A note on minimization problems and multistep methods

Summary. We use the qualitative properties of the solution flow of the gradient equation to compute a local minimum of a real-valued function . Under the regularity assumption of all equilibria we show a convergence result for bounded trajectories of a consistent, strictly stable linear multistep method applied to the gradient equation. Moreover, we compare the asymptotic features of the numerical and the exact solutions as done by Humphries, Stuart (1994) and Schropp (1995) for one-step methods. In the case of -stable formulae this leads to an efficient solver for stiff minimization problems. Received July 10, 1995 / Revised version received June 27, 1996     

Regularity of multiwavelets

The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L _p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields.     

三维流动传热空隙率计算程序FASTOR—3D开发研究

1引言大粘度（大r）和大系数（ss和sc）法是处理流动区域中障碍物的常用方法山。但当流动区域中障碍物数量较多时，宜采用空隙率来模拟障碍物，如模拟反应堆流动传热的商用程序COMMIX［’］。我们根据空隙率模拟的基本概念，针对采用交错网格的压力校正法，自行编制了多障碍物流动传热三维计算的全部源程序代码，应用于某核反应堆钠池流动传热的数值模拟，获得了比较合理的结果。2数学模型和数值方法2．1控制方程空隙率修整的质量、动量、能量及湍流动能与耗散率的守恒方程通式的三维柱坐标形式为其中中一1，。，。，。，T，k，。分别表…     

To the spectral theory of Krein systems

We consider the Krein systems. For the set of Stummel class coefficients, we establish the criterion in terms of these coefficients for the system to satisfy the Szegö-type estimate on the spectral measure.     

用计算机测量PN结的反向物理特性

本对PN结反向物理特性，应用电子技术和计算机技术实现了对实验过程的控制和效据处理。     

Joint extension of two theorems of Kotzig on 3-polytopes

The weight of an edge in a graph is the sum of the degrees of its end-vertices. It is proved that in each 3-polytope there exists either an edge of weight at most 13 for which both incident faces are triangles, or an edge of weight at most 10 which is incident with a triangle, or else an edge of weight at most 8. All the bounds 13, 10, and 8 are sharp and attained independently of each other.