On alternative form of the characteristic polynomial and the problem of graph recognition

The characteristic polynomial of a structure (molecule or a graph) is usually expressed as a function ofx. Here we explore an alternative representation of characteristic polynomials expressed in terms ofL _n , the characteristic polynomials of linear chains havingn atoms. While the new forms of the characteristic polynomials are mathematically equivalent to the old forms, they appear to reflect selected structural similarities among homologous molecules better. Besides arriving at general expressions for the form of the characteristic polynomials for numerous families of compounds previously unavailable, the approach is of some interest for the old problem of graph isomorphism and graph recognition in cases of structures which can be associated with a homologous series.     

On the molecular structure and nmr spectrum of cis-[PtPh2(Ph2PCH2PPh2)]

The X-ray crystal structure analysis of cis-[PtPh₂(Ph₂PCH₂PPh₂)] suggests that the unusually low PtP coupling constant is a consequence of distortion of the valency angles at the platinum and phosphorus atoms; the restrictive geometry of the chelate ring does not effect the lengths of the metal—ligand bonds.     

Determination of the diffusion coefficient of substances in the plasma of a d.c. arc in air using a photometric method

An experimental method is developed for the determination of diffusion coefficients of substances in an arc plasma. Pulsed injection of a substance in the form of “liquid bullets” of an aqueous solution was used for the determination of the diffusion coefficient of Na. The evaluation was based on observations of the spatial intensity distribution of Na radiation and its dependence on time as recorded with a high-speed camera.     

Interface delocalization in the three-dimensional Ising model

The interface delocalization in the three-dimensional Ising model is studied by real-space renormalization group methods. The first-order cumulant expansion approximation is used. Defect free energies for a boundary plane of defects and an internal plane of defects are calculated in the whole temperature region. The phase diagrams are also obtained. The method and the model analyzed may give a correct phase diagram only in the regime of continuous interface delocalization. The interface delocalization is obtained for the boundary defect and also for the internal defect if the systems on two sides of the internal defect plane have a different degree of order. The delocalization transition does not occur in the case of the internal defect plane between two equally ordered systems.