In this paper , we discussed k - uniform convexity , k - uniform smoothness and the dual relationship between them . at the same time we discussed near - uniform convexity , near - uniform smoothness and the dual property between them 本文讨论了k一致凸性、 k一致光滑性及二者之间的相互对偶关系，同时也讨论了接近凸性、接近光滑性及二者之间的相互对偶关系。
Criteria were derived for functions to be quasiconvex under lower semicontinuity or upper semicontinuity conditions by mukherjee and yeddy ( ref . l ) . in the first part of this paper , we generalized almost all of the results there Mukherjee和yeddy在文献[ 1 ]中，分别在函数的下半连续性和上半连续性的条件下，对于函数的各种拟凸性给出了一些判别方法。
Under the different conditions of the constrained functions , dividing constrained sets properly , and under generalized ( f , ) convexity , the theorems of the weak duality , strong duality and strictly reverse duality are testified 依所给约束函数的不同条件来恰当划分约束集，在广义( f ， )凸性下，证明了弱对偶定理、强对偶定理以及严格逆对偶定理。
It guarantees that the boundary polygons of the triangulations preserve convexity all the time during the morphing , and that the intermediate triangulation at any time is compatible with the source and target triangulations , i . e . free of self - intersection 本文方法能够保证网格边界在变形过程中始终保持凸性，且任意时刻的中间网格与初末网格同构，即不产生自交现象。
We have proved that the properties of convex risk measures can be characterized by that of the acceptable set . further more , as a case study , we considered convex measures of risk defined by the notion of bounded shortfall risk 结果证明凸性风险测度和与其相伴随的可接受集之间可相互表出的关系，进一步，作为例证研究，本文考察了以有界亏空风险的形式定义的凸性风险测度。
Furthermore , a sufficient condition for robust stability is given for closed - loop uncertain system , which is based on the convexity of optimization and can provide a guide to the choice of cost function to guarantee robust stability . 3 同时，根据在线优化问题的凸性，给出了闭环系统鲁棒稳定的一个充分条件，据此条件可为在线优化问题构造能够确保鲁棒稳定性的成本函数； 3
The algorithm uses the geometric feature of a single convex rice kernel to search the concave regions merged with rice kernels during the region growing with scanning and disconnect the regions at the concave positions in image 该方法充分利用了单个米粒图像区域为凸性区域这一几何特点，通过区域增长的方法在图像中寻找由凸性米粒靠接在一起所形成的融合凹性区，并从凹处将融合区域分离开来。
Then get the relationship between k - convexity and near - convexity and the relationship between k - smoothness and near - smoothness . so we simplified the proposition " k - uniform convexity is near - uniform convexity ' , which had been proved by yu xin - tai in reference [ 39 ] , and got some new results 简化了俞鑫泰关于k一致凸空间是接近一致凸空间的证明，并且给出了其它k -凸性和接近凸性、 k -光滑性和接近光滑之间的关系，得到了一些新的结果。
On the basis of cash flow analysis , this dissertation offers the key methods of cmo pricing , for example , discounting cash flow method and option - adjusted spread ( oas ) analysis . additionally , ir also contains a deep analysis of cmo duration and 在现金流分析的基础上，本文探讨了cmo证券的定价方法，如现金流折现法、选择权调整利差法（ oas分析） ，另外，本章对cmo证券的持续期和凸性也进行了深入分析，给出了它们存在提前还款条件下的求解方法。
2 . reliability of rock slope was done using responding surface method ( rsm ) and monte - carlo method ( mcm ) respectively . reliability index 0 calculated by rsm and mcm are different , which indicates the non - convexity of limit state curved surface in representation of stability of slope 采用响应面法( rsm )和monte - carlo法( mcm )对边坡进行了可靠度分析，两者计算所得的可靠指标存在着一定的差异，这表明：代表边坡稳定的极限状态曲面存在着非凸性。
