光滑的

Let G be the domain whose inverse image is the cross section of u definedin (H1) where the mapping is affine,g and ψ are smooth functions and g＞0,thenthere is a unique smooth convex-monotone function which satisfies the followingproblem 〓Furthermore,if 〓 where C is a constant,ψis an affine function,〓 is astrictly interior sub-domain of G in the sense of"parabolic distance",then

若G为按（H1）中定义的u的截影经仿射变换而得的区域，g和〓为光滑函数且〓，则〓存在惟一的凸单调光滑解。若〓常数，〓仿射函数，〓为G在"抛物距离"下的严格内子域，则

G^k continuous piecewise algebraic blending surface patches are obtained by solving the system via the generator basis algorithm of module over polynomial ring.

借助围绕一个顶点处的代数曲面光滑拼接条件，利用多项式环上的素模中的生成基方法，给出了凸组合和非凸组合情形下三个坐标平面间的的任意阶几何连续的光滑拼接方法。

The compositions and FTIR spectral characteristics of hydrolysis product were studied using GC and FTIR. The results indicated that ASP3 is a kind of pectic polysaccharide which contained the main part of homogalacturonan fragments as "smooth regions" with galacturonic acid and rhaminose, and rhamnogalacturonan segments as "hairy regions" backbone. Galactose, arabinose, mannose and glucose were linked as arabinogalactan, galactan and arabinan, which were the mainly constitution of the branch.

实验结果表明，ASP3是一种果胶多糖，主要由光滑区和毛发区（富含中性糖侧链的鼠李半乳糖醛酸聚糖）两部分组成：GalA和Rha位于多糖分子的主链，由于Rha含量较低，大部分GalA相连形成半乳糖醛酸聚糖光滑区；Gal、Ara、Man及Glc位于多糖分子的支链，其中Gal以较高的聚合度与主链相连，Ara以还原性末端或低聚寡糖的形式与主链相连或与半乳聚糖末端相连形成阿拉伯半乳聚糖。

Key words:the three dimensional contact problem with friction;nonlinearcomplementary;nonsmooth equations;generalized derivative;nonsmoothmethod;convergence analysis

给出了三维摩擦接触问题的一个非光滑混合不动点模型及算法，这种算法无须求导数，没有引进任何额外变量，并且可视为一种三维摩擦接触问题的迭代法，利用非光滑分析和不动点理论对算法做了分析，给出了算法的不动点理论背景及算法的理论分析，为模型解的存在性及算法收敛性提供分析依据，最后给出了相应的数值算例。

By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth L-M method based on the subdifferential.

将概率最优潮流表述为随机非线性规划问题后，利用非线性互补函数将该问题的KKT条件进行转化，基于转化后的非线性代数方程组，利用一次二阶矩法确定了以待求量的数字特征表示的概率最优潮流模型，由于该模型包含不光滑函数，因此采用基于次微分的半光滑L-M方法求解。

Based on the theory of B spline,this paper discusses the sufficient and necessary conditions of G 1 continuity between two patches of bi cubic tensor product non uniform B spline surfaces in a special type,and gives a kind of sufficient condition of G 1 continuity so as to satisfy the need of application.

依据有关B样条理论，研究了一种特定类型的双三次张量积非均匀B样条曲面间G1光滑拼接的充要条件，且给出了此种类型的两张双三次张量积非均匀B样条曲面间G1光滑拼接的一个充分条件，以满足实际应用的需

Insection 4.3, semi-discrete and fully discrete Fourier spectral and pseudo-spectral schemes are constructed. The convergence and stability for the schemes are proved, and the error estimates are obtained.Chapter 5, consider the damped coupled generalized nonlinear wave equations. In section 5.2, by coupled a priori estimates and Galerkin method, prove the existence and uniqueness of the global smooth solution for the periodic initial value problem and obtain the existence of global attractors.

第四章，考虑一类具耗散的广义KdV方程组的周期初值问题，在第二节中证明了整体光滑解的存在性和唯一性，得到整体吸引子；在第三节中构造了半离散和全离散的Fourier谱格式和拟谱格式，在整体光滑解存在的条件下，证明了这些格式解的收敛性，并得到了误差估计。

The unsmoothed characteristics of some living beings in soil have wear reduction and wear resistance function . The research benefits the revelation that a tungsten carbide reinforced Cu-base alloy wear-resistant composite coating was produced on mild steel by spark plasma sintering.Under the condition of two bodies abrasive wear ,the coating with the structure that hight hardness and good wear resistance WC particles embedding in tough fine Cu-base alloy matrix resist the abrasion wear and manifest the good wear reduction and wear resistance properties that the unsmoothed bodysurface of some living beings in soil have.

本研究受到某些土壤动物体表非光滑几何特征具有减磨、耐磨特性的启示，应用放电等离子烧结工艺，选取具有优良塑性的Cu基合金作为复合层基体，硬质点WC颗粒作为增强相，在碳钢表面形成WC\ Cu基合金耐磨复合层，在两体静载荷磨粒磨损条件下，高硬度、耐磨WC颗粒镶嵌在高塑性的Cu基合金基体中，共同抵抗磨粒的磨削，表现出某些土壤动物体表非光滑几何特征所具备的优良减磨、耐磨特性。

The objects surface often possesses some particular continuities, so it is indispensable to be able to control the desired continuities between adjacent NURBS patches.

物体的表面一般都具有一定的光滑性，因此拟合小曲面片的这些NURBS曲面之间就必须达到一定程度的光滑连接。

A smooth approximation algorithm is then proposed based on hinge-finding algorithm via curved faces approximated to the hinging hyperplanes model, which can obtain a smooth approximation result and hold some good properties of hinge-finding algorithm such as simplicity and effectiveness.

本文对找链接算法做了两点改进，其一是扩充了链接超平面模型，在二维空间上弥补了链接超平面模型表示能力不足这一弱点。仿真实验显示使用扩充后的模型得到了更好的分片线性逼近结果。另一点改进是使用双曲光滑函数构造出了基于找链接算法的光滑逼近算法。理论分析证明了算法的可行性。仿真实验验证了理论分析。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。