正交极

Based on conditions on the conjugate quadrature filters constructing the orthogonal scaling function and wavelet, the orthogonal conditions were designed as an objective function which was minimized by the parameter optimization in the parameterized formula of complex conjugate quadrature filters. The compact support, symmetry, quasi-orthogonal filters and wavelets were obtained.

从构建正交尺度函数与小波的共轭正交滤波器的条件出发，把滤波器的正交条件设计成目标函数，利用共轭正交复滤波器的参数化算式进行参数优化使目标函数极小，得到紧支、对称、准正交的滤波器及其小波。

Polar decomposition of deformation gradient in three dimensional states is often rather difficult, although it has already been solved success fully for plane problems. It is a commonly used technique to obtain the solutions through Cayley-Hamilton formula and three invariables of U. The paper introduces a nonlinear elimination method by use of orthogonal matrix's property, and gives a computation formula for polar decomposition.

变形梯度的极分解在平面问题中得到了很好解决，在三维空间问题中一直认为是相当困难，利用Cayley-Hamilton公式和U的三个不变量求解是目前普遍采用的方法，文章利用正交矩阵的特性，介绍了非线性逐次消除的方法，给出了右极分解的计算式。

The system parameters are determined by optimizing an output-error cost function. To deal with the non-uniqueness of the fully parameterized state-space system, a projected gradient search algorithm is presented by restricting the update of the parameters to the tangent space to the manifold of observationally equivalent state-space systems. The sufficient condition to employ L-M algorithm for optimizing parameters is also introduced. The proposed hierarchical optimization identificationmethod includes two steps: First, the parameter search direction is determined by the proposed adaptive L-M projected gradient approach; Second, the optimum step size is computed according to a line search method.

通过极小化输出误差目标函数获得了系统参数估计；提出了正交梯度搜索方法用于解决系统参数的非唯一性问题，正交梯度搜索的本质是在输入-输出等价类相切平面的正交垂空间更新系统参数；给出了用 L-M 算法进行参数优化的充分条件；提出的系统参数递阶优化辨识方法包括两步：首先用给出的自适应 L-M 算子正交梯度方法确定参数优化方向；其次由一维搜索方法计算最佳步长。

Combining the experimental results and theoretical analysis, the following work has been accomplished.(1) Reasons of the decrease of interelectrode capacitance and the increase of discharge gap caused by the powder suspended in dielectric fluid are explained. And the mechanism that surface quality of workpiece improved by powder-mixed EDM is analyzed from this viewpoint.(2) The variation regularity of the percentage of silicon on the machined surface of workpiece has been summarized according to the experiment results when silicon powder was added into the working fluid. The entropy is introduced to explain the reasons for this variation regularity by thermodynamics.(3) The dimensional accuracy is greatly influenced by the overcut resulting from discharge gap and electrode wear in practice application. Empirical formulas for the overcut in EDM and powder-mixed EDM are established based on the experimental results using the ternary linear regressive method in this paper.(4) The influence of main factors on the machined surface characteristics has been evaluated based on the orthogonal experimental design method.

通过一系列普通电火花加工与混粉电火花加工的对比实验，运用工艺实验和理论分析相结合的方法，重点做了以下工作：(1)探讨了粉末颗粒导致极间电容减小、放电间隙增大的原因，并从这个角度解释了混粉电火花加工可以改善工件表面质量的机理；(2)以混合硅粉的电火花加工为例，实验得出峰值电流和脉冲宽度对加工表面层成分中硅元素含量的影响规律，并引入熵的概念从热力学的角度对硅元素含量变化的原因寻找了理论依据；(3)在实际加工中，由于粉末的加入使放电间隙变大，这使得混粉电火花加工的尺寸精度难以控制，本文利用三元线性回归的方法，在实验数据的基础上，建立了两种电火花加工过切量的计算公式；(4)将正交试验法应用于混粉电火花加工实验研究，并通过对实验指标极差的直观分析，得出各电参数对加工指标影响的敏感程度。

This invention relates to MIMO test method in a multi-user MIMO radio communication system including: estimating the channel matrixes of all users at the base station, computing an orthogonal projecting matrix M of the interference matrix of each user and transmitting M to each user periodically, receiving data sent by the base station at the user end and getting the orthogonal projecting matrix M from the received data, transforming the MIMO test of a desired user to the minimum value of a K-element secondary convex function, in which, K expresses the number of sending antennas and getting estimation of the test data by a ball test method.

一种多用户多输入多输出无线通信系统中的MIMO检测方法，包括步骤：在基站估计所有用户的信道矩阵；计算每个用户的干扰用户矩阵的正交投影矩阵M，并将每个用户的正交投影矩阵M定期发送给每个用户；在用户端接收基站发送的数据，并从接收的数据中得到正交投影矩阵M；利用正交投影矩阵M将期望用户的MIMO检测转化为K元二次凸函数的极小值，其中K表示对期望用户而言，发送天线的个数；利用球检测的方法，得到检测数据的估计。

Exive least-squares solutions, antire?exive least-squares solutions, bisymmetric least-squaressolutions, symmetric and antipersymmetric least-squares solutions, symmetric or-thogonal symmetric least-squares solutions, symmetric orthogonal antisymmetricleast-squares solutions and their optimal approximation to the linear matrix equa-tion AX = B, and solve them successfully. 2. For Problem II, we can convert it to another problem of finding the least-squares solutions with the least norm of a new consistent matrix equation. Onthe base of the solutions of Problem I we can apply the iterative method to get

本文所构造的迭代法的优点在于先利用法方程变换将求矩阵方程的最小二乘解转化为求一个相容矩阵方程的解的问题，再利用迭代法对于任意给定的初始矩阵进行迭代，均可在有限步内迭代出所求问题的一个解；可将问题II转化为求新方程的极小范数解的问题，同样用迭代法求解，从而系统且全面地解决了问题I、II在约束矩阵类如中心对称、中心反对称、自反矩阵、反自反矩阵、双对称、对称次反对称、对称正交对称、对称正交反对称矩阵中的最小二乘解及其最佳逼近问题。

Finally, some limitations of Krylov subspace methods and some potential improvements to this type of methods are furtherly presented.

计算结果表明本文的预处理GMRES方法优于目前使用较多的预处理正交极小化ORTHMIN方法，最后还讨论了投影类方法的局限和今后的可能发展方向。

A new method named HOMGA is proposed to improve the ability of GA, which is the combination of micro-GA, orthogonal design and Solis-Wets, moreover the substructural identification is also used.

本文提出将微遗传算法、改进的正交交叉算子和多变量Solis-Wets局部搜索算法结合，组成混合正交微遗传算法，并进一步应用子结构法，降低问题求解的规模，减少计算中陷入局部极小点的可能。

The effects of compositions on UV prinking ink,such as prepolymer,monomer,photoinitiator and pigment on curing rate,cohesive force,resistency and other properties were investigated. The range analysis and variance analysis method were applied to the assessment of results. The results based on orthogonal experiment design indicated that an optimum component composition of UV printing ink can be obtained from prepolymer PQ611,monomer A,photoinitiator B and active amime.

摘 要：探讨了预聚物、单体、光引发剂、颜料等组分对UV油墨固化速度、附着力、耐抗性等性能的影响，应用正交实验设计方法对UV油墨各组分种类进行选择，对正交试验结果做极差分析及方差分析，结果表明：根据预先设计的组分比例，采用预聚物PQ611，单体A，光引发剂B，活性氨为加速剂，获得性能较好的UV油墨。

Of 12 tomato lines, the analysis on the 4 fruit nourishment quality traits (the contents of vitamin C, total soluble solids and dry matter and ratio of sugar-acid ) was carried out to study the four kinds of disparities, which included the interspecific one, the one between two varieties in the same species , the one between the lines bred by different means in the same variety ,and the one between the different fruit-shaped lines in the same variety .The analytic method of orthogonal comparison of single degree of freedom was applied. The results showed that the line of Lycopersicum pimpinellifolium was better than the average of the lines of L.esculentum in the 4 traits at significant level of 1%, the average of the lines of var.cerasiforme was better than the average of the lines of var.vulgare in the 4 traits at significant level of 5% or 1%,and the two space mutation line(YH02-2 or YH02-6) was better than the average of the other lines of the same variation in the 4 trait, respectively, at significant level of 1%. Of the lines of var.cerasiforme , the lines with pear fruit were lower than the average of the lines with round-shaped or plum-shaped fruits in the 2traits(the contents of vitamin C and total soluble solids), at significant level of 1%,the lines with plum-shaped fruits were higher than the average of the lines with round-shaped fruits, at significant level of 1%,and the lines with yellow-colored fruits(YH02-11) was lower than the average of the lines with red-colored fruits(YH02-1and YH02-7) in the trait of the contents of vitamin C.

对12个品系进行种间、种内变种间、变种内不同选育方式间、变种内不同果实形状间在果实营养品质（果实维生素C含量、可溶性固形物含量、干物质含量和糖酸比）上的差异进行分析，采用统计学上单一自由度正交比较分析法与植物学分类相结合的方法进行分析，结果表明：醋栗番茄种品系YH02-12在4个营养品质性状上，极显著高于普通番茄种品系；樱桃番茄变种品系在4个营养品质性状上的平均水平极显著或显著高于普通番茄变种品系的平均水平；2个空间诱变品系YH02-2、YH02-6在4个营养品质性状上均极显著高于同变种的其他品系的平均水平；樱桃番茄变种品系中，梨形果品系YH02-5、YH02-8的果实维生素C、可溶性固形物含量均极显著地低于樱桃番茄变种中圆形或李形品系的平均水平，李形果品系YH02-9在4个营养品质性状上均极显著地高于圆形果品系的平均水平，黄色圆形果品系YH02-11的果实维生素C偏低于红色圆形果品系YH02-1和YH02-7。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。