对边

We can not apply Galerkin methods with radial basis functions to the first boundary value problem (the Dirichlet boundary value problem) of the second-order elliptic equation, because it requires that the approximate functions should fit the essential boundary condition, while the spaces spanned by the radial basis functions fails to satisfy this kind of boundary condition, and it is the same for the higher-order elliptic equation.

我们不能直接应用这样的无网格算法求解二阶椭圆型方程的第一类边值问题(Dirichlet边值问题)，因为第一类边界条件是本质边界条件(对二阶椭圆型方程为Dirichlet边界条件)，而径向基函数的支集通常是全空间，由它们所生成的近似函数空间一般不满足这样的条件。

In this paper, the author estimated the module of quasiconformal mapping in curved fan, by the expression of local maximal dilatation function of quasiconformal mapping, Riemann′ s existence theorem and extremal length method, the author obtained a result of moduler deviation on curved fan.

本文对曲边扇形内的拟共形映照的模进行估计。借助拟共形映照的局部最大伸张函数来表达，利用黎曼存在定理和极值长度方法，得到关于曲边扇形的一个模偏差定理。

After that , he had some ideas of Fabianism in his mind : the top priority task of China's revolution was anti-imperialist and anti-feudal , patriotism and democratism were needed , the socialist system could not be implemented gradually until after the victory of the democratic revolution setting up the diversified forms of ownership on the economic system implementing the cabinet system of responsibility in government organization practising a single system in relation between the central government and the local government the democratic revolution should be led by the intellectuals of the petty bourgeoisie and capitalist class .

在英国师从拉斯基对费边社会主义理论进行研究之后，王造时形成了一些费边社会主义式的想法：中国革命的当务之急是反帝反封建，需要的是爱国主义和民主主义，待民主革命成功后，才能逐渐实施社会主义；经济制度上，建立多种形式的所有制；在政府组织方面，实行责任内阁制；在中央政府和地方政府的关系方面，实行单一制；应该由小资产阶级和资产阶级的知识分子来领导民主革命。

The product of Fourier series and a finite sum of complex Gaussian functions is used to approximate the window function of a hard-edged aperture, an improved algorithm for the beam propagation through a paraxial ABCD optical system with hard-edged aperture is proposed.

使用傅里叶级数与有限个复高斯函数之和的乘积作为硬边光阑的窗口函数的近似式，提出了含硬边光阑近轴ABCD光学系统对光束变换的改进算法。

A new process of which flotation is carried out while simultaneously the grinding is presented.

提出了边磨边浮创新思想，提供了一种在磨矿过程中对矿石进行浮选的新工艺。

First, the physical models associated with dislocations and cracks are respectively converted to mixed boundary value problems in mathematics. Secondly, by using the Fourier transform, a dual integral equation for a crack and an algebraic equation for a dislocation can be derived from the boundary conditions relating with a crack and a dislocation, respectively. Solving these equations, exact analytical solutions can be obtained in terms of Bessel functions in close-form.

先把位错和裂纹的物理模型写成与它们相关的边值问题，然后，利用Fourier变换将这些边值问题化成一个对偶积分方程(对位错而言，得到一个代数方程)，求解此对偶积分方程，可以获得以Bessel函数给出的封闭形式的分析解。

By Galerkin meshless method, the equations of motion of static rectangular membrane is established. The first ten natural frequencies of the different aspect ratios and the different pull ratios of rectangular membrane with four clamped edges, three clamped edges and one free edge, two opposite free edges and other two clamped edges were calculated. It is feasible and valid to solve the transverse vibration problem of membrane by Galerkin meshless method.

采用伽辽金无网格法，建立了矩形薄膜横向自由振动的运动方程，并对四边固支、三边固支一边自由、一对边固支另一对边自由三种边界条件下，薄膜的不同长宽比及不同单位长度拉力比作用下的矩形薄膜的前十阶固有频率进行了数值计算，结果说明伽辽金无网格法用于求解薄膜横向振动问题是切实可行的。

In order to study the propagation of partially coherent modified Bessel-Gaussian beams passing through a paraxial ABCD optical system with hard-edge aperture,the approximate analytical propagation equation was derived with the hard-edged aperture function expanded into a finite sum of complex Gaussian functions.

为了对部分相干修正贝塞尔－高斯光束通过有硬边光阑近轴4BCD光学系统的传输进行研究，采用将硬边光阑窗口函数展开为有限个复高斯函数之和的方法，得到了近似的解析传输公式。

Using the relations between Hermite and Laguerre-Gaussian modes and expanding the window function of two-dimensional rectangular hard-edged apertures into a finite sum of complex Gaussian functions, the propagation of complex- argument Laguerre-Gaussian beams through a paraxial optical ABCD system with a rectangular hard-edged aperture is studied. An analytical propagation equation is derived and used to study the diffraction at the rectangular hard-edged aperture and the focusing properties of complex-argument LG beams.

利用拉盖尔－高斯模和厄米－高斯模的变换公式，并使用将二维矩孔光阑窗口函数展开为有限个复高斯函数之和的方法，得到了复宗量拉盖尔－高斯光束通过含矩形硬边光阑近轴ABCD光学系统的变换的解析传输公式，并对复宗量LG光束通过矩形硬边光阑的衍射和聚焦特性进行了研究。

Through to the mining area west the side slope engineering geology condition research, obtains slope the structure characteristic and the crag body structure characteristic, as well as gneiss and structure surface physics mechanical properties.

2通过对矿区西侧边坡的工程地质条件的研究，得出边坡的结构特征和岩体结构特征，以及岩土体和结构面的物理力学性质。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。