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With the result of convergence we derive a computational formula of subdivision depth for Catmull-Clark surface.

而且，推导出一个计算细分后控制网格到Catmull-Clark曲面的距离公式。

The rules include not only the complete procedures to construct the three-powered interpolation used by Shoushi Computus in calculating the solar, lunar and planetary equations of center, but also the detailed routines, namely the Geyuan Shu (the procedure of circle division), to derive the table contained in the Shoushi Computus for transferring the pseudo-ecliptic longitudes of the sun into equatorial coordinates, which turns out to be compatible with the results obtained with spherical trigonometry.

从总体角度来看，他在《授时历》立法原理方面的工作已经超过了嘉靖年间顾应祥和周述学等学者的工作，不过，在弧矢割圆术中应用的高次方程解法方面，邢云路的工作则可能直接受到了顾应祥、周述学等学者相关工作的影响，而且邢云路在高次方程解法方面也没有超出明代历算家对高次方程数值解法的认识水平。

Some choanal polyp derive from concha nasalis media, endoscopic sinus surgery is a good method for treatment.

部分鼻后孔息肉发源于中鼻甲，鼻内窥镜手术是治疗的较好方法。

It is the first time to derive the pesudo-steady-state flow equation of gas condensate involving non-darcy flow of gas.

这些发现对研究高含蜡凝析气相变特征和生产动态具有重要的理论和应用价值。

Under the condition of the steady flow, by means of conformal transformation , the authors derive a production formula of a horizontal well in the center of a reser.

文中在保证地层内具有稳定流动的基础上，利用保角变换对顶底不渗透油藏中心有一口水平井的产量公式进行了重新推导，给出了水平井产量公式的修正公式，并且利用等值渗流阻力法进行了解

We suggest a consistency principle to derive velocity models. It states that we should search for an imaging velocity field that yields the same image position independent of source or receiver position.

建议用一个相容原理来导出速度模型，这就要求寻找一个合适的成像速度场，该速度场不受震源和接收器位置的约束而有相同的成像位置。

In this paper,using life annuity theory combining with State Department's 'the decision of establishing consolidated corporation employee pension system',we derive the actuarial model of measuring fund gap in the fundamental pension insurance.

根据1997年国务院《关于建立统一的企业职工基本养老保险制度的决定》文件，利用生存年金理论得到测算我国基本养老保险基金缺口的精算模型。

Derive the equations of continuity by using the method of infinitesimal based on the mass balance equations and the differential equations of gas and oil phase fluid flow.

再根据物质平衡原理，利用微元法分析凝析油气渗流规律，建立连续性方程，从而导出凝析油气渗流微分方程。

As to the risk model with random premium rate, we concerned with discrete random variable, continuous random variable and general random variable. We derive the formula of ruin probability, the extreme during the total duration of negative surplus and the joint distribution of the surplus immediately before ruin and the deficit at ruin.

对于保费率为随机变量的一类风险模型，本文就离散的随机变量、连续的随机变量、一般的随机变量三个方面进行讨论，运用概率方法和风险理论的方法推导出破产概率、末离前最大盈余分布、破产前瞬时盈余与破产赤字的联合分布等精算量分布的一般公式。

The third part has tried to analyze the universality and diversity in syntacticdistributions among Shi Shi, Bu Shi , Shi Bu Shi , statement adverbs and descriptionadverbs. Pointing out the function doubleness (embody the statement and description)derive from the semantic doubleness (embody the meanings of "Chang Chang and PinPin),The three words bridge the function of statement adverbs and descriptionadverbs,the part also points out that the "Shi Shi "shoud be divided into "Shi Shi1"whichexpresses continuousness and"Shi Shi2 which expresses repeatlity.

第三章对"时时"、"不时"、"时不时"同判断类频率副词与描写类频率副词分别进行了句法分布上的比较分析，指出这三个词功能的双重性来源于它们语义的双重性(既有"常"类副词的意义，又用"频"类副词的意义)，指出了它们在频率副词系统中所起到的桥梁作用；并对"时时"作了表延续义的"时时_1 "和表重复义的"时时_2 "的区分。

No complex distressful things on your mind but only our love and care for each other.

无复杂痛苦的事情，对你的心，但只有我们的爱和照顾对方。

At first light, on his own initiative, Vick located the enemy emplacements andfired on them, using 15 rounds.

破晓时分，维克主动地去查找敌军的炮位并向它们开火，打了15发弹药。