算子域

The controller makes the closed-loop systems internally stable and minimizes the H2 norm of the transfer matrix Tzw from w to z. Two Riccati formulae based on 8 operator is deduced. The H2 problems for continuous time systems, Z operator models and 8 operator models are investigated respectively.The guaranteed cost control problem of robust stabilization and robust performance for uncertain systems which is described by 8 operator is discussed in this paper.

采用Riccati方程处理方法讨论了基于Delta算子描述下的离散系统存在输出反馈控制器的问题，得到了两个基于Delta算子的Riccati方程，设计了Delta域的输出反馈控制器，使得闭环系统内稳定，且满足从w到z的传递矩阵T_的H_2范数最小，设计了基于Delta算子描述下的离散系统的最优控制器，并与S域和Z域的H_2控制器进行了比较。

In order to solve the problem,We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential manifold. The travel time are expressed as polynomials of the horizontal offset between the two points, and the single-square-root operator in frequency-wavenumber domain are expressed as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddle-point method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量(地面点到地下相点的水平距离)的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

In order to solve the problem, We proposed a simple formula for computing paraxial travel time of single-way wave operator. The formula is based on the forward and inverse transform between time-space domain to frequency-wavenumber domain and from vector field to exponential as polynomials of wavenumber. Coefficients of travel time polynomials and that of single-square-root operator are related each other and calculated by Lie algebraic integrand, exponential map and the saddlepoint method.

针对此，基于时间空间域到频率波数域和向量场到指数流形上的正反变换，提出了计算单程波算子旁轴走时的简便公式，将走时表示成空间变量（地面点到地下相点的水平距离）的多项式，将频率波数域单平方根算子表示成波数的多项式，运用Lie代数积分、指数映射和鞍点法将走时多项式的系数与单平方根算子的系数联系起来，运用单平方根算子的系数计算走时多项式的系数。

In this paper,we build symplectic structure of 2-nd order and high order singular differential operators on infinite interval, we construct a symplectic space by the maximal and minimal operator domain .

本文研究了无穷区间上二阶、高阶奇型微分算子的辛结构，利用最大与最小算子域构造了一个辛空间，用辛空间中的线性流形来刻画定义在无穷区间上二阶、高阶奇型对称微分算子的自共轭扩张问题。

Eliminating the restriction of the characteristic of field ,the forms of invertible linear operator preserving inverses of matrices over full matrix space with at least four elements are described.

去掉了域的特征限制，刻画了至少包含4个元素的任意域 F上的全矩阵空间Mn的保逆的可逆线性算子形式。利用保幂等的结论证明了f为Mn上保持逆矩阵的可逆线性算子当且仅当存在P∈GLn，使得f=εPAP-1，A∈Mn，ε=±1∈F；或者存在P∈GLn，使得f=εPATP-1，A∈Mn，ε=±1∈F

Author, secondly, starts from the approximate expandness of square root operator, perform mathematical calculations for finite difference operator in frequency-space domain, Fourier finite difference operator in mixing domain(frequency-space and frequency-wavenumber domain) and general screen operator in mixing domain, compare and discuss their precision of their wavefield, adaptability for lateral velocity variations, computation efficiency and stability.

第二，从平方根算子的近似展开出发对频率—空间域的有限差分算子、混合域(频率—空间域；频率—波数域)的Fourier有限差分算子、混合域的广义屏算子进行了推导并对其波场描述精度、对横向变速的适应性、计算效率和稳定性进行了比较与评述。

By constructing different quotient spaces,using the method of symplectic geometry,the self-adjoint extensions of symmetric differential operators in the direct sum spaces for the different deficiency indices at(2,2)singular points was discussed. The classification and description of complete Lagrangian submanifold that correspond with self-adjoint domains of second order differential operators were given.

由于对称微分算子在端点处的亏指数取值情况不同，当微分算子在端点处的亏指数均取(2， 2)时，通过构造商空间，应用辛几何的方法讨论了直和空间的对称微分算子的自共轭扩张问题，并给出了与二阶微分算子自共轭域相对应的完全Lagrangian子流型的分类与描述。

For an abitrary set X, appropriate order relations on WCL (the set of all weak closure operators), WIN (the set of all weak interior operators), WOU (the set of all weak exterior operators), WB (the set of all weak boundary operators), WD (the set of all weak derived operators), WD*(the set of all weak difference derived operators), WR (the set of all weak remote neighborhood system operators) and WN (the set of all weak neighborhood system operators) can be defined respectively, which make WCL, WIN, WOU, WB, WD, WD*, WR and WN to be complete lattices that are ismorphic to CS(X,CS is the set of all closure systems on X.

证明了可以在WCL(X上的弱闭包算子的全体)、 WIN(X上的弱内部算子的全体)、 WOU (X上的弱外部算子的全体)、 WB (X上的弱边界算子的全体)、WD、 WD*(X上的弱差导算子的全体)、 WR(X上的弱远域系算子的全体)和WN(X上的弱邻域系算子的全体)上定义适当的序关系，使它们成为与CS(X，〖JX-*5[JX*5]同构的完备格其中CS(X是给定集合X上的闭包系统的全体。

In theory, it can be realized by frequency-wavenumber domain expression and transform from wavenumber domain to space domain.

大步长单程波算子是穿过厚层的单程波算子的积分，在理论上它可以通过频率波数域表达式和波数域到空间域变换来实现。

With phase shift plus correction, the wavefield extrapolation operator is implemented using FFT in spatial and wavenumber domains.

波场延拓算子通过相移算子加校正的方法，利用快速Fourier变换在空间域和波数域予以实现。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了