Supramolecular chirogenesis in zinc porphyrins: mechanism, role of guest structure, and application for the absolute configuration determination.

The achiral syn folded (face-to-face conformation) host molecule of the ethane-bridged bis(zinc porphyrin) transforms into the corresponding chiral extended anti bis-ligated species in the presence of enantiopure amine guests. The mechanism of the supramolecular chirogenesis is based upon the screw formation in bis(zinc porphyrin), arising from steric interactions between the largest substituent at the ligand's asymmetric carbon and peripheral alkyl groups of the neighboring porphyrin ring pointing toward the covalent bridge. The screw direction is determined by the guest's (amines) absolute configuration resulting in a positive chirality induced by (S)-enantiomers due to formation of the right-handed screw, and a negative chirality produced by the left-handed screw of (R)-enantiomers. The screw magnitude is strongly dependent upon the structure of the chiral guests. The amines with bulkier substituents result in stronger CD signals and larger (1)H NMR resonance splittings of enantiotopic protons. This system possesses a high degree of chiroptical activity, which allows the differentiation of one of the smallest homologous elements of organic chemistry, that is, the methyl and ethyl groups attached to the asymmetric carbon, and additionally, which senses a remote chiral center at a position beta to the amine binding group.     

Well-posedness of parabolic equations containing hysteresis with diffusive thresholds

We study complex systems arising, in particular, in population dynamics, developmental biology, and bacterial metabolic processes, in which each individual element obeys a relatively simple hysteresis law (a non-ideal relay). Assuming that hysteresis thresholds fluctuate, we consider the arising reaction-diffusion system. In this case, the spatial variable corresponds to the hysteresis threshold. We describe the collective behavior of such a system in terms of the Preisach operator with time-dependent measure which is a part of the solution for the whole system. We prove the well-posedness of the system and discuss the long-term behavior of solutions.     

Mass spectrometry of π-complexes of transition metals 38—keto-enol tautomerization of molecular ions of acetyl- and propionyl-ferrocenes in the gas phase

Fragmentation of the acetyl- and propionyl-ferrocenes under electron impact together with the rupture of C? CO bonds, characteristic of ketones, also includes elimination of water and migration of the OH group to the central metal atom, which is due to keto-enol tautomerization of the acyl group in molecular or fragment ions.     

An approach for an algorithmic solution of discrete optimal control problems and their game-theoretical extension

We consider time discrete systems which are described by a system of difference equations. The related discrete optimal control problems are introduced. Additionally, a gametheoretic extension is derived, which leads to general multicriteria decision problems. The characterization of their optimal behavior is studied. Given starting and final states define the decision process; applying dynamic programming techniques suitable optimal solutions can be gained. We generalize that approach to a special gametheoretic decision procedure on networks. We characterize Nash equilibria and present sufficient conditions for their existence. A constructive algorithm is derived. The sufficient conditions are exploited to get the algorithmic solution. Its complexity analysis is presented and at the end we conclude with an extension to the complementary case of Pareto optima.Dmitrii Lozovanu was Supported by BGP CRDF-MRDA MOM2-3049-CS-03.     

Subharmonic bifurcation from infinity

We are concerned with a subharmonic bifurcation from infinity for scalar higher order ordinary differential equations. The equations contain principal linear parts depending on a scalar parameter, 2π-periodic forcing terms, and continuous nonlinearities with saturation. We suggest sufficient conditions for the existence of subharmonics (i.e., periodic solutions of multiple periods 2πn) with arbitrarily large amplitudes and periods. We prove that this type of the subharmonic bifurcation occurs whenever a pair of simple roots of the characteristic polynomial crosses the imaginary axis at the points ±αi with an irrational α. Under some further assumptions, we estimate asymptotically the parameter intervals, where large subharmonics of periods 2πn exist. These assumptions relate the quality of the Diophantine approximations of α, the rate of convergence of the nonlinearity to its limits at infinity, and the smoothness of the forcing term.     

A structural study of (1RS,2SR,3RS,4SR,5RS)‐2,4‐dibenzoyl‐1,3,5‐triphenylcyclohexan‐1‐ol chloroform hemisolvate and (1RS,2SR,3RS,4SR,5RS)‐2,4‐dibenzoyl‐1‐phenyl‐3,5‐bis(2‐methoxyphenyl)cyclohexan‐1‐ol

(1RS,2SR,3RS,4SR,5RS)‐2,4‐Dibenzoyl‐1,3,5‐triphenylcyclohexan‐1‐ol or (4‐hydroxy‐2,4,6‐triphenylcyclohexane‐1,3‐diyl)bis(phenylmethanone), C₃₈H₃₂O₃, (1), is formed as a by‐product in the NaOH‐catalyzed synthesis of 1,3,5‐triphenylpentane‐1,5‐dione from acetophenone and benzaldehyde. Single crystals of the chloroform hemisolvate, C₃₈H₃₂O₃·0.5CHCl₃, were grown from chloroform. The structure has triclinic (P) symmetry. One diastereomer [as a pair of (1RS,2SR,3RS,4SR,5RS)‐enantiomers] of (1) has been found in the crystal structure and confirmed by NMR studies. The dichoromethane hemisolvate has been reported previously [Zhang et al. (2007). Acta Cryst. E 63 , o4652]. (1RS,2SR,3RS,4SR,5RS)‐2,4‐Dibenzoyl‐3,5‐bis(2‐methoxyphenyl)‐1‐phenylcyclohexan‐1‐ol or [4‐hydroxy‐2,6‐bis(2‐methoxyphenyl)‐4‐phenylcyclohexane‐1,3‐diyl]bis(phenylmethanone), C₄₀H₃₆O₅, (2), is also formed as a by‐product, under the same conditions, from acetophenone and 2‐methoxybenzaldehyde. Crystals of (2) have been grown from chloroform. The structure has orthorhombic (Pca2₁) symmetry. A diastereomer of (2) possesses the same configuration as (1). In both structures, the cyclohexane ring adopts a chair conformation with all bulky groups (benzoyl, phenyl and 2‐methoxyphenyl) in equatorial positions. The molecules of (1) and (2) both display one intramolecular O—H...O hydrogen bond.