Generic curve families on 2-dimensional manifold

In the last paper [1] we show the local classification of generic curve families defined by symmetric bilinear forms on a compact 2-dimensional Riemannian manifold M. Here we give the definition of generic symmetric bilinear forms similarly to the definition of a Morse-Smale vector field in flows on M. The Morse-Smale theory is shown in [2],[3],[4],[5]. And we show that generic symmetric bilinear forms make open, dense and structural stable subset in bilinear forms on M.Article信州大学理学部紀要 27(1): 1-6(1992)departmental bulletin pape

Curve families on the plane defined by linear matrix fields

We give the topological classification of curve families on R2 that is given by the set of integral curves of the eigen space field of a matrix field where component functions of the matrix are linear functions.Article信州大学理学部紀要 29(1): 1-7(1994)departmental bulletin pape

Weighted Trace Functions as Examples of Morse Functions

Article信州大学理学部紀要 6(2): 85-96(1972)departmental bulletin pape

Singular points of curve families on surfaces

Article信州大学理学部紀要 20(1): 1-11(1985)departmental bulletin pape

Starfish saponins, 45. Novel sulfated steroidal glycosides from the starfish Astropecten scoparius

Five sulfated steroidal glycosides were isolated from the aq. exts. of the whole bodies of the starfish A. scoparius. One of them was identified as indicoside B, a sulfated steroidal xylofuranoside previously isolated from A. indicus, and the remaining 4 are new compds. Three of them, scopariosides A, B, and C (I, II, and III, resp.) have the same (24SS)-5a-cholestane-3β,6α,8,15β,24-pentaol aglycon as indicoside B but differ in the sugar moieties. The aglycon is also present in the aq. exts. as 24-O-sulfate deriv. The 4th new glycoside, scoparioside D (IV) was also identified. These glycosides are accompanied by 4 known polyhydroxysteroids and 1 known asterosaponin, the hexaglycoside marthasteroside A1