二次函数

In the numerical simulation, the new formulation not only remedies the boundary deficiency problem in the original SPH but also more efficiently repairs the truncated integral in kernel approximation caused by discontinuity and eliminates the errors from particle inconsistency in discontinuous region.

比较不同SPH方程近似二次函数的结果，新方法不仅改进了传统SPH方法存在的边界缺陷问题，同时在非连续区域内也能更有效地修复由非连续引起的核近似截断积分和消除粒子不一致性所造成的误差。

This paper has discussed four different gridding methods in space domain, i.e., linear interpolation, multiquadric function, ordinary Kriging and inverse interpolation. The calculation of these gridding methods is illustrated by both theoretical model and real aeromagnetic data examples.

文中介绍了线性插值法、多元二次函数法、普通克里格法、反插值法等4种空间网格化法的原理，并利用这些网格化方法进行了理论模型和实际航磁数据的试验分析。

The research of both theories and practices of gridding in the dissertation shows that: Linear interpolation based on triangulation is simple computationally and fast, but its gridding results isn't smooth and its precision is low; Multiquardric method is also simple computationally with high precision and good effect, but its gridding is slow because it is based on global calculation; Minimum curvature method is fast with high precision and good effect, but its gridding quickly degrades over areas with sparse data control when grid spacing smaller than the actual grid spacing is used; Ordinary Kriging method is high-precision, but its gridding is slow because of large calculation; Inverse interpolation is a computationally fast, efficient and robust method with high accuracy and perfect effect, and its gridding results of different gridding orientations are basically identical. Inverse interpolation is suitable for thegridding of geophysical irregular data, especially for large-scale geophysical irregular data.

本文的方法研究和数据试验分析表明：基于三角网的线性插值法计算简单，速度快，但其网格化结果不光滑，精度不够；多元二次函数法计算简单，网格化精度高，效果良好，但它是基于全局计算的，计算速度较慢；最小曲率法计算速度快，网格化精度高，效果良好，但其在稀疏控制点的网格化容易出现振荡现象；普通克里格法网格化精度高，效果良好，但其计算量较大，一般计算速度慢；反插值法网格化计算稳定，速度快，精度高，效果好，而且在网格化方向不同的情况下其网格化精度效果都达到基本一致，适合于地球物理不规则分布数据的网格化，特别是大规模地球物理不规则分布数据的网格化。

An algorithm has the Q-property if it will find the minimizer of a convex quadratic in a finite number of iterations.

如果一个算法能在有限步叠代内找到凸二次函数的最小值就称其具有Q-属性。

Taking advantage of polynomials of second degree used in Hill yield criterion, and assuming that the yielding of orthotropy is not influenced by orthotropic hydrostatic pressures, a concise and practical yield criterion is put forward for orthotropy.

保持Hill准则二次函数描述的优越性，并假定具有正交特性的静水压力对正交各向异性材料的屈服不产生影响，提出了一种简洁实用的正交各向异性屈服准则。

Instead of widely used parametric representation of surfaces, a planar facet scheme was used to obtain the painting surfaces approximately.

根据实验数据确定平面上的涂层累积速率二次函数后，建立了自由曲面上的漆膜厚度数学模型。

The accumulation of nitrogen in plant increased with time, and the relationship was a quadratic function.

随着NaCl含量的增加，植株的总氮累积量将减少，且植株中累积氮量随时间呈二次函数增长。

In each instance the relationship was sigmoidal rather than linear and it was best modeled using a quadratic function.

两种情况下的关系都是S形，而非线性，最适合使用二次函数模型。

This method takes the advantages of fast convergence of CG and not easily to trap the local extreme of SH, which make it can converge to global extreme at a high rate of speed in solving the problems of quadratic function optimization.

这种方法结合了共轭梯度法的快速收敛和随机爬山法的全局收敛的优点，在求解二次函数极值的问题上具有收敛速度快，并能收敛到全局极值的特点。

In the specific quantum numbers configuration of holon-isospin excitation where the excited momentum approach to the ground state, the dispersion relations can be expected as a quadratic dispersion, so we can define the effective mass of the spin wave excitation.

在激发能动量接近基态的特殊的isospin 量子数选取下，可以把色散关系看成为二次函数的形式，由此得到了有效质量与能隙、激发态动量的关系。

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。