关于罗尔定理的进一步讨论

对罗尔定理进行深入系统的探讨和研究.给出在更弱条件下的各种区间类型(包括有限区间和无限区间)的罗尔定理的推广形式.     

On Pseudo-Holomorphic Curves from Two-Spheres into a Complex Grassmannian G（2, 5）

Let s ： S2 → G（2, 5） be a linearly full totally unramified pseudo-holomorphic curve with constant Gaussian curvature K in a complex Grassmann manifold G（2, 5）. It is prove that K is either 1 4 1 or 4/5 if s is non-±holomorphic. Furthermore, K = 1/3 if and only if s is totally real. We also prove that the Gaussian curvature K is either 1 or -4/3 if s is a non-degenerate holomorphic curve under some conditions.     

Cold crystallization behavior of polyamide 6 in PS‐g‐PA6 graft copolymers

TEM micrographs show that the PA grafts of PS‐g‐PA6 graft copolymers, which are obtained directly by extracting homo‐PA6 out from the homo‐PA6/PS‐g‐PA6 blends, are in the form of wormlike structure. The wormlike PA6 domains can shrink into droplets after annealing at 250 °C for 15 min. The diameter of the droplet determined by TEM and SAXS is in the range of 50–60 nm. This article reports on a unique crystallization behavior of the PA6 grafts in PS‐g‐PA6 graft copolymers. In a DSC cooling scan, PA6 grafts do not crystallize from the melt with a cooling rate of 10 °C/min. However, there is a cold crystallization peak around 65 °C in the subsequent heating scan. This cold crystallization phenomenon, which has not yet been reported in the literature till now, follows well the homogeneous nucleation mechanism and is depressed at relatively slow cooling rates (2 °C/min) or even completely eliminated after annealing within a specific temperature range. It may be caused by the slow diffusion or transport rate of the less flexible PA6 grafts to the crystal fronts when crystallization takes place around its glass transition temperature. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 65–73, 2010     

The characteristic‐based split (CBS) meshfree method for free surface flow problems in ALE formulation

A semi‐implicit characteristic‐based split (CBS) meshfree algorithm in the arbitrary Lagrangian Eulerian (ALE) framework is proposed for the numerical solution of incompressible free surface flow problem in the paper. The algorithm is the extension of general CBS method which was initially introduced in finite element framework, this is due to the fact that CBS method not only can enhance the stability, but also avoid LBB condition when equal order basis function is used to approximate velocity and pressure variables. Meanwhile, a simple way for node update and node speed calculation is developed which is used to capture the free surface exactly. The numerical solutions are compared with available analytical and numerical solutions, which shows that the proposed method has better ability to simulate the free surface incompressible flow problem. Copyright © 2009 John Wiley & Sons, Ltd.     

Synthesis of 14-Bromo and 14-Hydroxy Baccatin III Derviatives

Numerous efforts towards synthesis of anticancer drug paclitaxel (Taxol(r), 1a) with improved activities led to the modification at 13-phenylisoserine side chain and different positions of its core structure-baccatin III 1c1. At the same time, the activities of searching new taxoids for starting materials of new semi-synthetic paclitaxel analogs from Taxus spp. plant have not ever been stopped. Among these taxoids, 14?-hydroxy-10-deacetylbaccatin III 22 and 13-acetyl-9-dihydrobaccatin III …     

Two New Diterpene Alkaloids from the Roots of Spiraea japonica var. Acuta

Spiraea japonica L. (Rosaceae) is widely distributed in Yunnan Provence, P. R. China. Previous chemical investigations on S. japonica and its varieties have led to the report of 7 new atisane-type diterpenoids and 38 new diterpene alkaloids of atisine- and hetisine-type1-11. This paper describes the isolation and structure elucidation of two new diterpene alkaloids named spiratines A and B (1-2). Their structures were elucidated on the basis of 1D and 2D NMR experiments (HMQC, HMBC, 1…