Application of modified information criterion to multiple change point problems

The modified information criterion (MIC) is applied to detect multiple change points in a sequence of independent random variables. We find that the method is consistent in selecting the correct model, and the resulting test statistic has a simple limiting distribution. We show that the estimators for locations of change points achieve the best convergence rate, and their limiting distribution can be expressed as a function of a random walk. A simulation is conducted to demonstrate the usefulness of this method by comparing the powers between the MIC and the Schwarz information criterion.     

On functional improper Volterra integral equations and impulsive differential equations in ordered Banach spaces

In this paper we derive existence and comparison results for discontinuous improper functional integral equations of Volterra type in an ordered Banach space which has a regular order cone. For this purpose we prove Dominated and Monotone Convergence Theorems for improper integrals. The obtained results are then applied to first-order impulsive differential equations. Concrete examples are also solved by using symbolic programming.     

Persistence and stability of solutions of Hamilton-Jacobi equations

Given a convergent sequence of Hamiltonians (Hn) and a convergent sequence of initial data (gn) for the first-order evolutionary Hamilton-Jacobi equation, we look for conditions ensuring that the sequences (un) and (vn) of Lax solutions and Hopf solutions respectively converge. The convergences we deal with are variational convergences. We take advantage of several recent results giving criteria for the continuity of usual operations.     

修正的LMS方法

ＢｉｔｍｅａｄＲ．Ｒ和ＡｎｄｅｒｓｏｎＤ．Ｏ在文献［１］中为任意线性方程组的求解提出了一种颇为有效的算法，称为ＬＭＳ方法．文献［２］详细地论述了算法的收敛性，指出收敛极限是方程组的最小二乘解．本文为使解线性方程组的ＬＭＳ算法具有更广泛、更方便的应用性．对文献［２］中的ＬＭＳ算法作了修正．理论和实践证明修正后的算法是成功的．     

Convergence to equilibria in the Lorenz system via monotone methods

In this paper, we provide some parameter values of the Lorenz system for which its flow is monotone with respect to the order induced by quadratic cones. This implies that its attractor is contained in a two-dimensional invariant manifold. An application of Dulac's criterion to the induced flow over that manifold leads to conditions under which every positive semiorbit converges to an equilibrium.     

I-fuzzy拓扑空间中的Moore-Smith收敛

用方进明提出的I-fuzzy拟重邻域系研究I-fuzzy拓扑空间中的Moore-Smith收敛性，给出它的应用，并获得了很多重要结论。     

求解大规模非Hermite线性方程组的Krylov子空间型方法的收敛性分析

本文用统一的方式研究了当系数矩阵Ａ亏损且其谱位于右（左）半开平面时很多求解大规模非Ｈｅｒｍｉｔｅ线性方程组的Ｋｒｙｌｏｖ子空间型方法的收敛性，建立了有关的理论收敛界，揭示了收敛速度和Ａ的谱之间的内在联系．结果证明，当如下三种情形之一出现时，这些方法的收敛速度将会减慢：Ａ亏损，其谱的分布不理想，或Ａ的Ｊｏｒｄａｎ基病态．在证明中，我们给出了Ｃｈｅｂｙｓｈｅｖ多项式的高阶导数在复平面中某椭圆域上的若干新性质，其中之一修正了文献中广泛使用的一个结果．     

解非凸规划问题的一种连续化方法

针对一类非线性规划问题的解存在的新等价性条件，给出了大范围收敛的连续化方法及证明了收敛性的结论．     

可交换随机变量序列的完全收敛性

本文探讨了可交换随机变量的完全收敛性问题，从充性和必要性两方面都作了研究，并把ｉ．ｉ．ｄ．情形下的部分结果作了为特例推出。     

Convergence acceleration of orthogonal series

The aim of this paper is to verify efficiency of two acceleration methods for orthogonal series (more strictly, for series defined at the beginning of Section 1). These methods are quite different although they use the same transform of such a series given there. The first method (Section 3) has some features common with Levin’s and Weniger’s methods. It may be profitably used in numerical calculations for a vast class of series. The second one (Sections 4 and 5) is somewhat similar to the Euler–Knopp transform of power series. Also this method is numerically realizable but more important is that for a narrower class of series, including some ones having applications in physics, it gives explicit analytic formulae of their transform.