Stationary solutions of the bogoliubov hierarchy equations in classical statistical mechanics. 2

In the preceding paper under the same title we have formulated a theorem which describes the set of states (i.e., probability measures on phase space of an infinite system of particles inR ^v) corresponding to stationary solutions of the BBGKY hierarchy. We have proved the following statement: ifG is a Gibbs measure (Gibbs random point field) corresponding to a stationary solution of the BBGKY hierarchy, then its generating function satisfies a differential equation which is conjugated to the BBGKY hierarchy. The present paper deals with the investigation of the conjugated equation for the generating function in particular cases.     

High iso Aldehyde Selectivity in the Hydroformylation of Short‐Chain Alkenes

The hydroformylation of propene to give predominantly iso‐butanal has been achieved; class‐leading selectivity is possible even at higher temperatures that deliver fast conversion. Racemic rhodium complexes of bidentate phospholane phosphites derived from tropos‐biphenols and unusual solvent systems are the key to the selectivity observed.     

Circuit simulation for synchronization of a fractional-order and integer-order chaotic system

We design a new three-dimensional double-wing fractional-order chaotic system with three quadratic terms, confirmed by numerical simulation and circuit implementation. We then study the synchronization between the new double-wing fractional-order chaotic system and different Lorenz systems with different structures. In the process of the synchronization, the definition of ‘the simplest response system’ and the practical method of designing the circuit have been originally proposed. The circuit of ‘the simplest response system’ (even the simplest incommensurate-order response system), holding different structures with the drive system, of any one integral or fractional drive system now can be designed effectively and sufficiently. Our results are supported by numerical simulation and circuit implementation.