A Construction of Partial Difference Sets in {\mathbb{Z}}_{p^{2 \times } } {\mathbb{Z}}_{p^{2 \times \cdot \cdot \cdot \times } } {\mathbb{Z}}_{p^2 }

In this paper, we give a construction of partial difference sets in _p ² x _p ² x ... x _p ²using some finite local rings.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe work of this paper was done when the authors visited the University of Hong Kong.     

A finiteness theorem for maximal independent sets

Denote bymi(G) the number of maximal independent sets ofG. This paper studies the setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG K ₁) or duplicated vertices. We determineS(1), S(2), andS(3) and prove that |V(G)| 2 ^k–1 +k – 2 for anyG inS(k) andk 2; consequently,S(k) is finite for anyk. Supported in part by the National Science Council under grant NSC 83-0208-M009-050     

Self-assembly of highly oriented one-dimensional h-WO3 nanostructures

A new self-assembled and highly oriented one-dimensional single-crystal nanostructure of WO3 with hexagonal form was successfully prepared by a mild, solution-based colloidal approach.     

Algebraic study of chiral anomalies

The algebraic structure of chiral anomalies is made globally valid on non-trivial bundles by the introduction of a fixed background connection. Some of the techniques used in the study of the anomaly are improved or generalized, including a systematic way of generating towers of descent equations.This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under contract DE-AC03-76SF00098 and in part by the National Science Foundation under research grant PHY81-18547