积分因子

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 integral area for calculating the beam width by using the definition of generalized second-order moments is selected to ensure the energy in the angular domain more than 75% of the total beam energy and the measurement method and steps still follow the relevant ISO standards. The generalized M2 factor of truncated Gaussian beam has been measured. The experimental results for different truncated parameters have been compared with the theoretical results, showing the validness of the method proposed.

在利用广义强度二阶矩计算光束束宽时，以积分角谱范围能够包含光束总能量的75%以上作为积分范围的选取标准，并遵循现有的国际标准化组织规定的测量步骤和方法对截断高斯光束的广义M2因子进行了测量，并将不同截断参量时的实验结果与理论计算结果进行了比较，证明了该方法的正确性。

When the stress and displacement fields in a specimen are calculated by finite element method, the stress intensity factors K and K of mixed-mode crack can be obtained immediately by a contour integral.

此方法与积分路径的选择无关，用有限元法计算出远离裂纹尖端的位移场和应力场，就可通过计算绕裂端的围线积分，精确地给出混合型裂纹的应力强度因子KⅠ和KⅡ的数值解。

In this paper,the boundary singular kernel method in Reproducing Kernel Paicle Method has been applied to impose the essential boundary conditions in EFGM by revising the MLS shape function.The stress field and the displacement field are analysed by linear elastic theory.The contour integral method is used to calculate the J-integral,then the stress intensity factors of mixed-mode crack is acquired.The correctness and the validity of the method are validated.

本文将再生核质点方法中的边界奇异权方法引入EFGM中，通过对MLS形函数进行修正实现了本质边界条件在节点处的精确施加；运用线弹性断裂理论分析裂纹板的应力应变场，采用围线积分法计算J积分，给出了复合型裂纹板的应力强度因子的无网格伽辽金方法。

It is difficult to compute directly the coefficients from the integral formula, since the integral function in the formula of the ideal digital fractional differentiator is a high-order oscillating function.

从理想数字分数微分器系数计算公式的特点考虑，利用变量代换把积分函数中的振荡因子转换成积分上限，避免高阶振荡函数积分计算，给出了计算分数微分器系数的递推公式。

By using the Copson method, one of these equations is transformed into a Fredholm integral equation of the second kind to obtain the solution. Furthermore, the intensity factors, the total energy release rate and the mechanical strain energy release rate are obtained and compared with the classical results without considering the electric field gradient effects.

采用了Copson方法，将其中一组对偶积分方程转化为第二类Fredholm 积分方程来进行数值求解，得到了裂纹尖端的强度因子、总能量释放率和机械应变能释放率，并与经典理论中的结果进行了比较。

By introducing a weight function, a best extension of Hilbert integral inequlity and the reverse form are given. The constant factor of the two inequalities is proved to be the best.

引入单参数及估算权函数，给出一个核为－λ齐次的新的Hilbert型积分不等式及与之对应的逆向积分不等式，并证明这两个不等式的常数因子是最佳的。

In the path integral formalism, we represent the generating functional and Green functions of Φ〓 theory by taking account of that the partial and the functional derivatives commute. Also we discuss the effective action for noncommutative scalar fields, and show how the noncommutative phase factors appear in path integral formalism. We realize that the two approaches (path integral and canonical quantizations) are completely equivalent each other.

在用路径积分方法对非对易标量场进行研究时，我们利用偏微商和泛函微商的可交换性，给出了Φ〓场格林函数和格林函数生成泛函的具体表达形式，得出了非对易相因子在路径积分方法中的具体表现形式，并对连通格林函数和有效作用量等问题做了讨论。

Golikov as the general and single-valued criterion for evaluating the acoustics of rooms and auditori- ums have been critically examined,with detailed discussionsconcerning:(1) the empirical foundation of the articulation-Q"functional relationship A= f,(2)the derivation of the"particular criterion"or the optimum re- verberation condition form Q",(3)the meaning of a time integration of the "noise-interference factoras viewed from the theorey of auditory perce- ption...

主要内容有：(1)以在不同的条件(如语言、测试人员、宣读方式以及声学场所等)之下的清晰度测验结果来验证 A=f函数的适用性，(2)判断了从Q&来推求以体积为参数的最佳混响时间的可能性，(3)，从听觉理论来讨论&混响干扰因子&对时间积分的意义，(4)讨论了原作者对&噪声因子&的看法，指出了&噪声因子&定义中的一些值得存疑之处。

Based on data of per mu yield of spring-sown soybean and of cli-mate in Hengyang from 1975 to 1981,the tendency yields are estimatedfirst by the method of orthogonal polynomial regression,and then by theFisher's integral regression equation for the out-tendency yields andclimatic factors in this city.

依据1975～1981年衡阳市的气象资料和春大豆亩产量资料，首先用正交多项式回归方法估计了趋势产量，然后用费希尔积分回归模式和逐步回归方法计算出了该市气候因子和离趋势产量间的积分回归公式。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐