Reducible Dupin submanifolds

Pinkall's standard constructions for obtaining a Dupin hypersurface W in ^N from a Dupin hypersurface M in ⁿ , N>n, are studied in the context of Lie sphere geometry. It is shown that a compact Dupin hypersurface W in ^N with g distinct principal curvatures at each point is reducible to a compact Dupin hypersurface M in ⁿ if and only if g=2.This research was supported by NSF Grant No. DMS 87-06015.     

Intra- versus intermolecular hydrogen bonds in salicylamide derivatives

The crystal structures, solid-state infrared patterns, and thermal properties of two polymorphs of 4-nitrosalicylanilide are presented. In both polymorphs, intramolecular hydrogen bonds are found between the phenol oxygen and the amide proton, and intermolecular hydrogen bonds are found between the amide carbonyl oxygen and the phenol proton. These hydrogen bond patterns are compared to those found in other known salicylamide derivatives and an analysis is given of the factors contributing to preferences for intra- or intermolecular hydrogen bonds in these structures. Crystal data: polymorph, orthorhombic,Pbca,a=11.003(4),b=27.959(7),c=7.622(5) Å,Z=4,V=2345(3) ų, andR=0.038 (1351 reflections); polymorph, monoclinic,P2₁/a,a=28.36(1),b=11.64(1),c=7.293(8) Å,=90.68(6)°,Z=8,V=2408 ų, andR=0.043 (2425 reflections).     

Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails. Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.     

男性型秃发患者发中K,Na,Ca,Mg元素含量分析

采用火焰原子吸收法对３０例男性型秃发患者及３８例毛发健康男性对照者发中宏量元素Ｋ、Ｎａ、Ｃａ、Ｍｇ的含量进行了测定。结果表明，男性型秃发患者发Ｋ含量明显高于对照组，具有统计学上的显著差异（Ｐ〈０．０１）。发Ｎａ、Ｃａ、Ｍｇ含量在两组间未见显著差异（Ｐ〉０．０５）。本文提示，体内某些宏量元素变化对男性型秃发可能产生一定影响。     

Study on structural variation of silica gel using Nd3+ as a probe by photoacoustic spectroscopy

The structural variations of silica gels heated at different temperatures have been firstly studied using Nd(3+) as a probe by photoacoustic spectroscopy (PAS), together with IR spectroscopy and thermal analysis. With increasing temperature, the f-f transitions of Nd(3+) show a red shift and the PA intensities increase. The PA branching vector of the transitions from ground state to 4G(5/2)+(2)G(7/2), which are hypersensitive transitions, increase and the others decrease or change little. These indicate that the covalency of the bond that Nd(3+) forms increases and the symmetry around Nd(3+) decreases, which reflects the structural variations of silica gels.