On the Grigorchuk–Kurchanov conjecture

 Let denote the free group of rank 2g. An automorphism φ? Aut(F _{2 g} ) is generating if N _a φ (N _b ) = F _{2 g} , where N _a is the normal closure of and N _b is defined analogously. We present a characterization of generating automorphisms in Aut(F ₂) and observe that there exists a unique (up to equivalence) epimorphism F ₂→Z×Z: this is a particular case of the Grigorchuk–Kurchanov conjecture. This leads to further investigations for splitting homomorphisms for the pairs (F _{2 g} , F _g) and (G _g, F _g) where G _g denotes the fundamental group of a closed orientable surface of genus g and a reformulation of the Poincaré and Grigorchuk–Kurchanov conjectures is derived. Received: 1 October 2001     

The group of holomorphic automorphisms in certainJ *-Algebras

Summary The group of all holomorphic automorphisms of the infinite-dimensional analogue of the Cartan domain of type I is determined, by the characterisation of all surjective linear isometries ofL(K, H) (K, H Hilbert spaces). Also a linear representation of the group is given, and the study of the fixed points set for a holomorphic automorphism of the unit ball of a J*-algebra.Lavoro eseguito nell'ambito del G.N.A.F.A. del C.N.R.     

The first gas chromatographic resolution of carnitine enantiomers

The enantiomers of carnitine are converted on-line in the injection port of a gas chromatograph into beta-hydroxy-gamma-butyrolactones and are separated on a derivatized beta-cyclodextrin chiral stationary phase.     

Computer simulation study of thermodynamic scaling of dynamics of 2Ca(NO3)2·3KNO3

Molecular dynamics (MD) simulations of the glass-former 2Ca(NO(3))(2·3KNO(3), CKN, were performed as a function of temperature at pressures 0.1 MPa, 0.5 GPa, 1.0 GPa, and 2.0 GPa. Diffusion coefficient, relaxation time of the intermediate scattering function, and anion reorientational time were obtained as a function of temperature and densitiy ρ. These dynamical properties of CKN scale as ρ(γ)∕T with a common value γ = 1.8 ± 0.1. The scaling parameter γ is consistent with the exponent of the repulsive part of an effective intermolecular potential for the repulsion between the atoms at shortest distance in the equilibrium structure of liquid CKN, Ca(2+), and oxygen atoms of NO(3)(-). Correlation between potential energy and virial is obeyed for the short-range terms of the potential function, but not for the whole potential including coulombic interactions. Decoupling of diffusion coefficient and reorientational relaxation time from relaxation time take place at a given ρ(γ)∕T value, i.e., breakdown of Stokes-Einstein and Debye-Stokes-Einstein equations result from combined thermal and volume effects. The MD results agree with correlations proposed between long-time relaxation and short-time dynamics, lnτ ∝ 1∕, where the mean square displacement concerns a time window of 10.0 ps. It has been found that scales as ρ(γ)∕T above and below the glass transition temperature, so that thermodynamic scaling of liquid dynamics can be thought as a consequence of theories relating short- and long-time dynamics, and the more fundamental scaling concerns short-time dynamical properties.     

Herringbone Infinite Networks Formed by Terpyridine and Haloperfluoroarene Modules

Abstract

4′-(4-Methylphenyl)-2,2′:6′,2″-terpyridine (1) self-assembles with dihaloperfluoroarenes (2). A chemo- and site-selective supramolecular synthesis occurs which preserves in the solid cocrystal the most stable s-trans, s-trans conformation of the pure terpyridine module. The single crystal X-ray structure of 3a, prepared from 1 and 1,4-diiodotetrafluorobenzene (2a) (monoclinic, a = 14.608(1), b = 13.276(1), c = 13.970(2) Å, β = 109.808(8)°, U = 2549.4 (4) ų, T = 291 (1) K, space group C2/c Z = 4; μ(Mo-Kα) = 2.519 mm^?1; d _calc.: 1.890 g cm^?3; 5748 reflections measured, 3715 unique (Rint = 0.024) which were used in all calculations; the final R and wR (F ²) were 0.043 and 0.069, respectively) shows the presence of infinite ribbons where the two modules alternate in a zigzag arrangement.