A proportional view: The mathematics of James Glenie (1750–1817)

The mathematical work of James Glenie (1750–1817) was published at irregular intervals during a turbulent life. His ideas, mostly deriving from his time as an Assistant in Mathematics at St Andrews University in Scotland, were developed intermittently over a period of thirty-seven years. His mathematical achievements, underestimated by previous historians, were deeply rooted in Euclidean geometry and his own generalized theory of proportion. Among them are many new geometrical constructions and proofs, a novel demonstration of the binomial theorem, and an alternative approach to the differential calculus.     

Orientation-dependent depletion interaction in rodlike colloid-polymer mixtures

Depletion interaction in a suspension of rodlike colloids with added non-adsorbing polymer coils is theoretically studied. We calculate an overlap volume of depletion zone between two rodlike colloids, based on the second virial approximation. We examine nematic-isotropic phase transition (NIT) and two-phase coexistence between an isotropic and a nematic phase at low polymer concentrations. We find that the depletion interaction is dependent on the orientational order parameter of rodlike colloids and leads to a decrease in the NIT concentration on the addition of polymer. The coexistence curves have a leaning-chimney shape and are shifted to lower rod concentrations on increasing the polymer concentration. Received 23 May 2001 and Received in final form 18 July 2001     

Heavy sterile neutrinos: bounds from big-bang nucleosynthesis and SN 1987A

Cosmological and astrophysical effects of heavy (10–200 MeV) sterile Dirac neutrinos, mixed with the active ones, are considered. The bounds on mass and mixing angle from both supernovae and big-bang nucleosynthesis are presented.     

一组适合于带纵向裂纹柱体圣维南扭转的等参数元素

本文给出一组新的适合于带纵向裂纹柱体圣维南扭转的等参数元素,它们分别是八结点等参数元素、在裂纹尖端具有r-1/2奇异性的“1/4”八结点等参数元素及八结点过渡元素.利用这些元素,对含有径向纵裂纹的圆柱体进行了圣维南扭转计算.计算结果表明,本文给出的等参数元素有较高的精度、较好的收敛性及快的收敛速度,同时还具有程序简单、省机时等优点,所以特别适合于实际的工程计算.