条件表达式

Based on the method of matrix transformation used in the compound material mechanics, the anisotropic flexibility matrix of the anisotropic sand with a certain stress state is transformed to be an isotopic one of a certain isotropic reference material with the corresponding stress state, and a corresponding stress matrix is obtained simultaneously.

借鉴复合材料力学中矩阵转换的数学方法，将各向异性砂样的柔度矩阵转化为各向同性等效参考砂的柔度矩阵，同时导出与其相当的应力状态的表达式，以使对各向异性岩土材料的分析可转换为对各向同性状态进行分析，由此可将以前基于各向同性假设的强度条件能够用于各向异性土体。

A Special Maximum Likelihood method for building mathematical models in dynamic calibration is proposed, which is a kind of maximum likelihood method with a special noise model.

提出了误差估计表达式以及在带宽有限测量假设条件下，辨识离散时间模型时，采样频率的选择与模型辨识误差的关系。

The interpolate algorithms of three-order NURBS curve and double three-orders NURBS surface are presented. The expressions of partial derivative and normal curvature of NURBS surface are derived by the theory of differential geometry. The geometric characteristics of different curvature area of the free-form surfaces are analyzed in detail. All these work lays a theoretical foundation for constructing the cutter location calculating model of free-form surfaces NC machining. 2 On the basis of analyzing the methods of cutter path generation, the standard of evaluating the various methods of cutter path generation is presented. The method of generating cutter path with constant scallop height is presented for the first time.

本文以提高复杂曲面多坐标数控加工精度和加工效率为目的，在对国内外研究现状进行深入分析的基础上，对数控编程中各环节的关键技术问题进行了深入研究，主要内容包括以下几方面： 1 分析了复杂曲面各种造型方法的优缺点，给出了根据各种边界条件所确定自由曲面的NURBS表示方法以及三次NURBS曲线曲面反算算法；用微分几何理论推导了NURBS曲面的偏导矢及法曲率计算表达式；对曲面不同曲率特性区域的几何特征进行了深入分析，为建立复杂曲面的数控加工刀位计算模型奠定了理论基础。

If variables are subjected to normal distribution, an adjusted expression is obtained, which can improve our precision.

同时，在假设连接的分布满足正态分布条件下，给出了Large-Deviation理论分析结果的修正表达式，提高了分析的精度。

All is done in the mapping plane about the developed plane of acylindrical shell.Furthermore,applied orthogonal function expansion technique,the problem can be finally summarized into the solution of a series of infinitealgebraic equations.

在第四章中，在保角映射平面上给出了大开孔圆柱壳在外部载荷作用下，广义内力、边界条件以及孔边应力集中系数的一般表达式。

The transformation between coordinates of light wave and coordinates of polarimeter was determined by Euler's angles. The direction of vibration passed by polarimeter and its value was studied.

利用欧拉角表示光波坐标系和偏振器坐标系之间的变换，得到透过偏振器后偏振光的振动方向及其大小的数学表述，给出了简化表达式及其使用条件。

Based on the variational principle of virtual voltage and virtual displacement derived in this thesis and the classical theory of linear laminated plates, and by using the constitutive equations of elastic piezoelectric materials, and the DKQ quadrilateral plate bending element, the finite element modeling for the fabric reinforced laminated plates with nonlinear voltage-electric strain relationship of piezoelectric actuators has been established for the first time in this thesis. And the expressions for the electric loadings with obvious mechanical meaning and convenient for computation are established, which can be used to the deformation analysis of laminated plates with piezoelectric actuators under specified voltages.

以本文直接导出的压电结构的虚电势—虚位移变分原理为基础，依据经典线性层合板理论和压电弹性体的本构方程，采用基于离散法线假设的DKQ四结点任意四边形薄板弯曲单元，首次建立了考虑非线性电压—电应变关系的含压电致动器的纤维增强型层合板的有限元分析模型，并推导建立了力学意义明确、便于计算的电荷载表达式，可用于指定电压条件下纤维增强型叠层合成板的变形分析。

Following the latter idea, a general form of scalar eddy viscosity models is derived in this paper by introducing two hypotheses. Meanwhile, the realizability of this kind of models is discussed too.

本文遵循后一种思想，在引入两个假设后，推导出标量涡粘性模型雷诺应力的一般表达式，并讨论了其可实现性条件。

Based on up_ and down_going wave decomposition and elastic wave power reciprocity theorem, this paper derives, in the lateral velocity varying case, linear prediction operators expression and the generalized spectral factorization equation for reflection dataset.

本文基于上下行波分解及弹性波互易定理，导出横向变速介质条件下线性预测算子的表达式和反射数据的广义谱分解方程。

As the orientation of optical axis is arbitrary, the polarization states and the amplitudes of the o ray and e ray and the refracted ray were given, and the theoretical expressions of the reflectivity and the transmissivity representing energy relations between the rays were obtained, which provide a theoretical basis for developing and applying crystal devices.

在晶体光轴取向任意的条件下，给出了反射的o光、e光以及折射光的偏振状态和振幅以及表明各光束间能量关系的折射率和反射率的理论表达式，为晶体器件特性的研究提供了有力的理论工具。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。