凸的

In view of that conventional algorithms of collision detection spend a lot of detection time on complex polyhedrons, an algorithm to divide a convex polyhedron was presented and proved.

针对传统的碰撞检测算法对于复杂多面体之间的碰撞检测时间过长的缺陷，提出并证明了一种凸多面体的剖分算法，该算法能将复杂的凸多面体剖分为简单四面体，利用基于MPI(Mes-sagePassingInterface)并行处理的方法来提高碰撞检测的实时性。

The pattern of camber die-drawing are optimized. The physical innate character of drawing with camber die is analyzed thoroughly. For the first time, the periodical relation between the limit drawing coefficient and the large longitudinal stress in dangerous section is established. Furthermore, the rationale to judge limit deforming degree is developed. Then, the limit drawing coefficient of drawing with camber die is proposed. Based on the criterion that the large stress in flange is smaller than that of limit value, the formula of drawing with camber die without wrinkles is deduced.

对拉深凹模的型式进行了优化；深入地分析了曲面凹模拉深成形的物理本质，首次定量地确定了极限拉深系数与危险断面最大径向应力的关系，提出了判断极限变形程度的依据，分析了极限承载能力，建立了曲面凹模拉深的极限拉深系数的表达式；以凸缘切向最大压应力小于凸缘切向压应力临界值为准则，推导出了曲面凹模拉深不起皱的理论表达式。

The peak of the bulge accorded with the vertical line through the posterior convexity of superior articular surface of atlas. The superimpose rate of the vertical line with the M line were 48% to left and 65% to right. The surplus existed in l～2mm to lateral of M line. The exit point of screw was the median point of vertical line on the anterior cortex of lateral mass. The superimpose rate of BB line the line linked with the

寰椎后结节中点及上关节突后凸尖下的骨质弧形隆起的顶点可作为寰椎椎弓根螺钉进钉点的准确标志，上关节突后凸尖及横突尖可作为寰椎椎弓根进钉点的大体标志；沿寰椎椎弓根轴线进钉较为安全，内倾17°，仰角变异大，出钉参照前结节顶点；椎动脉沟中外的厚度及进钉点处寰椎后弓的高度是寰椎椎弓根螺钉固定的主要限制性因素。

In order to study vector-valued optimization problem, in chapter 5, a class of vector -valued function, that is, uniformly same-order set-valued function is introduced , which includes the separated functions as its proper subset; without hypothesis of convexity, new minimax theorem and saddle point theorem for uniformly same-order set-valued function are established. Next, by employing Ky Fan\'s lemma and H-KKM mapping , several existence results for generalized vector equilibrium problem established.

为了研究向量优化问题，作为可分函数的推广，第五章引入了一致同阶集值函数类，在没有凸性条件的假设下，对一致同阶集值函数建立了新的极小极大定理与鞍点存在定理；利用H-KKM映射，对一般向量均衡问题建立了(来源：A73BcbC论文网www.abclunwen.com)几个存在性定理；最后讨论了集值向量均衡问题系统，利用集值映射的拟凸性，在较弱的条件下证明了解的存在性。

Polymethyl methacrylate is the most used filling materials at present; There is not significant difference between unipedicular and bipedicular vertebroplasty; Using vertebral body venography and appropriate dense bone cement can reduce leakage of bone cement; Bolster for self-replacement can rebound vertebral body height, and balloon kyphoplasty and sky bone expander kyphoplasty can be avoided; In order to reduce refracture of vertebral body, anti-osteoporosis drugs should be used in the treatment of percutaneous vertebroplasty.

聚甲基丙烯酸甲酯是目前最常用的填充物；单侧注射和双侧注射疗效没有明显差别；应用对比剂及掌握合适的骨水泥黏稠度可以减少骨水泥的渗漏率；成形前腰部垫枕自身复位可以恢复椎体的高度，避免采用操作复杂及价格昂贵的球囊后凸成形及骨膨胀椎体后凸成形；进行经皮椎体成形时应该配合应用抗骨质疏松药物，以减少椎体再骨折的发生。

The existence theorem of generalized weak efficient solutions with respect to variable, cone for a linear G〓teaux differentiable mapping is proved with set valued mapping fixed-point theorem and the relation between a vector optimization and a variational inequality problem. The existence of weak efficient solutions for multi-objective convex vector optimization is characterized.

建立映射在线性G〓teaux可微条件下关于可变锥的广义弱有效解的存在性及多目标凸向量优化问题在G〓teaux可微条件下弱有效解的特征，利用集值映射不动点定理及向量优化与变分不等式的关系证明线性G〓teaux可微锥凸映射关于可变锥的广义弱有效解的存在性定理。

By applying existence theorems of maximal elements for a family of GB-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces.

通过应用G-凸空间的乘积空间内一族GB-优化映象的极大元的存在定理，在G-凸空间的非紧设置下证明了某些重合点定理，Fan-Browder型不动点定理和极小极大不等式组的解的存在性定理。

First,a proposition is presented:for a general kind of biobjective deci-sionmaking problemin real linear topological space satisfyiny someuniversal convexity assumpltions,the Pareto frontier is a piece-wise smoothconvex curve,each piece being either a Ⅰ-curve or a Ⅱ-curve.

对于满足一般凸性假设的实线性拓扑空间上的双目标决策问题，本文提出了"其非劣前沿为分段光滑的凸曲线，每一段要么是工型弧线，要么是直型弧线"的观点，据此详细研究了决策人的偏好与加权和问题之间的关系，提出了4种对话式决策方法，这些方法既适用于一类静态双目标决策问题，又可适用于一类双目标控制问题。

By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem,several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces.

应用局部凸H－空间内具有闭零调值的上半连续集值映象的Fan－Glicksberg型不动点定理和极大化定理，对无限最优化总理2和约束对策问题在没有线性结构的局部凸H－空间内证明了解的某些新的存在定理，这些定理改进和推广了最近文献中的许多重要结果。

In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.

在巴拿赫空间理论中，Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一，分隔性定理是Hahn-Banach定理的重要应用，本文利用&超平面&的方法，改进了一个分隔性定理的证明；另外，本文利用邻域的&平移&方法，给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷