积分元

The arithmetic of the point charges integral is similar to that of nuclear attraction potential.

前者的计算类似于核吸引积分的单电子积分，后者可以通过点群对称性操作从原子簇内的积分矩阵元得到。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

In calculation of definite integral,beginners tend to use three methods of calculation:(1)Leibniz formula,(2)integration by substitution of definite integral,(3)integration by parts of definite integral.

在定积分计算中初学者常用的计算方法有三种：(1)利用牛顿-莱布尼兹公式，(2)定积分的换元积分法，(3)定积分的分部积分法。

The quaternion calculation for spacecraft attitude determination is investigated in this paper,including the transformation between quaternion and the direction cosine matrix,the quaternion differential equation,the selection of time steps for integrating the quaternion equation,and the compensation methods for the noncommutativity error in high dynamic motion.

介绍了四元数计算中的相关问题，包括四元数与方向余弦阵之间的转换、四元数运动方程、求解四元数运动方程时积分步长的选取和高动态应用中非互易误差的补偿，此外还介绍了对偶四元数的发展。

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

The direct problem was solved by DRBEM, which eliminated the drawback of domain integral for classical boundary element method and resulted in pure boundary integral calculation.

正问题采用双倒易边界元法求解，该法避免了传统边界元法需进行区域积分的缺点，仅需纯边界积分计算。

Using the characteristic of the regular curve boundary for a bending plate in engineering,the analytic integral formulae of assistant states in boundary element method with the linear element for a Kirchhoff circular plate are introduced and the systematic equation of BEM is established in this paper.

利用一般弯曲薄板边界为规则曲线的特点，对工程常用的圆形弯曲薄板，采用线性单元，导出K irchhoff圆板各辅助态的边界积分解析表达式，建立问题的边界元法系统方程，从而使薄板的边界元分析完全避免通常使用的高斯积分，明显提高计算精度。

The results show the high accuracy quality of spectral element method and the stability of Newmark time integral method. Then some computational parameter is changed in example one such as the subdivision style of computational domain, time step length and such on. Some important conclusions and strategies for spectral element method with Newmark integral method for computational aeroacoustics can be given. The feasibility of spectral element method for computational aeroacoustics is verified.

计算结果表明谱元方法的高精度及Newmark时间积分方法的稳定性，并改变算例的计算参数，例如计算区域剖分方式、时间推进步长等进行了计算，得出了一些重要结论，为使用谱元方法结合Newmark积分求解气动声学问题积累了重要的经验，最终证明了谱元方法求解计算气动声学问题的可行性。

This paper presents an alternative way to transform the double integral in elasticity problem on 3-d into the linear integrals on the boundary of each subdomain, so that all the singular integrals and nonsingular integrals are calculated by analytical method.

采用积分区域变换和高斯定理，将三维弹性问题的二维积分化为一维积分，使奇异积分和非奇异积分能使用精确积分的方法计算，为边界元奇异积分的计算和处理提供了新的思路。

Also the elimination of singular integrands is discussed and treated properly.

在积分求解过程中，提出了动态分配积分阶次的方法，在保障计算精度的前提下，减小了计算量，并结合边界元法理论和实现冷却分析的数值积分过程；消除了积分的奇异性。

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。