正螺面与悬链面相互贴合的图解法

正螺面与悬链面是一对等距,等价曲面,它们在局部范围内经过连续弯曲(或变形)可以相互贴合,这一结论在微分几何中已有用公式推导法作出的证明。本文采用图解法解决了这一问题。图解法直接揭示了正螺面与悬链面相互贴合的几何意义,其近似程度可以满足工程上要求的精度。     

螺旋展开面计算机辅助几何设计

本文提出一种参数化绘制螺旋叶片展开图的方法及其计算机应用程序。该程序用VBA语言编写，在AutoCAD环境下运行，一旦调用，即可按给定的螺旋叶片的外径D、轴径d、螺距S，自动计算图形尺寸及确定绘图比例，从而绘出有完整尺寸的螺旋面展开图。     

Theory of a helicoidal cholesteric phase induced by an external field

We present a mean field theory to describe a helicoidal cholesteric phase for mixtures of a chiral nematic liquid crystal (LC) and a polymer chain as well as for pure chiral nematic LC molecules in the presence of a longitudinal external field parallel to the pitch axis of a cholesteric (Ch) phase. The free energy of the helicoidal Ch phase (Ch_H) is derived as a function of a usual orientational order parameter and an order parameter of the Ch_H phase. On increasing the strength of the external field, we find that the Ch phase changes to the nematic (N) phase through the Ch_H phase. Depending on the temperature and the strength of the external field, we find the second-order N–Ch_H and Ch_H–Ch phase transitions and the first-order paranematic (pN)–N, pN–Ch_H and pN–Ch phase transitions. We also predict phase diagrams in mixtures of a flexible polymer and a Ch LC molecule under the external field.     

离心通风机蜗壳流场的试验研究

本文介绍了用五孔探针对离心通风机矩形蜗壳流场进行测试的结果,得出的结论对离心通风机蜗壳的研究与改进及优化设计计算提供了试验的依据。     

Embedded minimal ends of finite type

We prove that the end of a complete embedded minimal surface in with infinite total curvature and finite type has an explicit Weierstrass representation that only depends on a holomorphic function that vanishes at the puncture. Reciprocally, any choice of such an analytic function gives rise to a properly embedded minimal end provided that it solves the corresponding period problem. Furthermore, if the flux along the boundary vanishes, then the end is -asymptotic to a Helicoid. We apply these results to proving that any complete embedded one-ended minimal surface of finite type and infinite total curvature is asymptotic to a Helicoid, and we characterize the Helicoid as the only simply connected complete embedded minimal surface of finite type in .