凸点

Mixed monotone operator; Singular two-point boundary value problem; Generalized e-concave operator; Generalized e-convex operator; Mixed monotone multivalued operator; Fixed point

基础科学，数学，数学分析混合单调算子；奇异两点边值问题；广义e-凹算子；广义e-凸算子；混合单调多值算子；不动点

Based on nonsmooth analysis theory, the viability criterion is verified under the condition that the set-valued mapping in the right hand side is a polytope and the boundary function of the region is subdifferentiable and its subdifferential is a convex hull of finitely many points.

当右端集值映射为多面体，边界为次可微函数，且次微分为有限点集凸包时，基于非光滑分析理论，给出了在一点处检验生存性条件是否成立的方法。

Seed cones borne in groups of 1-6, globose or subglobose, 0.9-1.6(-2.5)× 1-2(-2.5) cm; cone scales 20-30, proximal 2 margins often convex in outline, or all 4 margins ± concave in outline, middle part with or without distinct shoulders at widest point, apex usually recurved, umbo rhombic, distally with 4 or 5(-7) toothlike projections 1-3.5 mm. Seeds 2-5 per cone scale, brown or dark brown, irregularly ellipsoid or multiangular and ± compressed, 4-6.5 × 2-3.5 mm; wings 0.2-0.25 mm wide.

1-6个中的成群忍受的球果，球状或近球状， 0.9-1.6(-2.5)* 1-2(-2.5)厘米；珠鳞20-30，轮廓的下部的2个边缘通常凸面，轮廓的或全部4个边缘多少凹面，有或没有在宽点的离生的肩的中部，先端通常下弯，鳞脐，上部每珠鳞具4或5(-7)种子2-5 1-3.5毫米的齿状预测， 4-6.5 * 2-3.5 毫米；翅0.2-0.25毫米宽。

In this paper, the problem of an iterative sequence approximation a common fixed point for nonexpansive non-self mappings is studied in real uniformly convex Banach space, then we obtain a strongly convergence theorem.

在实一致凸Banach空间中，讨论了关于非扩张非自映射序列逼近公共不动点的问题，获得了一个强收敛定理，改进和推广了现有文献的一些相应结果。

For example, U-space is uniformly regular and which makes it has fixed point property, U-space is uniformly non-square and thus super-reflexive, uniformly convex space and uniformly smooth space are U-spaces, and an Banach space is an U-space iff its dual space is U-space, etc. In1990s, a lot of work had been done on U-space theory, e.g., Tingfu Wang and Donghai Ji introduced the concepts of pre U-property and nearly U-property. Under the structure of Orlicz space, they made systematic investigation of these properties, and gave the criteria for an Orlicz space to have U-property.

U-空间具有一致正规结构进而具有不动点性质；U-空间是一致非方的，进而也是超自反的；一致凸空间和一致光滑空间是U-空间；Banach 空间为U-空间的充要条件是其对偶空间为U-空间，等等。20世纪90年代，国内外学者对U-空间理论做了很多工作，王廷辅，计东海等人先后引入了准U-性质与似U-性质的概念，并在Orlicz空间框架下对有关性质进行了系统研究，完整给出了Orlicz空间具有各种U-性质的判据。

Since the lengths of the line segments and the angles between line segments are treated as representation parameters, it is convenient to construct energy function and to deal with displacement and length constraints. Based on this advantage, a parametrical model for human body is proposed, which can easily produce human body models with different feature sizes. The above method is just suitable for polylines. Therefore, a generic deformation method for both discrete curves and surfaces is presented. The energy function is constructed by analyzing the relationship of the points before and after deformation. Together with the displacement constraints, the deformation problem is converted to a convex quadratic programming. A necessary condition for constraint points and a sufficient condition for the uniqueness of solution are given. The proposed method can be combined with skeleton-driven animation to control the deformation.

将线段长度与线段之间的角度作为表示参数，既有利于能量函数的构造，又便于处理位移约束和长度内蕴约束条件，利用这一优势，将其应用于三维人体的参数化建模，可以方便地产生具有不同特征尺寸参数的人体模型，由于这种方法只适用于折线变形，具有较大局限性，因此，本文进一步提出一种较通用的离散曲线曲面变形方法，通过分析变形前后的位置关系来构造能量函数，再加上位移约束条件，将变形问题转化为一个凸二次规划问题，并且给出了约束点应满足的必要条件及模型解唯一的充分条件，这种方法还可以与骨架驱动变形的思想相结合，能更好的控制变形。

For a class of nondifferentiable generalized fractional programming problems with the norm \$‖Bx‖\-p\$ in the objective function involving, a new incomplete Lagrange function is given, and the saddle point optimal criteria are proven by using the existing necessary optimality conditions, under the assumptions of the class of generalized (\$F,α,ρ,d\$)-convexity.

对于一类目标函数中含范数‖Bx‖p的非可微广义分式规划，给出了一个新的非完全Lagrange函数，并利用已有的最优性必要条件，在一类广义-凸性的条件下，证明了鞍点最优性准则。

Seed horizontal or oblique, black, sublustrous, lenticular, ca. 2 mm in diam., distinctly granular pitted, rim margin obtuse or acute; perisperm scant.

种子水平或偏斜，黑色，近有光泽的，透镜状，直径约2毫米，清楚颗粒状具洼点，凸缘边缘钝或锐尖；外胚乳不够。

Therefore, the research of pointwise properties showed the great significance.

因此，点态凸性的研究有重要的意义。

First of all, we present the development background and process of covex theories and geometric properties of Banach spaces, the significance of pointwise geometric constants and geometric constants of spaces, and we provide discu-ssion of content of each part of the paper.

首先，本文详细叙述了Banach空间凸性理论与空间几何性质的发展背景和进程，及空间几何常数与点态几何常数的研究意义，并给出了本文各部分所讨论的内容。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。