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.     

Efficient degradation of organic pollutants mediated by immobilized iron tetrasulfophthalocyanine under visible light irradiation

Supported iron tetrasulfophthalocyanine can efficiently catalyze the degradation of organic pollutants by H2O2 under visible light irradiation in an aqueous solution, and the catalyst can be easily recycled without apparent loss of activity.     

Theoretical study of the ring‐closing reaction of 5′‐AMP to cAMP and H2O in the gas phase

The ring‐closing reaction of 5′‐adenosine monophosphate (5′‐AMP) to generate cyclic 3′, 5′‐adenosine monophosphate (cAMP) and H₂O was theoretically investigated at the B3LYP/6‐31G**level. It was found that the ring‐closing reaction of 5′‐AMP may proceed in a synchronous way or in a stepwise way. For the latter, the reaction is a multichannel elimination reaction including inner H transfer. The potential energy surface of Path 3 is lowest in all the ring‐closing reaction paths. In addition, H shuttling reaction with the participation of a water molecule to act as a shuttle were also studied at the same level. The calculations indicate that the participation of a water molecule facilitates hydrogen transfer reaction. Our present calculations rationalized all the possible reaction channels. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005