数值的

This semi-analytical method is accurate and widely used. It overcomes the limitation of the analytical solution such as conformal mapping. The position of cracks can be arbitrary.

这种解析数值相结合求解应力强度因子的方法，充分利用了解析方法精度高和数值方法适用性广的特点，同时又克服了保角变换等解析解的局限，各裂纹位置可以是任意的。

The main works include: In this thesis, we use Finite Difference Time Domain method to study the relationship between diffraction efficiency, angular dispersion and grating constant, to discuss how the grating figure influence the diffraction efficiency, and to research the frequency spectrum characteristic.

主要工作包括：本文分别在垂直入射和自准直入射（光垂直于光栅刻槽面入射）情况下，采用时域有限差分方法，利用商业数值计算软件OptiFDTD对二维闪耀光栅进行了矢量电磁场数值计算，研究了光栅的衍射效率和角色散随光栅常数的变化情况，研究了光栅形状对光栅衍射效率的影响，还讨论了各种光栅的频谱特性。

If SUBNAME is specified, it gives the name of a subroutine that compares two list elements and returns an integer less than, equal to, or greater than 0, depending on whether the elements are in ascending sort order, equal, or descending sort order, respectively.

如果指定了SUBNAME，也就是说，指定一个子程序名来比较列表中的两个元素，根据它们的关系是升序排列、相等，还是降序排列，来返回一个小于0的整数值、0，大于0的整数值。

This paper presents the boundary value problem solved as the biharmonic equation of upper plane and strip domain with Green functional method and it deals with the numerical solution of bihormonic equation, using the Matlab program calculation to realize the visualization of numeric solution.

用Green函数法求解了区域为上半平面和带形区域的双调和泊松方程的边值问题；以及探讨了双调和方程的数值解，并用Matlab编程计算实现了双调和方程数值解的可视化。

This method is based on the work of reference [1]. By using the Riesz present theory in Hilbert space, we first transform the iterative procedure of variational inequalities into a fixed point form. Then, using the Schauder fixed point theory, we construct a numerical verification method with high efficiency that through numerical computation generates a bounded, closed, convex set in which the approximate solution is included.

通过Hilbert空间中的Riesz表示定理，首先将变分不等式问题的迭代过程转化为一种不动点形式，再利用Schauder不动点定理构造了一个高效率的数值证明过程，即通过数值计算产生一个包含近似解的有界闭凸子集。

Marc this paper carried out a finite element numerical simulation on the forming process of cold extruding for the starlike sleeve of constant speed cardan joint of car. The interrelated technological problems of numerical simulation were discussed in detail, the variation curve of extruding force during the course of loading, the cloud chart, which varies along with time, of temperature field distribution of workpiece, the equivalent plastic strain cloud chart of workpiece and the stress distribution cloud chart of diem inner ring were obtained thus explained fairly nice the reason of fatigue damage of dies.

Marc对轿车等速万向节星形套冷挤压成型过程进行了有限元数值模拟，详细讨论了有关数值模拟技术问题，得出了挤压力在加载过程中的变化曲线、工件随时间变化的温度场分布云图、工件等效塑性应变云图及模具内圈的应力分布云图，较好地解释了模具疲劳破坏的原因。

This paper uses the non-uniform grid model successfully to fulfill the three-dimensional simulation modeling of the double post-hole convolute whose structures are complex; uses strut to fulfill the load modeling of the computer implementation; explores the feasibility and application value of using MPI parallel algorith into the simulation.

成功地使用了非均匀网格模型，实现了对结构复杂的中心汇流区的三维数值建模；运用金属支撑杆模型，实现了负载的数值建模。探讨了MPI并行算法运用到模拟中的可行性及其应用价值。

The characteristic function of the probability density function of response variable is obtained by the high efficient multidimensional numerical integration method or convolution integral based on response surface method. Then the discrete probability density function of response variable is calculated using the fast Fourier inverse transform technique, at last the cumulative distribution function of the response variable can be quantitatively determined.

首先利用高效多维数值积分方法或基于响应面法的卷积积分求解功能函数的分布函数的特征函数，也就是进行Fourier正变换；然后利用快速Fourier逆变换数值求解功能函数的概率密度函数，进而求得失效概率。

Whether the number is printed using decimal or scientific notation depends on the value of the floating-point number being printed. The library chooses a format that enhances readability of the number. Very large and very small values are printed using scientific notation. Other values use fixed decimal.

使用小数形式还是科学记数法显示数值取决于被显示的浮点数的值，标准库选择增强数值可读性的格式，非常大和非常小的值使用科学记数法显示，其他值使用小数形式。

This paper studies the main geometrical parameter such as angle, height, width, stagger and the upper width in dentation and trapezoid flow path, firstly, uses the single-phase numerical simulation of the computational fluid dynamics technique to analyse the influence of different geometrical parameter on discharge coefficient and flow state exponent of drip emitter. Secondly, uses the two-phases numerical simulation of CFD (1% sand content ) to analyse the influence of the above mentioned geometrical parameter on the contribution regulation of sand and anti-clogging performance. Thirdly, uses the PIV （ particle Tracking Velocimetry ） technique which can see the small-scale flow path to observe and test the trajectories and velocities of solid particles in labyrinth flow path, and analyses the basic factors which can influence the movement characteristic of solid particles and the flow state in flow path.

本文以齿形流道、梯形流道为主要研究对象，以流道转角、流道高，流道宽、偏差量及梯形流道上底宽为主要结构参数，首先应用 CFD 单相流数值模拟技术对不同结构参数灌水器流道水力性能进行模拟，分析了不同结构参数对流态指数和流量系数的影响，其次，应用 CFD 两相流（含沙量为1%）数值模拟技术分析了结构参数对含沙量分布规律和抗堵塞性能的影响，然后，应用 PIV 可视化测试方法测试了固体颗粒在流道内运行轨迹及速度，分析了影响固体颗粒运动特性及流道内流体流态的基本因素，最后，对上述流道结构形式通过模具加工及滴灌带试制，进行了标准化测试（ GB/T 17187-1997 农业灌溉设备滴头技术规范和试验方法与 ISO 标准 ISO /TC23 /SC18 /WG5N4短周期堵塞测试程序），测试结果验证了 CFD 模拟结果，并提出了迷宫结构流道灌水器的抗堵塞设计方法。

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。