正交的

Based on general orthogonal polynomials and general hybrid orthogonal functions, a new linear, continuous and bounded operator has been proposed in the dissertation. The definitions and properties of PGOPO are given, a various operational rules of the operator have been set up in a systematic way, the convergence of approximate solutions has been discussed. After introducing PGOPO and discussing its main properties and operational rules, a systematic methodology for solving various control problems via PGOPO has been developed.

本文在广义正交多项式及广义混合正交函数的基础上，提出了一种新的线性、连续、有界算子—分段广义正交多项式算子，探讨了这种算子的基本性质，并系统地建立了与该算子有关的各种运算规则及收敛性结论，给出了它在控制理论中的各种应用。

This paper researches linear maps preserving orthogonality,obtains the linear maps preserving othrogonality,it is either a rank -declining or rank -keeping map or a map with nilpotent element in its codomain.

利用分块成向量的方法证明了MnMn(F为域F上所有n×n矩阵构成的乘法半群上的n×n拟正交矩阵组至多含有n个矩阵，利用方程组的解的理论证明了Mn中与给定矩阵A构成两两拟正交矩阵组的矩阵个数不超过n-Rank+1，从而得到Mn上保持拟正交性的线性映射φ要么是降秩的或者保秩的映射，要么φ的值域中含有幂零元。

Built up dimensional reference frame and vector equation of movement model of orthogonal turn-miling.

为了提高数控车铣的编程效率，论述了正交车铣运动的特征，同时通过对正交车铣运动过程的分析，建立了一个描述其运动的空间坐标系，从而建立了正交车铣运动模型的矢量方程。

We paid special attention to the complex linear space consisting of all linear mappings from dimensional complex inner product space into dimensional complex inner product space .

2是与基的选择无关的概念。容易验证内积(2)满足内积的公理，从而是一个位的复内积空间。当是的正交归一基，是的正交归一基，可以证明构成的正交归一基。

In the parallel program, the in-core and out-of-core algorithms can be identified and chosen to use automatically. So the algorithms are united.(3) The re-orthonormalization technique is used to solve the loss of orthonormality of basis vector during the classical GMRES method solving large-scale three dimensional elasto-static BE problems.

3采用重正交技术解决了经典GMRES方法在求解大型三维弹性静力边界元问题过程中出现的基向量正交性丧失的问题；结合边界元基本解和系数矩阵的特点以及并行化的要求，研究了几种预条件技术；并以重正交技术和预条件技术实现了经典GMRES的实用化。

The new set of orthonormal vectors is generated using the Gram-Schmidt orthonormalization procedure, with the " promising" direction from the just-completed stage used as the first vector in the orthonormalization process.

新的正交向量集是用Gram-Schmidt正交化过程产生的，将刚完成阶段的"有希望的"方向做为正交化过程的首向量。

It realizes the global optimal computation via the local interacting agents with abilities of local perceptivity, competition and cooperation, self-learning etc. Then orthogonal design is introduced to generate an initial population of points that are scattered uniformly over the feasible solution space and to generate a crossover operator. As a result, the resulting algorithm is more robust and statistically sound. For high dimensional functions, a large memory is needed in generating an initial population with orthogonal design. To overcome this problem, a method called subspace partition is proposed, so that the memory is one tenth that of original one.

它以Multi-Agent系统为基础，通过Agent间的相互作用与每个Agent所具有的知识和自学习功能来提高算法的全局优化能力和收敛速度；同时利用正交试验设计方法产生较好的初始种群和设计正交交叉算子以获得更好的后代；针对正交试验设计产生初始化种群在函数维数很高时需很大存贮空间的缺点，提出了子空间分割法来产生所需的初始化种群，它只需要原来存贮空间的十分之一。

Here a simple technique for parametrization construction of 17/11 biorthogonal wavelet family is presented: first, the associated synthesis filter is formulated as one trigonometric polynomial represented by two free parameters; then the perfect reconstruction condition of the filter bank is reduced to one system of linear equations; finally the analysis filter is obtained by solving this system of linear equations. Thus, the exact free parameter expressions for the 17/11 biorthogonal wavelet filter banks are derived.

该文给出了一种参数化构造17/11双正交小波组的简便方法：首先把小波合成滤波器表示为用两个自由参数表达的三角多项式，然后把双正交小波的精确重构条件归结为一个线性方程组，最后求解此方程组得到对应的小波分解滤波器，从而得到了17/11双正交小波滤波器的参数表达式。

The constraint conditions of quasi optimal and strict optimal OOCs constructed by recursive method are theoretic analyzed. Based on these constraint conditions, as the initial conditions of OOCs obtained by direct construction, some quasi optimal and strict optimal OOCs with larger code length and sizes are obtained by recursive method.

2理论研究了基于递归法构造准最佳和严格最佳光正交码的约束条件，在此基础上，以直接构造法得到的光正交码为初始条件，利用递归法构造了一些具有相同相关特性的码长更长、容量更大的准最佳和严格最佳光正交码。

This method first maps training data into a high dimensional feature space through kernel function concept in Support Vector Machine and constructs orthogonal space in the feature space. Then it maps the data from feature space into the orthogonal space and computes Fisher criterion based global orthogonal discriminants.

首先应用支持向量机中核函数的概念，将样本隐式地映射到特征空间，然后构造特征空间的正交空间，再将特征空间样本映射到特征空间的正交空间，求解基于Fisher的全局正交鉴别矢量集。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。