空间曲线

The unsaturated and compacted soil triaxial test result under constant suction describes the unsaturated soil critical state surface in p-q-s three dimensional space: in p - q plane, the slope M of critical state line is independent of suction; the cross line of LC yield surface and critical state surface is a curve with extremum in three dimensional stress space, and its projection in p-s plane is located in quadrant 1 in triaxial compression state; its projection in q-s plane has asymptote, and there should also be asymptote in respect of the curve that stands for the function relationship between cohesive and suction.

基于局部变形测量的常吸力非饱和压实土三轴剪切试验结果，全面描述了非饱和土p—g—s三维应力空间中临界状态面的合理形态：在p—q平面，临界状态线斜率M是与吸力无关的物理量；临界状态面与LC屈服面交线在三维应力空间中是一条存在极值的曲线；该交线在p—s平面的投影曲线在三轴压缩应力状态下应位于第一象限；该交线在q—s平面的投影曲线应存在渐近线；反映凝聚力与吸力关系的函数曲线也应存在渐近线。

Discusses algebraically and geometrically the properties of the ruled surfaces in the Euclidean three-space, especially, the principal normal surfaces on which there are some special curves, such as Mannheim curves, Bertrand curves and general helices.

在三维欧氏空间中，作为特殊曲线，Mannheim曲线、Bertrand曲线以及一般螺线具有良好的几何和代数性质。讨论了三维欧氏空间中特殊曲线的主法线曲面。

In this paper,We define the notions of lightcone Gauss map ,lightcone pedal curve and lightcone height function of a spacelike curve in Minkowski 4-space, and established the relationships between singularities of these objects and geometric invariants of curves under the action Lorentz group ,and as an applications of standard techniques of singularity theory classified singularities of a spacelike curve in this space .

在本文中我们定义了四维Minkowski空间内类空曲线的光锥高斯映射，光锥垂足曲线，光锥高度函数的概念，建立了这些对象的奇点与在洛仑兹群作用下曲线的几何不变量之间的关系，并且运用奇点理论的标准工具对该空间中类空曲线的奇点进行分类。

In this paper,We define the notions of lightcone Gauss maps ,Hghtcone pedal curves and lightcone height function of a spacelike curve in Minkowski 4-space, and established the relationships between singularities of these objects and geometric invariants of curves under the action Lorentz group ,and as an applications of standard techniques of singularity theory classified singularities of a spacelike curve in this space .

在本文中我们定义了四维Minkowski空间内类空曲线的光锥高斯映射，光锥垂足曲线，光锥高度函数的概念，建立了这些对象的奇点与在洛仑兹群作用下曲线的几何不变量之间的关系，并且运用奇点理论的标准工具对该空间中类空曲线的奇点进行分类。

For a monotone twist map the well-known Birkhoff fixed point theoremsays that the circles with rational rotation number will break up whence a finitenumber of pairs of periodic points arise,half of which are elliptic and the othershyperbolic.Moreover,around each elliptic periodic point a few of new invariantcurves will appear and make a picture of phase space with a self-similar structure.Again one may ask is there a similar picture for higher dimensional Hamiltoniansystems?

对于单调扭转映射，著名的Birkhoff不动点定理指出，在通有情况下旋转数为有理数的不变曲线一般会破裂，在原来的不变曲线附近会产生有限多对周期点，其中一半是双曲的，一半是椭圆的，而在椭圆型周期点的周围又会产生一圈圈的不变曲线，使得椭圆周期点附近的动力学行为和整个相空间的动力学行为十分相象，换句话说，整个相空间具有无限嵌套的自相似结构，自然又产生了一个问题：对于自由度数目大于2的高维哈密顿系统，其相空间是否有类似的图象？

The results showed that the semivariogram of S.granarium was described by a spherical model,and indicated an aggregated special pattern ranging from 21 to 61cm. The semivariogram of Aphidius sp.could be also well described by spherical model, and indicated an aggregated spatial pattern ranging from 36 to 55cm.The amount and spatial distribution of Aphidius sp. w...

结果表明，不同时期麦二叉蚜种群的半变异函数曲线皆为球型，其空间格局为聚集型，变程在 2 1～6 1cm之间；蚜茧蜂种群的拟合半变异函数曲线也表现为球型，呈聚集空间格局，空间变程在 36～ 5 5cm之间，并与麦二叉蚜种群在数量和空间上有较强的追随关系，说明蚜茧蜂种群是麦二叉蚜种群的优势种天敌。

The shell roof of steel structure on the site of Jinsha in Chengdu is the truss structure with unstiffen tubular joints ,and the chords of circumferential truss are irregular space curves.

成都金沙遗址大棚钢结构工程为圆钢管相贯节点桁架结构，环桁架弦杆为不规则空间曲线，通过采取弯管与胎具双重控制的方法，使环桁架尺寸得到精确控制；由于施工条件限制，采取了钢丝绳加固、结合已有结构辅助的方法将平面桁架移动到指定位置。

Tubular belt conveyor is a kind of new material conveying system and have many characteristics such as good seal environmental protection, the conveying line curving to arrange along the space, big transport obliquity, a long stand-alone distance at sophisticating geography term and have many advantages, for instance, low construction cost, convenient installation and maintenance convenience, dependable usage etc.

管状带式输送机是一种新型物料输送系统，具有密封环保性好、输送线可沿空间曲线灵活布置、输送倾角大、复杂地形条件下单机运输距离长等特点，同时还具有建设成本低、安装维护方便、使用可靠等优点。

Because there is no GRIP function which can scan along the special curve, so the method of suturing the free surface with the bounded-plane is applied to solve this kind of sweep problem.

因没有沿空间曲线扫描的GRIP函数可供使用，故采用缝合自由曲面与有界平面的方法来解决这个问题。

Because of dipping bed during drilling process,the wellhead crossed trace of well is no longer vertical line,but is the spatial curve,which resulted in deviation of first break time used by cross hole tomographic calculation,affecting the imaging precision.

在钻井过程中由于地层倾斜等原因，导致井的轨迹不是过井口的垂线，而是一条空间曲线，这就造成井间地震成像计算所用的初至旅行时存在偏差，影响成像精度。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。