奇异

Thirdly,we study certain Riemann boundary value problems and Singularintegral equations with values in a universal Clifford algebra 〓,by com-bining the classical methods of solving Riemann boundary value problems andsingular integral equations with the Taylor's expansion of regular function in Clif-ford analysis,proving a lemma which is similar to the Painleve theorem in theclassical complex analysis,and the Plemelj formula in Clifford analysis,we obtainthe better results under weaker condition than before.

第三，本文第一次借助于用来解决经典的Riemann边值问题与奇异积分方程的方法来研究Clifford分析中的某些Riemann边值问题与奇异积分方程，获得了在比以前文献中条件更弱的情况下，结论更广的结果，并且，它为更进一步地解决在Clifford分析中一般的Riemann边值问题与奇异积分方程提供了基本的解决思想，为这一新的研究领域奠定了基础。

In this paper we suggesst a finite element method for singular two point boundary value problems with singular solution by introducing singular basis with local support.

采用具有小支集的奇异基函数的有限元方法求解奇异两点边值问题的奇异解。

A kind of concise nalytic-graphic approach for singular position analysis of complex multilooped planar mechanisms was put forward,I.e,firstly,let the mechanism be deconposed into basic kinematic chains,then deduce the singularity conditions of these BKC and lastly determine the singular position of the mechanism from the corresponding singular geometric figure.

提出了复杂多环路平面机构奇异位置分析的一种简明的分析图解方法，即先将机构分解为基本运动链，再导出基本运动链的奇异性条件，后由其相应的奇异几何图形，解出其机构的奇异位置。

In chapter 3, prediction theory of time series is reviewed, then non-linear autoregressive model of time series-feedforward neural networks is presented, at the same time a new method-SVD is proposed to design the architecture of feedforward neural networks. By using a trained network with a sufficient number of hidden nodes, according to the distribution of singular values of hidden nodes outputs, we can decide the optimum number of hidden nodes, then the reduced network will be retrained.

第三章：先回顾了时间序列的预测理论，提出了时间序列的非线性自回归模型-前馈神经网络模型，并提出了一种设计前馈神经网络的新方法-奇异值分解法，初始网络结构足够大，网络训练后，对网络隐层节点输出所形成的矩阵作奇异值分解，根据奇异值分布情况，决定网络隐层节点的个数，优化后的网络重新开始训练。

The examples given have proved the advantage of the Boundary Element Method. In the analysis of the fracture mechanics using Boundary Element Method, the calculation model of one-quarter singular element has been established, and has been proved its validity.

把边界元法应用于线弹性结构断裂分析中，建立了裂尖奇异区分析的四分之一奇异元计算模型，算例表明，用四分之一奇异元分析断裂力学问题是一种有效的逼近裂尖场的数值方法。

In accord with the characteristics of singular integrals in boundary element method for solving problems of thick plates on two parameter foundation,all formulas for calculating singular integrals are set up by selecting the displacements and stresses which satisfy the governing differential equations in this paper,on the principle of virtual energy.

根据双参数地基上厚板弯曲问题边界单元法中所遇奇异积分的特点，选取满足该问题微分控制方程的位移及内力场，建立了全部奇异积分的计算公式，有效地解决了边界元法在该问题应用中高阶奇异积分的计算问题

In chapter 4,on the basis of chapter 3,a new formulation of hybrid/mixedsingular plate element based on Reissner's plate theory is set up,and 4-node arbitraryquadrilateral hybrid/mixed singular bending plate element formulas including theeffects of transverse shear deformation is derived,then by the use of this method,alarge quantity of numerical computations are carried out,at the same time,the resultsare compared with theoretical solutions and the results obtained by other singularfinite element methods.

第四章 在第三章的基础之上，建立基于Reissner型板理论之上的杂交/混合奇异板单元列式，推导出了考虑剪切效应的四节点任意四边形杂交/混合奇异弯曲板单元公式，并进行了大量的数值计算，同时与理论解析解和其它有限元解进行了比较，计算结果表明：本文提出的杂交/混合奇异板单元方法是可以用于计算含裂纹平板弯曲应力强度因子的一种高效、可靠、简便易行的方法。

We extended the Safety Margin theory, the flight parameters transferred to the singular space through the SVD method. This conception created the Safety Margin Terrain and showed the geometry properties of current flight.

而将飞航安全几何化的观点再做推展，透过奇异值分解的方法，将参数转换至奇异空间，再利用几何方程式，拟合飞航安全裕度於奇异空间中的曲线，求得安全裕度地形，并由此模型计算出每一航班之几何变化，并藉由此方法可求得当下飞航安全裕度的几何特性，表示当飞航安全的状态。

Through the hypersingular integral equations of 3-d crack perpendicular to the interface given in the preceding, the principles of finite-part integrals and of limit are further made use of to pick the hypersingular integral equations of 3-d crack terminating at the interface On the basis of the equations, starting strictly from 3-d theory of elasticity, stress singularities of intersection-line near the front edge of the 3-d crack terminating at the interface are analyzed by virtue of dominant-part analysis of 2-d hypersingular integrals.

根据前面所得到的与界面垂直的单片裂纹超奇异积分方程，进一步运用有限部积分原理和极限理论，推导出了与界面垂直相抵的三维平片裂纹的超奇异积分方程。在此基础上，严格从三维理论出发，使用二维超奇异积分的主部分析方法，对与界面垂直相抵的三维平片裂纹前沿交线上的应力奇性指数进行了分析。

In section 3, on the base of the iterative algorithm, we obtain a new iterative algorithm which is convergent to the signal faster than the old one. In section four, if the form of φ is simple and the sampling set is the integer set Z, then a direct reconstruction formula is presented.

在第二节，我们通过计算对偶框架来重建信号，这与传统的计算对偶框架方法不一样，该算法是通过计算一个矩阵的逆矩阵来计算对偶框架，当矩阵是奇异矩阵时，可通过奇异值分解方法或截断奇异值分解算法来求矩阵的广义逆矩阵。

What are your goals and strategies for growth?

你的成长目标和策略是什么？

And unto the angel of the church in Sardis write; These things saith he that hath the seven irits of God, and the seven star I know thy works, that thou hast a name that thou livest, and art dead.

3：1 你要写信给撒狄教会的使者，说，那有神的七灵和七星的，说，我知道你的行为，按名你是活的，其实是死的。