积分元

II.Based on the above fundamental solutions,the fundamental solutions ofplane and antiplane problems in two dimensional elasticity body are constructedunitedly by using the reduce dimension technique of integration and consideringtwo dimensional problems as particular cases of three dimensional ones.

将二维问题视为三维问题的特殊情形，由三维问题的基本解，采用积分降维技巧，统一导出了平面问题及反平面问题的单位集中不连续位移基本解；建立了一般边界积分方程；完成了相应的不连续位移边界元方法；给出了在断裂力学中的应用。

Spectral element methods for partial differencial equation is introduced in this study from viewpoint of the collocation approximation of Chebyshev polynomial. Wave Equation and its space discretization are deduced. Two time integral methods, central difference method and implicit Newmark method, are introduced, and their stability and applicability are also discussed in some details. The significance of absorbing boundary conditions in spectral element methods for Aeroacoustics is explained, and Clayton-Engquist-Majda absorbing boundary conditions is emphasized and introduced, then the discrete scheme of this boundary conditions is deduced and applied to spectral element methods for wave equation.

本文从Chebyshev多项式逼近理论出发，详细介绍了谱元方法求解偏微分方程的过程；推导了流体中的声波动方程并在空间上对其进行了谱元离散；详细讨论了两种时间积分方法──中心差分法和Newmark方法，分析了它们的稳定性条件，并从理论上对比了两种方法的优缺点和适用范围；将吸收边界条件推广应用于谱元方法求解气动声学问题中，重点介绍了Clayton-Engquist-Majda吸收边界条件的原理和公式，推导了该吸收边界条件的变分形式，并将其引入波动方程的离散形式中。

The so called indirect integral operation means that Eular angles can be gotten from the direction cosine matrix which is received by the integral operation of quaternions or direction cosine.

飞行器导航中，姿态角的获取可以通过直接或间接的积分运算求得的，所谓间接获取即是指通过四元数或方向余弦的积分运算求得姿态矩阵，再从姿态矩阵中提取姿态角。

The beamforming is an important measure of the orientation estimation in theunderwater sound positioning. The Generalized Correlation Beamformer isstudied and the algorithms of FIM and WFIM(WeightedFourier Integral Method) are given. In most circumstances, the performance of these two algorithms is better than Delay-Sum Beamformer. The MVDR(MinimumVariance Distortionless Response) adaptive beamformers are investigated in element andbeam domain. The research results show that the beam-domain MVDR algorithm notonly increases the resolution, but also saves computer when using it to aim orientationestimation.

4水下声定位中波束形成技术是方位估计的重要手段，重点研究了广义相关波束形成算法傅氏积分方法(FIM和加权傅氏积分方法，大多情况下FIM、WFIM算法的性能优于时延—求和波束形成；研究了阵元域和波束域MVDR自适应波束形成，结果表明，利用波束域MVDR进行目标方位估计，既可以获得高精度的方位估计，又可以大大减少计算量。

The solvability can not be sidestepped, for it relates the problem of equivalence of boundary reduction.

人们在用直接边界元方法进行计算时，并不刻意去考虑积分方程的可解性，但可解性的问题是不能回避的，这涉及到原问题的解与边界积分方程的解的等价性问题。

In the last chap-ter,the natural integral equation and natural boundary element method forharmonic problem on exterior elliptic domain are introduced.Then,based onthis,the natural boundary reduction method for a kind of exterior problem ofanisotropic constant coefficients elliptic equation is discussed, the natural inte-gral equation and its solving method on circular boundary and elliptic bound-ary are obtained.These results can be directly applied in coupled methodand DDM for exterior boundary value problem.

最后，讨论了椭圆外区域调和问题的自然积分算子即D-N算子及自然边界元方法，并基于此研究了一类各向异性常系数椭圆型方程外问题的自然边界归化方法，首次得到其在圆周边界及椭圆边界上的自然积分方程及其求解方法，并将这些结果直接应用于外边值问题的耦合算法。

The non_singular fictitious boundary integral equations are derived by using the fundamental solutions and the singular points exterior to domain techniques.

利用基本解和域外奇点技术导出了弹性力学平面问题的非奇异虚边界积分方程，然后利用虚边界元－边界子段法对导出的积分方程进行数值求解。

Methods From the fundamental equation in Laplace domain, using Multiple Reciprocity Method-Boundary Element Method, the integral equations and the boundary integral equations are derived and solved numerically.

方法由 Laplace 变换域中的基本方程出发，利用多重互换边界元方法，得到了积分方程和边界积分方程，并求得数值解。

The result is generalized to a sequence of Banach spaces.

由此得出：Banach空间X上n次积分C-半群序列S强收敛于Banach空间X上n次积分C-半群S的充分条件是其生成元序列A强收敛于A，并将这一结论推广到一般的Banach空间序列上。

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活动期间，一楼、四楼的化妆品区不仅开展了&满200抵30&等买抵和买赠活动，DIOR、SISLEY、GUERULAIN等国际名品还准备了精美的圣诞套装，其中伊莉莎白·雅顿更是将优惠折扣力度提到最大，额外开设了&空瓶换购&活动；服装区的TIME、JINDO、AQUASCUTUM、ST JOHN、CK等各国名牌不仅6折起售，更开展了10倍/20倍积分和&满1000元送100元礼品卡&等活动，消费者购物满1800/3800/6800/13800元还将获得几米拖鞋、LABELLE皮手套、DIOR迪奥真我香水礼包或者DIOR迪奥彩妆礼盒等圣诞礼物。

No clear conclusions can be made about the predictie alidity of specific measures, they found, except for criteria for the underuse of drugs for cardioascular disease.

除了心血管病不合理用药标准外，对于特定评价方法的预测效度没有明确的结论。

The third and last is that almost all of them, being infinite in number, have been impostures, and by idle and crafty brains merely contrived and feigned after the event past.

第三、即最后一点是：几乎所有这些不胜枚举的预言都是欺人之谈，都是在事件过后由无聊而狡猾的脑筋推测与凭空捏造的。