二次函数

During the calculation the results got by quintic spline kernel was the best so it was chosen as the proper kernel for the SPH simulation. By comparison of the simulation results got by SPH and finite volume method, it was proved that the buffer cells method proposed in the SPH simulation to implement the Dirichlet boundary conditions was accurate, and this is of great importance for the simulation of flows pass a pipe. At last, the SPH method was improved to simulate the liquid-solid two phase flows and the results show that this method was appropriate for the simulation of flows containing viscous fluid and macroscopic solid components. Now the two methods are both able to predict the continuum flows and rarefied flows severally, but the hybrid program still has some aspects to be improved.

首先用标准算例验证了SPH方法的理论模型和计算程序的准确性；通过比较确定选用五次样条核作为计算低雷诺数下的粘性连续流动时的核函数；采用SPH方法和有限体积法分别对同一管道流动进行了对比计算，证明了本文提出的边界缓冲区方法在实现SPH方法中的流体边界条件时的有效性，解决了SPH方法模拟管道流动时的一个关键问题；巧妙地使用SPH方法对化工分离流动中常见的固液两相流及固液耦合作用进行了模拟尝试，获得了较好的结果；在跨尺度计算方面，目前两个子程序已经能够分别模拟连续的和稀薄的二维管流问题，二者的耦合计算程序还处于调试和优化阶段，各个参数对于计算精度和计算速度的影响规律仍在探索中。

Taking the first boundary condition as an example, it used the second order derivative of the junctions to represent the cubic spline interpolation function, and solved the relative equations with chasing method.

以第1边界条件为例，用节点处二阶导数表示三次样条插值函数，用追赶法求解相关方程组。

In the first chapter,the Riemann-Hilbert boundary value problem of non-normal type for biregularfunctions and some boundary value problems of the inhomogeneous secondorder equation

共有三章，在第一章中主要运用文[2]中的理论与方法讨论了平面上双解析函数的非正则型Riemann-Hilbert边值问题及非齐次二阶方程

In order to compute the failure probability of structural systems for stability of gravity retaining walls, firstly, two performance functions against overturning and sliding of gravity retaining walls were established. Then, the first order second moment theory in structural reliability analysis, i.e., the checking point method was introduced to compute the two failure modes respectively, and two corresponding reliability indexes could be obtained.

为了计算重力式挡土墙稳定性的结构体系失效概率，首先分别建立重力式挡土墙结构抗倾覆稳定性和抗滑移稳定性的功能函数，然后引入结构可靠度分析一次二阶矩法中的验算点法分别对两种失效模式进行计算，得出两个相应的可靠度指标。

Assuming infinite diffusion medium, based on the diffusion equation for prestressed concrete structure, and accounting for the effects of concrete chloride binding capacity, time dependence of diffusion coefficients, temperature and moisture, models of chloride diffusion in two-dimensional infinite body with both power function and constant homogeneous boundary conditions were formulated.

针对无限大的扩散介质，以综合考虑氯离子结合能力、氯离子扩散系数的时间依赖性和环境温湿度影响的实际预应力混凝土氯离子方程为基础，分别在常数和幂函数边界条件下，推导出二维氯离子扩散理论的齐次模型。

For this purpose, the compactly supported radial basis function and the moving least squares approximation based ones are integrated into the aforementioned two global optimizers. As a result, two novel hybrid algorithms are introduced.

其次，为解决电磁场逆问题分析、计算中由于随机类优化算法需进行数以千计次电磁场的数值分析，以致计算时间和计算量难以满足工程分析实际要求的难题，本文将表面响应模型法引入电磁场逆问题的求解，研究了基于紧支径向基函数和基于移动最小二乘法的两种表面响应模型，并将其分别与改进的遗传算法和粒子群算法相结合，提出两种不同的混合快速全局优化算法。

The variation of density with depth is expressed as a function of n order polynomial function to deduce general gravity anomaly formula for 2 D density variable body having arbitrary and regular shapes.

本文把密度随深度的变化表示成任意次多项式函数，推导出了计算任意和规则形状二度变密度体重力异常的通用解析公式。

The multi point-fitting criterion model is built based on n-rank polynomials and orthogonal function least squares fitting criterion.

用n次多项式与基于正交函数的最小二乘拟合法，分别建立多点拟合模型。

Model structure is determined according to the principle of minimizing residual sum of squares, model parameters are estimated by optimum instrumental variable method and prediction error method and validation of the model is performed by examining the whiteness of model residuals.

采用最小二乘法估计制动器ARX模型的参数，以损失函数最小为优化准则，判断了制动器模型的阶次。运用最优辅助变量法和预报误差法，对制动器ARMAX模型的参数进行了估计。

Spline function is applied to both the calculation of the shift and the reconstruction of wave surface.

基于三次样条函数和最小二乘法，提出了一种改进的偏移算法。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。