Published by Duke University Press since its inception in 1935, the Duke Mathematical Journal is one of the world's leading mathematical journals. Without specializing in a small number of subject areas, it emphasizes the most active and influential areas of current mathematics.

### Volume 18, Number 4

#### Publication Date: December 1951

The product of the generators of a finite group generated by reflections

H. S. M. Coxeter; 765-782

Characteristic vectors for a product of $n$ reflections

J. S. Frame; 783-785

Integrability of trigonometric series. I.

R. P. Boas, Jr.; 787-793

The basis in Banach space

Albert Wilansky; 795-798

Prime rings

R. E. Johnson; 799-809

Some applications of a theorem of Chevalley

L. Carlitz; 811-819

A theorem on cyclic matrices

Joseph A. Silva; 821-825

Chains in the projective line

A. J. Hoffman; 827-830

Differential invariants of ruled surfaces belonging to one special linear complex

N. A. Goldsmith; 831-836

The representation of functions of bounded variation by singular integrals

L. C. Hsu; 837-844

The fundamental solution of $\Delta\psi+e(y)\psi_y=0$

M. H. Martin; 845-858

An extension of the sum theorem of dimension theory

G. H. Butcher; 859-874

Convex sets in linear spaces. II.

V. L. Klee, Jr.; 875-883

A simplification of games in extensive form

W. D. Krentel, J. C. C. McKinsey and W. V. Quine; 885-900

Continua and their complementary domains in the plane

C. E. Burgess; 901-917