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The stochastic expansions given here depend only on the independent normal random variables and curvature arrays, therefore they are easy to understand and to deal with.

f'(0)一f(二'，0)。二'为已知的自变量，相应的因变量和随机误差为y'和。'，0为p维未知参数，其参数空间为R中的子集习。在约束方程(2)中，甲(0)为k维向量k

The numerical techniques developed here, including the high accuracy method of using expansions in orthogonal functions in normal direction and the effective algebraic mapping to deal with the problem of infinite region, can raise the calculation precision and the convergence velocity greatly.

文中所发展的方法，如，在法向上采用高精度的高阶谱方法和对无限区域数值问题的更为有效的代数变换处理等，提高了计算精度和收敛速度；同时，通过预估校正迭代法，使抛物化稳定性方程中重要的正规化条件得到满足，保证了数值计算的稳定。

The asymptotic expansions for orthotropic plates in plane strain are given up to some constant coefficients to be determined.

给出正交异性板的平面应变渐近展开的具体列式，仅有一些常数待定。

The 20th century witnessed two great HE expansions in the Western countries, and various interpretations of the HE expansion, among which overeducation and mass higher education were two mainstream theories.

摘 要：20世纪西方高等教育经历的两次较大扩张导致了多种阐释扩张的理论，教育过度说与大众高等教育说是其中主要两种。

Then, base on the equivalent circuit model for cascaded coupled resonator filter, the method for measuring or computing the phase of the reflection coefficient of short-circuit terminated networks and synthesizeing all the inter-resonator couplings and resonant frequencies of the filters to be tuned is studied intensively. The phase loading effect is removed and the tuning steps are analyzed. The method based on the partial fraction expansions of admittance matrix is used to synthesize coupling matrix of the filters under tuning.

然后，通过分析级联耦合滤波器的等效电路模型，着重研究了利用测量或计算终端短路网络的反射参数的相位来综合出待调级联耦合滤波器各个腔体的谐振频率和腔体间的耦合系数的方法，并且消除了端口相位加载的影响，给出了具体的调试步骤；接着利用导纳矩阵部分分式的展开来求得待调滤波器耦合矩阵，着重研究了消除端口相位加载的方法。

Furthermore, we also consider two types of foreign expansions, where the first one is physical expansion by setting up new branches by foreign banks and the second one is financial expansion, including increasing invested capital, asset, deposit, loan, revenue and personnel expenses.

本文外国银行海外扩张的代理变数可分成二类，第一类为实体分支机构的扩张，第二类为财务面的扩张，包括银行资本、资产、存放款、营业收入与人事费用。

The hypotheses were tested using ordinal probit analysis and data on 2,159 expansions of 25 companies over a period of more than three decades.

我们使用序数概率单位分析和25家公司在三十多年中2159次扩张的数据来检验假设。

The computational formula of the gradient matrix in subspace is obtained by applying Taylor series expansions, decomposition theorem of space and projective theorem (The gradient matrixs in different subspace are different).

利用子空间上的泰勒展式、空间分解定理以及投影定理得到了子空间上梯度矩阵的计算公式(不同的子空间，梯度矩阵是不相同的)。

In Chapter 4 and Chapter 5, we discuss the quadratic finite element space with Regular mesh and the one with Criss-Cross mesh. We can respectively obtain the finite element asymptotic expansions and extrapolations in these situations. The high accuracy combination formulas are constructed.

在本文的第四、五章中，我们将在第二、三章中所使用的方法分别推广到Regular网格与Criss-Cross网格下的二次有限元空间中，得到了这两种情形下的有限元的渐近展式与外推结果，并构造出了相应的高精度组合公式。

This is achieved by avoiding changes in metal flow direction and large expansions or contractions of runner cross sectional area.

这能通过避免金属流动的方向改变和避免过大加大或缩小横截面积来达到。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。