Multicriteria decision making under uncertainty

Formalization for problems of multicriteria decision making under uncertainty is constructed in terms of guaranteed and weak estimates. A relevant definition of the vector maximinimax value is given. Parameterization and approximation of maximum, minimax, and maximinimax values based on the inverse logical convolution are suggested. An application for multicommodity networks is considered. Received: December 13, 2000 / Accepted: August 21, 2001?Published online May 8, 2002     

基于小波变换和数学形态学的运动物体检测

提出了一种基于帧差法和小波变换相结合的运动目标检测方法，充分利用帧差法计算简单和小波变换的多尺度特性。实验表明，这种方法可以有效地从复杂自然场景的图像序列中检测出完整的运动目标。而且能够有效的抑制噪声。同时减少计算时间，满足检测的实时性要求。     

Analytic calculation of scaling dimensions: Tricritical hard squares and critical hard hexagons

The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance.     

Adaptive Algorithm for Constrained Least-Squares Problems

This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.     

Solution of large‐scale weighted least‐squares problems

A sequence of least‐squares problems of the form min_y∥G^1/2(A^T y?h)∥₂, where G is an n×n positive‐definite diagonal weight matrix, and A an m×n (m?n) sparse matrix with some dense columns; has many applications in linear programming, electrical networks, elliptic boundary value problems, and structural analysis. We suggest low‐rank correction preconditioners for such problems, and a mixed solver (a combination of a direct solver and an iterative solver). The numerical results show that our technique for selecting the low‐rank correction matrix is very effective. Copyright © 2002 John Wiley & Sons, Ltd.     

混沌实验数据处理及仿真

大学物理实验中混沌实验大多采用观察现象的方法进行,本实验采用蔡氏电路(Chua s circuit)产生混沌行为.在观察不同初始值条件下出现的倍周期分岔、阵发混沌、奇异吸引子等相图及现象的基础上,通过对采集数据进行处理,对负电阻伏安特性进行分段线性拟合,用功率频谱法、计算机仿真方法(龙格-库塔数值积分法)对混沌现象进行描绘,将实验数据与非线性方程组的数值解相结合,呈现出混沌现象的本质.     

宽带膜厚实时监控过程中膜层折射率的确定方法

为了准确计算出镀膜过程中每层膜的折射率，介绍了实时监控过程中确定膜层折射率的2种方法：一种是由实测的透射比光谱直接反算出膜层的折射率；另一种是用最小二乘法的优化算法实时拟合折射率。试验结果表明：在线反算适合单点监控，所得折射率误差小于2%。然而在实际镀膜过程中,由于宽带内膜层参数误差较大,一般大于25%。为此，采用最小二乘法拟合，即在整个宽光谱范围内采集每个波长点的信息，所得结果误差很小，一般都在2％～5%之间,有时可达到10%,在很大程度上提高了实际镀膜时膜厚监控的精度。     

On completely irreducible operators

Let T be a bounded linear operator on Hilbert space H, M an invariant subspace of T. If there exists another invariant subspace N of T such that H = M + N and M ∩ N = 0, then M is said to be a completely reduced subspace of T. If T has a nontrivial completely reduced subspace, then T is said to be completely reducible; otherwise T is said to be completely irreducible. In the present paper we briefly sum up works on completely irreducible operators that have been done by the Functional Analysis Seminar of Jilin University in the past ten years and more. The paper contains four sections. In section 1 the background of completely irreducible operators is given in detail. Section 2 shows which operator in some well-known classes of operators, for example, weighted shifts, Toeplitz operators, etc., is completely irreducible. In section 3 it is proved that every bounded linear operator on the Hilbert space can be approximated by the finite direct sum of completely irreducible operators. It is clear that a completely irreducible operator is a rather suitable analogue of Jordan blocks in L(H), the set of all bounded linear operators on Hilbert space H. In section 4 several questions concerning completely irreducible operators are discussed and it is shown that some properties of completely irreducible operators are different from properties of unicellular operators. __________ Translated from Acta Sci. Nat. Univ. Jilin, 1992, (4): 20–29     

Extremes of deterministic sub‐sampled moving averages with heavy‐tailed innovations

Let {X_k}_k?1 be a strictly stationary time series. For a strictly increasing sampling function g:?→? define Y_k=X_g(k) as the deterministic sub‐sampled time series. In this paper, the extreme value theory of {Y_k} is studied when X_k has representation as a moving average driven by heavy‐tailed innovations. Under mild conditions, convergence results for a sequence of point processes based on {Y_k} are proved and extremal properties of the deterministic sub‐sampled time series are derived. In particular, we obtain the limiting distribution of the maximum and the corresponding extremal index. Copyright © 2003 John Wiley & Sons, Ltd.