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A revised branch and bound algorithm based on the idea of Horst (1976) is developed to minimize the tangent plane distance function to determine the thermodynamic stability of a postulated solution for the liquid phase equilibrium described by UNIQUAC or UNIFAC activity coefficient equations.

分支限界法是近年来发展起来的一种用于求解全局优化问题的确定性算法。在本文中，针对由UNIQUAC或UNIFAC活度系数方程描述的液相稳定性分析问题，我们发展了一种用于最小化切平面距离函数的改进的分支限界法。

By using tangent plane as local approximation of the security region boundary, computational cost for voltage stability online monitoring was greatly reduced on the premise of precision guarantee.

应用切平面作为该域边界的局部近似，进行电压稳定性的实时监控，从而在保证计算精度的前提下节约计算代价。

By means of the fractions of the equation of the non一ideal constrained motion of the particle along the plane curve on the tangential direction and normal direction,the motion speed expression of the particle under this condition is derived,the constrained counter force is further gained,thus some non一ideal constraint problems are solved from the given angle.

通过质点沿平面曲线的非理想约束运动方程在切线和法线方向上的分式，导出质点这一条件下的运动速度表示式，并进一步求出其约束反力，从一定角度解决一些非理想约束问

Inner layer heterogeneity, plane heterogeneity and microfacies heterogeneity are studied by using heterogeneity parameters: permeability variance coefficient, permeability tantivy coefficient and permeability differential.

应用渗透率的变异系数、突进系数和级差来分析储层层内、平面非均质性与各微相的非均质性。

In chapter two, based on the property of uniform plane wave, field at boundary node is expressed with field in the computation region and expanded as Taylor's series. By truncating it at second order, a concise ABC is obtained.

首先，在第二章中，利用均匀平面波的特性，将边界节点上的场用计算区域内部的场表示，利用Taylor级数展开并截断到二阶，得出了一种形式十分简明的频域二阶吸收边界条件。

The smaller ones are ca 70 nm wide and join the tectum and the larger columellae. These larger ones appear to be composed of several 70 nm in width rods. They join the distal surface of the foot layer. The proximal surface of the foot layer is marked by a white line (referred to as a junction plane) where it joins the endexine.

柱层中有种大小同的柱体，较小的宽约70 nm接盖顶层和较大的柱体，而较大的柱体是由多个宽70 nm的棒物所组成的，它们会和基层末端相，而基层顶端表面有著明显分布的白线特徵，就好像是它与外壁内层的接合面。

She said she had seen the plane flying very low over the Hudson and was shocked by how low.

她说她看到飞机在哈德逊河上非常低的飞以至于她很吃惊怎么可以这么低。

Firstly, the average equation under first,and second order of Van der pol-Mathieu-Duffing system are obtained through theatric methods. According to the stability criteria, the physical parameter plane is divided into different regions, associated with different types of steady state solutions, which are proved by employing numerical methods.

本文首先通过理论分析得到了Van der pol-Mathieu-Duffing方程在一、二阶近似下的定常解，分析了平均方程在不同参数平面内的幅值响应曲线，根据解的稳定性判据得到了物理参数平面上的分岔集以及定常运动在相应平面的分布情况，详细分析了该系统在各个区域内的动力学特性。

According to the principle of thermopile ,and the three-dimensional loop wire laying is substituted by new-style plane wire laying.

研究成果是基于热电堆的原理用新型的平面布线取代三维的线圈布线。

This paper presented a method for tracing the intersections of two implicit surfaces.the most obvious advantage of this method is: when tracing the intersections, it could quickly get the next tracing point by intersecting this square plane with the two implicit surfaces.

该方法最主要的优点是：在跟踪隐式曲面的交线时，在前一个跟踪交点已经求得的情况下，利用正方形与两个隐式曲面的交点，即可快速有效地求出下一个跟踪点，而不用涉及迭代收敛的判断。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。