A Novel Rearrangement Reaction of N‐Acyliminium Ions Leading to Heterobicycles Arylated at Bridgehead Atom

Starting with thiazolines, an important class of heterocyclic imines, a novel rearrangement reaction of corresponding N‐acyliminium ions is described. Furthermore, a new class of heterobicyclic compounds arylated at a single bridgehead atom is obtained diastereospecifically.     

Large deviation principles for Euclidean functionals and other nearly additive processes

We prove a large deviation principle for a process indexed by cubes of the multidimensional integer lattice or Euclidean space, under approximate additivity and regularity hypotheses. The rate function is the convex dual of the limiting logarithmic moment generating function. In some applications the rate function can be expressed in terms of relative entropy. The general result applies to processes in Euclidean combinatorial optimization, statistical mechanics, and computational geometry. Examples include the length of the minimal tour (the traveling salesman problem), the length of the minimal matching graph, the length of the minimal spanning tree, the length of the k-nearest neighbors graph, and the free energy of a short-range spin glass model. Received: 3 April 1999 / Revised version: 23 June 1999 / Published online: 8 May 2001     

Microwave backscattering by nonspherical ice particles at 5.6 GHz using second-order perturbation series

Scattering of microwaves by an ensemble of nonspherical ice particles is studied using a scattering model based on a second-order perturbation series at 5.6 GHz (C-band). Particle shapes are defined using a Gaussian random sphere geometry. Particle inhomogeneity is taken into account using three different effective-medium approximations: Maxwell–Garnett, Bruggeman, and Coherent Potential mixing rules. By systematically varying particle size, liquid water content, Gaussian shape parameters, and internal structure, it is found that liquid water content is the most important factor for the co-polarized backscattering; the shape is relatively unimportant. For depolarized backscattering, the shape is of fundamental importance, although the other factors are significant too. Surprisingly, the type of nonsphericity is found to be important for depolarization even for scatterers that are in the Rayleigh region: elongated targets depolarize clearly stronger than more irregular shapes. This finding seems not to be strongly size dependent, at least for size parameters from 0.0059 to 0.47, and indicates that the accurate modeling of shape is important for polarization quantities even in the Rayleigh region.     

An alkyl–palladium(II) complex with a bidentate phosphine ligand: [1,3‐bis(di­phenyl­phosphino)­propane‐P,P′]­dimethyl­palladium(II) toluene hemi­solvate

In the title compound, [Pd(CH₃)₂(C₂₇H₂₆P₂)]·0.5C₇H₈, the Pd atom is at the centre of an approximately square‐planar arrangement of two P atoms and two methyl groups. The P—Pd—P angle [93.19 (3)°] is significantly larger than that in the corresponding dichloride complex [Pd(dppp)Cl₂]. The toluene mol­ecule is disordered across an inversion centre.