并向量展开

Based on the analogy of structural mechanics and optimal contro1, and a1so based on carrying the minimum potential energy variational principle in elastici- ty to the generalized one, the theory of Hami1tonian system can be introduced into theory of e1asticity and e11iptic PDE. The transverse eigensolutions of the Hamiltonian operator matrix and its expansion solution method can be deduced.

利用结构力学与最优控制相模拟的理论，将弹性力学势能变分原理导向部分一般变分原理，并将哈密尔顿体系的理论引入到弹性力学与椭圆型偏微分方程之中，导出一套横向哈密尔顿算子矩阵的本征函数向量展开解法。

It is also the base of structure optimization.According to main object characteristics of structural dynamics design,structuraleigenveetor sensitivity computation is,first,be studied.A Neumann series expansionmethod is proposed in accordance with the modal method and is developed to agreewith the structure with rigid body modes.A rapid Neumann series expansion methodfor eigenvector sensitivity is formed;it may greatly improve the efficiency ofcomputing eigenvector derivation.

本文根据结构动力学设计的主要目标特性，首先进行了结构特征向量灵敏度分析研究：形成了计算特征向量灵敏度的Neumann级数展开法，并将其扩展到适用于具有刚体模态的结构特征向量灵敏度分析；研究出计算特征向量灵敏度的快速Neumann级数展开法，该方法大大提高了特征向量灵敏度分析的效率；建立了无需K-1运算的结构特征向量灵敏度分析的共轭梯度迭代法。

Firstly, the digital watermarking was transformed randomly, and then encrypted by chaos. The encrypted watermarking was transformed to one-dimensional row vector, and the pixel value was sorted. The coefficient of primitive image of stationary wavelet transformation was expanded to one-dimensional row vector, too, and then the sorted watermarking was embedded to the sorted low frequency and turned to two dimensions.

本算法先将数字水印图像进行置乱变换，然后将置乱后的水印图像进行混沌加密，将加密后的水印按行展开成一维行向量，并将像素值从大到小排序，将原始图像平稳小波分解得到的低频系数也按行展开成一维行向量，并按从大到小排序。

After illustrating the conception pseudo-symplectry ,the evolvement and extension of the conception symplectry and the formation of pseudo-symplectic space ,the nature of pseudo-symplectic space and the inner relationship and differences between pseudo-symplectic space and symplectic space are reflected here.

通过对辛空间的深入分析和研究，从空间中的度量与向量的迷向性问题入手并展开较为详细的讨论，定义"伪辛"的概念，阐述"辛"概念的演变、扩充与伪辛空间生成的事实，进而揭示伪辛空间的本质属性及其与辛空间的内在联系与区别。

In SMFSIA/CAG, to increase computational efficiency in solving the matrix equation, both the speed of the iterative convergence and the matrix-vector multiplication are picked up based on iterative theory. The extended formula of the high order Taylor's series about the horizontal distance is derived. The relationship between the Taylor's series or the neighborhood distance and the efficiency of the arithmetic are analyzed.

在SMFSIA/CAG中，基于迭代法的原理，通过加快迭代收敛速度和加速矩阵向量积两个方面对该算法进行了改进，推导了关于平面展开的高阶泰勒级数展开公式，并对近场相关距离和泰勒级数展开阶数对算法效率的影响进行了分析。

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。