多项式微分系统的不变直线的不同斜率的最大个数

本文证明了公式β（ｎ）＝σ（ｎ－１）＋１其中α（ｎ－１）是ｎ－１次多项式微分系统的不为直线的最多条数，βｎ）是ｎ次多项式微分系统的不变直线的不同斜率的最大个数。这里假设所讨论的多项式系统只有限条不变直线。     

On Modeling Bio-Scaffolds:Structural and Fluid Transport Characterization Based on 3-D Imaging Data

Bio-scaffolds which are most commonly open celled porous structures are increasingly used for tissue engineering and regenerative medicine. A number of studies have shown that the bulk properties of such irregular structures are poorly modeled using idealized unit cell approaches. The paper therefore uses novel image based meshing techniques to explore both fluid flow and bulk structural properties of a bone scaffold, as accurate modeling of bio-scaffolds with non-uniform cellular structures is very important for the development of optimal scaffolds for tissue engineering application. In this study, a porous hydroxyapatite/tricalcium phosphate (HA/TCP) bone scaffold has been scanned in a Micro-CT scanner, and converted into a volumetric mesh using image processing software developed by the authors. The resulting mesh was then exported to commercial FEA and CFD solvers for analysis. Initial FEA and CFD studies have shown promising results and have highlighted the importance of accurate modeling to understand how microstructures influence the mechanical property of the scaffold, and to analyze flow regimes through the sample. The work highlights the potential use of image based meshing for the ad hoc characterization of scaffolds as well as for assisting in the design of scaffolds with tailored strength, stiffness, and transport properties.