p Dissipative operator

In this paper the authors prove that the generalized positive p selfadjoint (GPpS) operators in Banach space satisfy the generalized Schwarz inequality, solve the maximal dissipative extension representation of p dissipative operators in Banach space by using the inequality and introducing the generalized indefinite inner product (GIIP) space, and apply the result to a certain type of Schrodinger operator.

An automata theoretic decision procedure for the propositional mu-calculus

The propositional mu-calculus is a propositional logic of programs which incorporates a least fixpoint operator and subsumes the propositional dynamic logic of Fischer and Ladner, the infinite looping construct of Streett, and the game logic of Parikh. We give an elementary time decision procedure, using a reduction to the emptiness problem for automata on infinite trees. A small model theorem is obtained as a corollary.

State-to-state dynamics of elementary chemical reactions using Rydberg H-atom translational spectroscopy

In this review, a few examples of state-to-state dynamics studies of both unimolecular and bimolecular reactions using the H-atom Rydberg tagging TOF technique were presented. From the H2O photodissociation at 157 nm, a direction dissociation example is provided, while photodissociation of H2O at 121.6 has provided an excellent dynamical case of complicated, yet direct dissociation process through conical intersections. The studies of the O(D-1) + H-2 --> OH+H reaction has also been reviewed here. A prototype example of state-to-state dynamics of pure insertion chemical reaction is provided. Effect of the reagent rotational excitation and the isotope effect on the dynamics of this reaction have also been investigated. The detailed mechanism for abstraction channel in this reaction has also been closely studied. The experimental investigations of the simplest chemical reaction, the H-3 system, have also been described here. Through extensive collaborations between theory and experiment, the mechanism for forward scattering product at high collision energies for the H+HD reaction was clarified, which is attributed to a slow down mechanism on the top of a quantized barrier transition state. Oscillations in the product quantum state resolved different cross sections have also been observed in the H+D-2 reaction, and were attributed to the interference of adiabatic transition state pathways from detailed theoretical analysis. The results reviewed here clearly show the significant advances we have made in the studies of the state-to-state molecular reaction dynamics.

Theoretical study on the mechanisms of some elementary reactions catalyzed by modified carbonyl cobalt

All structural geometries of intermediates, transition states and product are, optimized at HF/ LANL2DZ level under the effective core potential approximation. The potential energy profile for some elementary reactions of hydroformylation catalyzed by Co-2(CO)(6)(PH3)(2), consisting of carbonyl insertion, H-2 oxidative addition and aldehyde reductive elimination, are calculated, The transition states are further confirmed by having one and only one imaginary vibrational frequency, The activation energies of carbonyl insertion, H-2 oxidative addition and aldehyde reductive elimination are 54, 02, 134, 02 and 43. 44 kJ/mol, respectively.

High resolution time-of-flight spectrometer for crossed molecular beam study of elementary chemical reactions

In this article, we describe an apparatus in our laboratory for investigating elementary chemical reactions using the high resolution time-of-flight Rydberg tagging method. In this apparatus, we have adopted a rotating source design so that collision energy can be changed for crossed beam studies of chemical reactions. Preliminary results on the HI photodissociation and the F atom reaction with H-2 are reported here. These results suggest that the experimental apparatus is potentially a powerful tool for investigating state-to-state dynamics of elementary chemical reactions. (c) 2005 American Institute of Physics.