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 52, Number 2

#### Publication Date: June 1985

On Eisenstein series of half-integral weight

Goro Shimura; 281-314

Invariants of modular representations and polynomial algebras over the Steenrod algebra

Hyperelliptic quasi-periodic and soliton solutions of the nonlinear Schrödinger equation

Emma Previato; 329-377

Algebraic cycles and values of $L$-functions II

Spencer Bloch; 379-397

Geometry of a category of complexes and algebraic $K$-theory

V. A. Hinich and V. V. Schechtman; 399-430

Convexity of solutions of semilinear elliptic equations

Luis A. Caffarelli and Avner Friedman; 431-456

Le Brun’s nonrealizability theorem in higher dimensions

Hugo Rossi; 457-474

On the differentiability of $\mathbf{O}(n)$ invariant functions of symmetric matrices

John Sylvester; 475-483

On the elliptic equation $\Delta u+Ku^{(n+2)/(n-2)}=0$ and related topics

Wei-Yue Ding and Wei-Ming Ni; 485-506

Class-groups of function fields

David Goss and Warren Sinnott; 507-516

Transcendence theory over function fields

Jing Yu; 517-527

Supplement to: “Variation of mixed Hodge structure arising from family of logarithmic deformations II: Classifying space”

Masahiko Saito, Yuji Shimizu and Sampei Usui; 529-534

Characterization of simple closed geodesics on Fricke surfaces

Mark Sheingorn; 535-545