几个与Ros等周亏格相关的逆Bonnesen型不等式

研究了平面卵形区域的Ros等周亏格问题,利用R~2中卵形区域的Ros定理及其加强形式,著名的等周不等式,给出R~2中卵形区域与Ros等周亏格相关的几个逆Bonnesen型不等式.     

The chiral effects on the responses of osteoblastic cells to the polymeric substrates

In order to study the chiral effects of polylactides on responses of osteoblastic cells, poly(l-lactide) (PLLA), poly(d-lactide) (PDLA), poly(dl-lactide) (PDLLA) and the stereocomplex of PLLA and PDLLA (SC) films with different stereoforms were prepared. The surface properties of the four polylactide films were tested and the osteoblastic ROS 17/2.8 cells were cultured on the films. The protein adsorption behaviors of fibrinogen and bovine serum albumin on films were studied. The cell proliferation, total protein amount, DNA content and alkaline phosphatase activity of osteoblastic ROS 17/2.8 cells were evaluated. The results showed that the protein adsorption was dependant on the type of proteins. The observation of cell morphologies revealed that the PDLA film provide an unfavorable surface for cell attachment. The total protein amount, DNA content and ALP activity were closely related to the stereoforms of polylactide films. All the levels of total protein amount, DNA content and ALP activity of ROS 17/2.8 cells on PDLA film were decreased. The racemic stereocomplex of PLLA and PDLA showed relatively higher positive effects on both cell growth and proliferation.     

从积分几何的观点看几何不等式——纪念李国平院士吴新谋教授诞辰100周年

该文先介绍一些中国数学家在几何不等式方面的工作.作者用积分几何中著名的Poincarè公式及Blaschke公式估计一随机凸域包含另一域的包含测度, 得到了经典的等周不等式和Bonnesen -型不等式.还得到了一些诸如对称混合等周不等式、Minkowski -型和Bonnesen -型对称混合等似不等式在内的一些新的几何不等式.最后还研究了Gage -型等周不等式以及Ros -型等周不等式.