ON OPTIMAL BACKWARD PERTURBATION ANALYSIS FOR THE LINEAR SYSTEM WITH BLOCK CYCLIC COEFFICIENT MATRIX

Based on the block style spectral decomposition, this paper deals with the optimal backward perturbation analysis for the linear system with block cyclic coefficient matrix.     

强流直线感应加速器中束流质心横向运动初步计算

 “神龙一号”强流脉冲加速器由72个直线感应加速腔和18个用于测试和真空泵接口的多功能腔组成。直线感应加速器的研制建造中磁轴对中偏差和聚焦磁场的自然偏差所引起的束流质心偏移轨道中心是不可避免的，由于束脉冲期间存在能散，使束流产生Corkscrew运动,导致束流品质变坏。而束脉冲期间的能散只能减小到一定水平，因此必需采取一定的措施抑制Corkscrew幅度的增长。在加速器的安装阶段，脉冲悬丝技术被应用于准直加速段聚焦磁场，并在磁轴准直测试的同时对磁场固有倾斜偏差进行初步校正。根据脉冲悬丝测试所得实验数据，采用传输矩阵法对加速段束质心轨迹进行了初步估计，计算中考虑了各加速腔聚焦磁场的倾斜和偏移误差。给出了计算结果和分析。     

The PDE-preserving operators on nuclearly entire functions of bounded type

The PDE-preserving operators O on the space of nuclearly entire functions of bounded type H_Nb(E) on a Banach space E are characterized. An operator is PDE-preserving when it preserves homogenous solutions to homogeneous convolution equations. We establish a one to one correspondence between O and a set Σ of sequences of entire functionals, i.e. exponential type functions. In this way, algebraic structures on Σ, such as ring structures, can be carried over to O and vice versa. In particular, it follows that O is a non-commutative ring (algebra) with unity with respect to composition and the convolution operators form a commutative subring (subalgebra). We discuss range and kernel properties, for the operators in O, and characterize the projectors (onto polynomial spaces) in O by determining the corresponding elements in Σ. This revised version was published online in June 2006 with corrections to the Cover Date.     

Propagator matrices as matrices of power''s series. II. It''s relationship with HF''s stability problem and alternative solutions

Some non-singlet quasi-instabilities (QIs) cases that arise in the calculation of NMR-J parameters are analyzed within response theory. The relationship between ‘very close to zero’ eigenvalues of the principal propagator and the rate of convergency for specific coupling pathways is shown by a power series implemented to calculate the principal propagator matrix. A natural criterion for the analysis of the stability problem emerges from that series. This is more general and accurate compared with previous proposals. Its relationship with π-type molecular orbitals is given. We present an alternative scheme to minimize the effects of non-singlet QIs in such a way that the NMR-J parameters become close to the best theoretical calculations for H₂CX (X=CH₂, NH and O).     

利用计算机辅助装调检测矩形大口径离轴非球面的方法研究

通过非球面的零位补偿法,完成了对矩形大口径离轴非球面镜的检测。先用光学设计软件Zemax从理论上分析了在检测中会出现的现象,并结合计算机辅助装调技术,确定在检测过程中相对敏感的自由度,然后控制这些量,使补偿器和非球面的相对关系与理论设计相吻合,在Zygo相位干涉仪上测得最终结果。在λ=632.8nm时,中心圆口径与两个边缘圆口径面形误差RMS分别为0.022λ,0.037λ,0.032λ。检测结果,达到预期目的。     

Universality and summability of trigonometric polynomials and trigonometric series

Periodica Mathematica Hungarica -     

“矩阵有理插值及其误差公式”一文的注

本文对文[1]中所给出的错误的误差公式做了修订,并给出了相应的证明。     

The Ring of Invariants of Three (3 × 3)-Matrices over a Field of Prime Characteristic

We find a minimal system of generators and a homogeneous system of parameters for the algebra of invariants of three matrices of third order over a field of an arbitrary characteristic.     

Hochschild Cohomologies of the Algebra of Smooth Functions

Based on the previously developed technique using the Laplace transformation of distributions with compact support, we calculate the Hochschild cohomologies of the algebra of smooth functions on a finite-dimensional real vector space with coefficients in the adjoint representation.