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 30, Number 2

#### Publication Date: June 1963

A sequence of rational functions with application to approximation by bounded analytic functions

J. L. Walsh; 177-189

Some generating functions

L. Carlitz; 191-201

A problem in partitions

L. Carlitz; 203-213

Embedding a regular neighborhood of the singular locus of a $2$ dimensional polyhedron in $E^3$

Thomas R. Brahana; 215-220

Limits of entire functions whose growth and zeros are restricted

S. Hellerstein and J. Korevaar; 221-227

The $n$-${\rm th}$ derivative of a class of functions

David Zeitlin; 229-238

Invariant subspaces of tridiagonal operators

P. L. Duren; 239-248

Almost locally polyhedral $2$-spheres in $S^3$

J. C. Cantrell; 249-252

Modulary groups of $t \times t$ matrices

M. Newman and J. R. Smart; 253-257

Simultaneous representations in quadratic and linear forms over $GF[q,x]$

L. Carlitz; 259-270

Reducing the rank of ordinary differential equations

H. L. Turrittin; 271-274

Trace formulas for a perturbed operator

Richard C. Gilbert and Vernon A. Kramer; 275-296

Prime-like sequences generated by a sieve process

W. E. Briggs; 297-311

Determination of an unknown coefficient in a parabolic differential equation

J. R. Cannon; 313-323

Persistent Markov chains constructed from transient chains

Solon L. Rhode, III; 325-329

Abstract mean values

Trevor Evans; 331-347