积分公式

Then use it to prove a characteric properties of convex set and some other characteric properties.

这些公式能够被看作是各种交集测度的积分公式，它们对于解决几何概率问题是很有用的。

An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over histories between initial and final states; this is the quantum-mechanical counterpart of action principles in classical mechanics.

一个量子力学的代用公式是费曼路径积分公式，在其中量子力学振幅被认为是超过最初与最后态历史的总和；这就是在经典力学里量子力学作用原理的相似物。

Based on the Fresnel diffraction integral, the analytical expression for the field distribution of converging spherical waves passing through an annular aperture is derived and some special cases are discussed.

摘要基于菲涅耳衍射积分公式，推导出了会聚球面波通过环形光阑后场分布的解析公式，并讨论了一些特殊情况。

Staring from Fresnel diffraction integral,we deduced the optical intensity distribution in the Fresnel zone of the diffraction field of the annular-aperture lens axicon.

从菲涅耳衍射积分公式出发，推导多色高斯光束被球差透镜衍射后光强分布的解析公式，进行数值模拟和物理分析。

The use of two points Gauss formula for numerical integration of the solution and see its precision.

详细说明：利用Gauss两点积分公式，进行数值积分的求解，并看它所具有的精确度。

The author of this text has put out a kind of new-type quadrature formula by using the Gaussian quadrature formula and the orthogonality of Per Kai polynomial.

应用Gauss型求积法则和Per Kai多项式的正交性质，本文作者推导出了一种新型的求积公式—Gauss-Per Kai积分公式。

In this paper, an integral formula for elliptical flexure hinge is deduced by introducing centrifugal angle as the integral variable.

以椭圆的离心角为积分变量，得到椭圆柔性铰链的转角计算的积分公式，推导出椭圆柔性铰链的刚度表达式。

In Chapter Five, we compare numerical integration of the reproducing kernel with the integral equation of complexified trapezoid through a detailed solution to the initial-value problem of ordinary differential equation to exemplify that the method of interpolation spline integrating and the reproducing kernel is not only feasible in theory but also significant in pratice.

在第五章，我们通过具体的求解一个常微分方程的初值问题，把再生核方法的数值积分和复化梯形积分公式相比较，说明样条插值和再生核相结合的方法不仅是理论上可行的，而且还具有重要的实际意义。

The solution expression is suitable both for the inner and outer problem with a close boundary, and the calculation of velocity and pressure can be carried out separately, which is an advantage of boundary element scheme.

该方法的积分表达式可同时表示内、外边值问题的解，而且计算速度和计算压力的式子可以分别开，这是用边界积分公式求解的优点。

In this paper, firstly, the theory and the discretization schemes of LBIE and the concepts of MLS and GMLS are introduced; secondly, LBIE method is applied to solve the thin plate-bending problems and four typical examples are given to demonstrate the applicability and validity of the method. The results obtained from numerical examples agree well with the exact solutions and have an excellent rate of convergence.

本文首先介绍了无网格局部边界积分方程方法的理论基础和离散步骤，以及移动最小二乘近似法和广义移动最小二乘近似法等概念；其次将该方法初步应用于计算薄板的弯曲问题，建立了完整的积分公式，求解了四个典型算例，结果同精确解非常接近，且收敛快。

This paper analyzes the compound attractor structure of a new three-dimensional autonomous chaotic system.

分析了一种新的三维自治混沌系统吸引子的复合结构。

ON shut rivals out of their transmission systems and shy away from reinvesting their profits in network improvements.

ON将竞争者挡在了其输送体系之后，并不愿将其收益再投资于网络改建工作。