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 22, Number 4

#### Publication Date: December 1955

Finitely generated modules

Harley Flanders; 477-483

A theorem on upper semi-continuous decompositions

William R. Smythe, Jr.; 485-495

Representations by bilinear forms in a finite field

John H. Hodges; 497-509

Boundedness of the solutions of second order linear differential equations

Richard Bellman; 511-513

Binary, linear, elliptic, partial differential equations

Philip Hartman and Aurel Wintner; 515-524

The solutions of the differential equation $v'''+\lambda^2zv'+3\mu\lambda^2v=0$

Rudolph E. Langer; 525-541

An extension of Ramanujan’m. II. Additive properties

Eckford Cohen; 543-550

Fixed points, fixed sets, and $M$-retracts

Wayman Strother; 551-556

On the numerical integration of a parabolic differential equation subject to a moving boundary condition

Jim Douglas, Jr. and T. M. Gallie, Jr.; 557-571

The Hausdorff-Bernstein-Widder theorem for semi-groups in locally compact Abelian groups

A. E. Nussbaum; 573-582

A note on power residues

L. Carlitz; 583-587

Note on the class number of quadratic fields

L. Carlitz; 589-593

Arithmetic and limit theorems for a class of random variables

Edwin Hewitt and Herbert S. Zuckerman; 595-615

Summability of generalized Bernstein polynomials. I

P. L. Butzer; 617-623

Graphs and matching theorems

Oystein Ore; 625-639

Arithmetic properties of Bernoulli numbers of higher order

F. R. Olson; 641-653

Complements of maximal ideals in compact semigroups

W. M. Faucett, R. J. Koch and K. Numakura; 655-661