationary process as its stochastic errors. Then we will compare the asymptotic relative efficiencies of the above estimators.