多面体的

In order to solvepiecewise algebraic varieties, we propose a new method to compute an algebraic varietyon a convex polyhedron by adding hyperplanes with the method of Groebner bases. Thus,the algebraic variety on the convex polyhedron is transformed to the positive solutionsof a system of polynomials. Besides, the minimal decomposition is also obtained.

通过添加超平面技巧将Groebner基方法应用到凸多面体内任意维代数簇的计算上，从而把凸多面体内的代数簇转化为另外一组多项式方程组的正解，并且得到了该代数簇在凸多面体内的极小分解。

Then, we use the pattern method to represent the cube projection on Platonic solids, Archimedean solids and Catalan solids, and observe their dynamic variations.

在第二章至第五章，我们用切割的方法做出正立方体在正多面体、阿基米德多面体、卡塔兰多面体上的投影，并观察其动态变化。

Brown's attention was drawn to a brassy metallic rod three inches in diameter hanging down from the apex of the center of the room and at its end was attached a many-facetted red gem, which tapered to a point.

布朗的注意力被从中心的最高点顶端悬挂下来直径3 英寸象黄铜的金属竿吸引住了，而它的末端被附上许多有多面体的红色珠宝。

I will precise this concept of convex / concave volumes later because it's very important, for the moment let's come back to our definition of the portal : in this whole document it means my n-sided flat and convex polygon, but be aware that in other texts it can represent an elementary volume of the scene.

我会在后面详细分析凹凸多面体的概念因为这是很重要的。现在我们讨论入口的定义：这里入口表示一个平面的凸多边形，其他的文献中可能表示场景中间的一个基本的空间或者单元。

The discriminance methods and expression of generalized alternative optimum solutions of linear programming is given by proving that the equivalent of optimum extreme point and extreme point of optimum solution sets of linear programming and applying the theorem of convex polyhedron.

通过证明线性规划最优解集的极点与线性规划最优极点的等价性，利用凸多面体的表达定理，给出了广泛意义下线性规划无穷多最优解的判别方法及表达式。

The relationship between the orientation of tetrahedral [SO4]2- in sulfate crystals such as barite,anhydrite, epsomite and jarosite and their morphology was studied from the standpoint of crystal chemistry,and the formation inechanisin of their morphology was analysed according to the structural orientation of tetrahedral [SO4]2- and the bonding energy between [SO4]2- and metal ions [M2+] during growth.

本文从硫酸盐类晶体中负离子配位多面体的结晶方位和相互联结的稳定性出发，探讨了硫酸盐类晶体中[SO4]2-结晶方位与晶体结晶形貌之间的关系；认为[SO4]2-四面体与金属阳离子（Ba2+、Ca2+、Mg2+…）结合时，由于晶体结构和生长条件的不同，在晶体各族晶面上的叠合速率和取向不同；晶体的结晶形貌迥然有别。

In elliptic case,the compactness of"convex polyhedrons"is destinedto be true because of the"local Lipschitz continuity of convex functions",whilein parabolic case,we cannot expect convex-monotone functions have such goodproperties as convex functions.

在广义解存在性的证明中，参考椭圆情形由"凸多面体"逼近的思想，我们采用了由一种特殊构造的"凸单调多面体"逼近的途径，但在证明这种凸单调多面体族的紧性时，我们遇到了困难。

In the Ti film and the TiZr alloy film annealed at 800 ℃, there are a lot of regular hexahedron or octahedron bubbles, which are the same as the projections of equilibrium shape of their matrix crystal. With annealing temperature of 720 ℃, the bubbles in TiZr alloy annealed for 40 min are more round than those annealed for 130 min.

在800 ℃热处理后的Ti和TiZr合金中均观察到规则的六边形和八边形氦泡，对应基体材料单晶平衡外形多面体的投影。720 ℃热处理40 min后，TiZr合金膜中的氦泡比同样温度热处理130 min后的接近球形。

In aim at the complicity and high-dimensional state-space for the controlled system, it simplifies the calculation of geometric polytope by optimize with ellipsoidal approximate techniques, and the robust control effectiveness near to the optimal.

本论文所提示的基于几何理论的约束非线性控制算法是建立在最大输出允许集合的基础上，运用状态空间的有界子集表达鲁棒时优离散时间控制问题的价值函数，通过逆序计算该价值函数的水平集合，求得其所需的控制量，针对被控系统的复杂性及高维状态空间问题，运用椭球近似技术予以优化，使得几何多面体的计算得以简化，且鲁棒控制效果接近最优。

Then, the method is extended to the problems of decomposing a polyhedron with or without holes into the minimum number of terrain polyhedra, both of which are also shown to be NP-hard.

然后将证明方法推广到地形多面体剖分的问题：将一个带洞多面体或者简单多面体剖分成最小数量的地形多面体，这两个问题都被证明是NP-hard的。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新