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     

Quadratic Functionals with General Boundary Conditions

The purpose of this paper is to give the Reid ``Roundabout Theorem' for quadratic functionals with general boundary conditions. In particular, we describe the so-called coupled point and regularity condition introduced in [16] in terms of Riccati equation solutions. Accepted 27 February 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.     

Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution

Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper bounds on spectral gaps. Received: 10 June 1996 / In revised form: 9 August 1996     

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.     

TMS320C55x嵌入式实时多任务操作系统DSP/BIOSⅡ

DSP／BIOS是运行在数字信号处理器（DSP）中的一个小型韧件，它的软件部件不仅能使开发者实时监测和控制程序执行和程序变量，而且可以对实时多线程系统进行合理的时间规划。文章对DSP／BIOSⅡ的基本特征与应用作了介绍。     

内含低噪声可编程增益放大器的24位∑-Δ模数转换器AD1555/AD1556

美国ADI公司推出的24位∑-Δ模数转换器AD1555/AD1556内含可编程增益放大器,可用于低频、大动态范围的测量,并可实现模拟输入线性输出,AD1555/AD1556有五种不同的增益设定.将AD1555和AD1556数字滤波器/抽样器结合使用可组成高性能的模数转换器,因而可广泛应用于地震数据探测系统和自动测试装置.