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In this paper, the adjointness of the product of two differential operators generated by a third order normal and singular symmetric differential expression in the limit-circle case is discussed. The necessary and sufficient conditions which make the product operators being the adjoint operators obtained by the matrix analysis and calculation. At the same time, the adjointness of the product of the power and adjointness operator obtained.

本文首先讨论了正则和奇异两种情况下两个极限圆型三阶对称微分算式生成的微分算子的乘积的自共轭性，运用矩阵分析和计算，得到了乘积算子为自共轭算子时边界应满足的充分必要条件，同时得到了幂算子的自共轭性、自共轭算子乘积的自共轭性等乘积算子的其它若干性质。

The adjoint operator method and the theory of normal form are used to investigated the normal forms in the four dimensional nonlinear systems with cubic nonlinearities. We give two methods to compute the normal form for the four dimensional nonlinear systems. The corresponding Maple programs are also given in the appendix. The results obtained in this dissertation have a completely agreement with the results obtained in other papers.

利用共轭算子法和规范形理论研究了含有三次非线性项的四维系统的规范形，给出了计算四维非线性规范形的两种算法，给出了相应的Maple符号推导程序，所得到的结果与其它文献所得结果完全一致。

The optimal control law obtained consists of linear analytic functions and a compensation term which is a series sum of the adjoint vectors. The analytic functions can be found by solving a Riccati matrix difference equation and a matrix difference equation. The compensation term can be obtained by a recursion formula that solves adjoint vector equations.

得到的最优输出跟踪控制律由状态向量的线性解析函数和伴随向量级数形式的补偿项组成，其解析函数由一次性求解Riccati矩阵差分方程和矩阵差分方程得到，补偿项由求解伴随向量差分方程的递推公式得到。

Secondly, by applying inverse Fourier integral transform to the displacement, and uniting the constitutive and geometrical equations, the analytical expression of stress in Laplace domain were derived. Thirdly, by defining dislocation density functions, the Cauchy singular integral equations were obtained according to the boundary condition and interface connection conditions, and the problem was reduced to algebraic equations by Chebyshev orthogonal polynomial. Based the these, the unknown coefficient of the algebraic equations can be solved by Schmidt method. Finally, the time response of dynamic stress intensity factor and energy release rate are obtained by inverse Laplace transform.

首先，利用积分变换方法，推导出粘弹性层的控制方程组；其次，引入位错密度函数，并结合边界条件和界面连接条件，导出反映裂纹尖端奇异性的Cauchy型奇异积分方程组，然后，应用Chebyshev正交多项式化奇异积分方程组为代数方程组，并采用Schmidt方法对其数值求解，最后，经过Laplace逆变换，求得动态应力强度因子和能量释放率的时间响应。

The controller obtained through PSO significantly outperforms alterative schemes obtained with conventional design techniques.

证明了PSO方法能够替代传统的设计技术。

The invention aims at improving the quality of flour to researche a method for preparing new flour modifying agent, namely, the microencapsulation glucose oxidase, chitose-calcium alginate-glucose oxidase microcapsule which is obtained through the method is copolymer hydrogel which is obtained through double cross-linking, both amidogen and carboxyl group are fixed, and the whole system is a reticular formation.

本发明以改善面粉品质为目的，研究一种新型面粉改良剂――微胶囊化葡萄糖氧化酶的制备方法，采用上述方法制得的壳聚糖-海藻酸钙-葡萄糖氧化酶微胶囊，是经双重交联得到的共聚凝胶，氨基和羧基均被固定，整个体系为网状结构。

TPS the throttle valve position perceptron, this equipment might provide accelerator's immediate material to come with material and so on speed by engine revs to make the comparison judgment at that time engine's load conditions, adjusted engine's ignition angle of advance, obtained the good combustion efficiency, obtained the high power, and could achieve the province oil the effect, but the cost more then CDI .

TPS节流阀位置感知器，此装置可以提供油门的即时资料来跟引擎转速等资料作比较判断当时引擎的负荷状态，调整引擎的点火进角，来获得较佳的燃烧效率，获得较高的动力，并能达到省油的效果，但是成本比CDI来的高。

The angular distribution of the bistaticscattering coefficient of HH polarization were obtained by numerical implementation. Influences of the permittivity and the mean layer thickness of intermediate medium, friction velocity and the frequency of the incident wave on the bistatic scattering coefficient were discussed. The basic characteristics, the zonal characteristics and the characteristics with varying of frequency of the scattering coefficient from stratified sea surface were obtained. The numerical results show that the scattering coefficient has approximate "quantization" characteristics.

通过数值计算得到了HH 极化双站散射系数随散射角的变化曲线，讨论了中间介质介电常数和厚度、摩擦风速和入射波频率对双站散射系数的影响，得到改进的一维分形分层海面散射系数的基本特征、分区特征和随频率变化的特征，结果表明散射系数近似具有"量子化"特征。

The extraction from star anise fruits was obtained by supercritical carbon dioxide extraction(SFE-CO_2) method at the pressure 16 MPa,temperature 35℃,flow rate 30 L/h meanwhile time 2 h,and the star anise oil was obtained by steam distillation.

用超临界CO2萃取(SFE-CO2)技术，在压力16 MPa、温度35℃、反应时间2 h及CO2流量30 L/h的条件下，对八角茴香的果实进行了萃取，得到八角茴香萃取物，并用水蒸气蒸馏法提取八角茴香精油。

In the functionally graded elastic half-space and the functionally graded covered layer, the motion control equations for the antiplane shear wave are solved, the analytical solutions for displacement and stress are obtained, and with these analytical solutions, the dispersion equation of Love wave is obtained.

对功能梯度弹性半空间和功能梯度覆层的反平面剪切波的运动控制方程进行了求解，给出了半空间和覆盖层的位移、应力解析解，给出了Love波在该解析解下的频散方程。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。