Numerical Integration of Differential Algebraic Systems and Invariant Manifolds

The dynamics of a differential algebraic equation takes place on a lower dimensional manifold in phase space. Applying a numerical integration scheme, it is natural to ask if and how this geometric property is preserved by the discrete dynamical system. In the index-1 case answers to this question are obtained from the singularly perturbed case treated by Nipp and Stoffer, Numer. Math. 70 (1995), 245–257, for Runge-Kutta methods and in K. Nipp and D. Stoffer, Numer. Math. 74 (1996), 305–323, for linear multistep methods. As main result of this paper it is shown that also for Runge-Kutta methods and linear multistep methods applied to a index-2 problem of Hessenberg form there is a (attractive) invariant manifold for the discrete dynamical system and this manifold is close to the manifold of the differential algebraic equation.     

Criterion for uniform invertibility of families of strong approximations to one-dimensional singular integral operators with continuous coefficients

A criterion is obtained for the applicability of the approximation method based on strongly approximating operator families converging to a one-dimensional singular integral operator with coefficients continuous in the circle. Some special cases are considered. Translated fromMatematischeskie Zametki, Vol. 62, No. 3, pp. 430–439, September, 1997. Translated by A. M. Chebotarev     

On certain spectral properties of a quadratic self-adjoint matrix pencil with dominating main diagonals

Sufficient conditions for the “separation of the spectrum” of a quadratic matrix pencil with self-adjoint coefficients are found. A criterion for the representability of a positive operator in a finite-dimensional space in the form of a matrix with dominating main diagonal in each orthonormal basis is obtained. Translated fromMatematicheskie Zametki, Vol. 61, No. 3, pp. 381–390, March, 1997. Translated by A. I. Shtern     

微分流形上的变换群

本文主要讨论如何把仿射Ｋｉｌｌｉｎｇ向量场、共形Ｋｉｌｌｉｎｇ向量场和射影Ｋｉｌｌｉｎｇ向量场推广成为四种张量场．我们得到了仿射Ｋｉｌｌｉｎｇｐ（≥１）形式和射影Ｋｉｌｌｉｎｇｐ（≥１）形式的多种定义，文献［１］中的定义仅是其中之一．     

Partial decay on simple manifolds

Existence, uniqueness and weighted regularity of solutions of linear and nonlinear second-order uniformly elliptic differential equations on complete punctured compact N-manifolds, N > 2. Application to prescribed curvature problems: scalar curvature in a quasi-isometry class (including a contribution to the Lichnérowicz-York equation of General Relativity); Ricci curvature in a weighted Kähler class (with a related result in equiaffine geometry). A new asymptonic behaviour is allowed throughout, called partial decay, which requires its own maximum principle.Current support: CNRS; partial support; CEE contract GADGET # SC1-0105-C.     

Eberlein mulian定理在局部凸空间中的推广

设（Ｅ，Ｔ）是一个分离的局部凸空间．本文主要结果是：（１）如果（Ｅ，Ｔ）是次可分的，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．（２）如果（Ｅ，Ｔ）是强次可分且（Ｅ，β（Ｅ，Ｅ））是桶型空间，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．     

一个新型电子直线加速器的预制研究

文中给出了对一个新型紧凑的电子直线加速器(linac)证明原理的研究结果.在该linac中,通过偏转磁场选择特定能量和相位的大功率速调管用毕束流,然后将它们注入到加速节中,同时使速调管工作在自激振荡状态,使传统linac上的许多部件都可以省去.据此建成的linac的结构简单、维护容易、性能良好、造价经济.因此实现这种具有众多优点的新型linac将有助于linac应用的推广.要实现这样的linac有许多关键的问题需要解决.电子束团的性能参量,如能量、电流、发射度,以及速调管自激振荡的频率稳定度等都必须符合加速的要求.文中给出的计算机模拟和实验结果都表明了实现这种新型的linac的可行性     

加权Dirichlet空间Dφ^2上的复合算子

设D是复平面中单位圆盘，φ：D→R是一个次调和函数，Dφ^2是D上的加权Dirichlet空间．对某类次调和函数φ文章研究了Dφ^2上的复合算子Cφ，分别得到了Cφ为Dφ^2上的有界、紧、Schatten p-类算子的特征．