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     

On kinetics of the photodissociation iodine laser

The kinetics of iodine laser amplifiers is examined by solving the time evolution equations of chemical kinetics during optical pumping. The pumping radiation intensity is modelled by a black body of the temperature varying in time (corresponding to the flash lamp pulse). A brief comparison is made of pumping effects by long and short light pulses. Pumping by the long pulse is studied in more detail and it is found that there exists an optimum pulse strength beyond which the inversion in the laser mixture no longer grows appreciably, only its lifetime is shortened. In this connection the effect of pyrolysis of the alkyliodide molecule is also discussed. The pyrolysis is found to occur under very strong illumination, but it does not interfere with the photolytic decomposition and the optimum laser action. Finally, the influence of the reaction rate constants is studied in a systematic way and only few of them are found to carry real weight.The authors are obliged to Drs. S. V. Kuznetsova and A. I. Maslov who were consulted on the values of the reaction constants and who also drew our attention to some of the references.