The Journal of the Mathematical Society of Japan publishes original research articles of the highest scientific level in all fields of mathematics. It has been the official journal of the Mathematical Society of Japan since 1948. The journal is open to contributions from mathematicians worldwide.

### Volume 50, Number 4

#### Publication Date: October, 1998

The dimensions of self-similar sets

Wenxia LI and Dongmei XIAO; 789-799

Higher $v_{n}$ torsion in Lie groups

John HUNTON, Mamoru MIMURA, Tetsu NISHIMOTO and Björn SCHUSTER; 801-818

Actions of loop groups on simply connected $H$-surfaces in space forms

Atsushi FUJIOKA; 819-829

The first derived limit and compactly $F_{\sigma}$ sets

Stevo TODORCEVIC; 831-836

On the structure of the singular set of a complex analytic foliation

Junya YOSHIZAKI; 837-857

The Gaussian curvature of Alexandrov surfaces

Yoshiroh MACHIGASHIRA; 859-878

Codimension two nonsingular subvarieties of quadrics: scrolls and classification in degree $d\leq 10$

Mark Andrea A. de CATALDO; 879-902

Small divisor problems and divergent formal power series solutions

Masafumi YOSHINO; 903-913

Noncommutative 3-sphere: A model of noncommutative contact algebras

Hideki OMORI, Yoshiaki MAEDA, Naoya MIYAZAKI and Akira YOSHIOKA; 915-943

Jørgensen's inequality for classical Schottky groups of real type

Hiroki SATO; 945-968

On Macaulayfication of certain quasi-projective schemes

Takesi KAWASAKI; 969-991

Third order ordinary differential equations and Legendre connections

Hajime SATO and Atsuko Yamada YOSHIKAWA; 993-1013

Gevrey regularizing effect for a nonlinear Schrödinger equation in one space dimension

Kazuo TANIGUCHI; 1015-1026