有限维的

Dahlquist,Butcher,Burrage and Frank et.al.established early or late B-theory of Runge-Kutta methodsfor stiff problems in Euclidean space with finite dimensions.Afterward,Shoufu Li et.al.extended this theory to general linear methods and stiff problems in Hilbert space andfurther established B-theory of general multivalue methods in Banach space.

Dahlquist、Butcher、Burrage及Frank等人先后建立了有限维空间中刚性问题Runge-Kutta方法的B-理论；李寿佛等人将该理论推广到一般多值方法和Hilbert空间中的刚性问题，进而建立了Banach空间中刚性问题一般多值方法的B-理论。

A relative Szego projection is defined in the space of small deformations of 3-d CR structures of finite type, which is Fredholm. We also prove an index theorem, in whose proof we actually have the asymptotic expansion of the Szego kernel.

在三维有限型的CR结构的小形变空间上定义了相对Szego投影算子，并证明了相对Szego投影算子是Fredholm算子和相应的指标定理。

The problem that under what conditions the - resolvent operator of a maximal TJ - monotone set-valued mapping is a Lipschitz continuous single-valued mapping on whole space, which also answers the open problem mentioned above, is studied on finite dimensional Euclidean spaces.

借助于图收敛理论证明了有限维欧氏空间中的两个极大单调集值映射的和映射在较弱条件下仍是极大单调集值映射，并在此基础上讨论了一般集值变分包含问题解集的凸性、闭性和有界性。

Based on the three- dimensional coupled wave theory, the theory of diffraction of local volume holographic grating s recorded with arbitrary polarization plane waves is studied.

基于三维耦合波理论，研究了两束有限宽度的任意偏振平面波干涉产生的局域体全息光栅的衍射问题。

The Kolmogorov extension proceeds along the following lines: assuming that a probability measure on the space of all functions exists, then it can be used to specify the joint probability distribution of finite-dimensional random variables .

收益的Kolmogorov延长其内容大致如下：假设概率测度空间上存在的所有功能，那么它可以用来指定联合概率分布的有限维随机变量。

The notion of - resolvent operator of set-valued mappings is introduced.

利用η-预解算子在有限维空间中探讨了集值混合拟类变分不等式问题和广义集值变分包含问题存在唯一解的条件；利用分析的方法在实Hilbert空间中讨论了集值混合拟类变分不等式问题解集的非空性。

The existence condition of first and second boundary variation was given with boundary variation method. The numerical method was obtained.

应用测度理论，将经典的变分问题，利用线性分析的方法转化为在几个Randon测度空间中寻找最优测度的有限维线性优化问题；从而得到最优控制律。

The necessary condition for the equation to has a positive solution is that the norm,spectral radius,radius of numerical range of A and Q satisfy some conditions.

近年来，形如X+A*X-2A=Q的矩阵方程受到了国内外许多学者的关注，并在有限维希耳伯特空间中得到了一些相应的结论[1~3]。

In Chapter 2, for a prime p as 4κ+1, we represent the finite field of order p as a sublattice of Gaussian integers concretely.

在第二章中，具体考虑对形如4κ+1的素数p，给出了阶为p的有限域的二维高斯整数表示。

In Chapter 3, for a prime p as 6κ+1, we represent the finite field of order p as a sublattice of Eisenstein integers concretely.

在第三章中，具体考虑对形如6κ+1的素数p，给出了阶为p的有限域的二维Eisentein整数表示。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。