Groups with finitely many normalizers of non-abelian subgroups

Abstract A group is called metahamiltonian if all its non-abelian subgroups are normal; it is known that locally soluble metahamiltonian groups have finite commutator subgroup. Here the structure of locally graded groups with finitely many normalizers of (infinite) non-abelian subgroups is investigated, and the above result is extended to this more general situation. Keywords: normalizer subgroup, metahamiltonian group Mathematics Subject Classification (2000): 20F24     

Analysis of complex mixtures by capillary gas chromatography with statistical estimation of the number of components

Evaluation of the number of components by the Davis-Giddings single chromatogram method is applied to capillary gas chromatograms of a dichloromethane extract of camomile. Various runs with OV-1 or Carbowax 20M as the stationary phase were done under different experimental conditions (column temperature programming rate and column length). The results showed that the number of components obtained by this statistical procedure does not depend greatly on the nature of the stationary phase or on the experimental conditions. The component number of the camomile extract was about 200 and the stand-alone probability at unit resolution was 0.2–0.3.     

3,6-bis(2′,-pyridyl)pyridazine dinuclear complexes: Palladium(II), platinum(II) and first row transition metal(II) mixed complexes

New Pd(II) and Pt(II) 3,6-bis(2′-pyridyl)pyridazine (dppn) mononuclear complexes of the type M(dppn)Cl₂ were prepared and characterized. From M(dppn)Cl₂, the bimetallic homonuclear complexes M(dppn)MCl₄ were prepared by reaction with Pd(PhCN)₂Cl₂ or K₂PtCl₄. Bimetallic heteronuclear species of the type M(dppn)M′Cl₄, were prepared reacting the mononuclear complexes with the stoichiometric amount of M′Cl₂ (M′ = Cu, Co, Ni). All the described reaction give product in high yield. The isolated compounds, almost completely insoluble in most organic solvents, were characterized by elemental analysis, IR, ESR, reflectance spectra, and magnetic moment measurements. On the basis of these data the geometries around the metals are discussed.     

Special matchings and Kazhdan-Lusztig polynomials

In 1979 Kazhdan and Lusztig defined, for every Coxeter group W, a family of polynomials, indexed by pairs of elements of W, which have become known as the Kazhdan-Lusztig polynomials of W, and which have proven to be of importance in several areas of mathematics. In this paper, we show that the combinatorial concept of a special matching plays a fundamental role in the computation of these polynomials. Our results also imply, and generalize, the recent one in [Adv. in Math. 180 (2003) 146-175] on the combinatorial invariance of Kazhdan-Lusztig polynomials.     

Combinatorial Expansions of Kazhdan-Lusztig Polynomials

We introduce two related families of polynomials, easily computableby simple recursions into which any Kazhdan–Lusztig (andinverse Kazhdan–Lusztig) polynomial of any Coxeter groupcan be expanded linearly, and we give combinatorial interpretationsto the coefficients in these expansions. This yields a combinatorialrule for computing the Kazhdan–Lusztig polynomials interms of paths in a directed graph, and a completely combinatorialreformulation of the nonnegativity conjecture [15, p. 166].     

Properties of fluoroelastomer/semicrystalline perfluoropolymer nano-blends

Properties of blends of semicrystalline perfluoropolymers in fluoroelastomers strongly depend on the size of the dispersed phase and are at the best when dispersed phase dimension is well below 0.1 μm, i.e. in the nano-scale region. This fine dispersion is obtained with an innovative mixing technology based on microemulsion polymerization. Further increase of properties can be obtained by generating chemical links between fluoroelastomer and semicrystalline fluoropolymer. Nano-blends combine the performing properties of fluoroelastomers with those of semicrystalline perfluoropolymers. For example, these nano-blends have at the same time the sealing and mechanical properties of fluoroelastomers and the exceptional thermal and chemical resistance, low permeability and low friction coefficient of semicrystalline perfluoropolymers. In addition, as dispersed phase size is below visible light wavelength, finished items made with these nano-blends are optically transparent even when they contain as much as 40 wt.% of semicrystalline perfluoropolymer.     

Polycondensed nitrogen heterocycles. Part 24. Pyrrolo[3,4-c]isoquinolinone by thermal rearrangement of a pyrrolylbenzotriazinone

Rearrangement under acidic conditions of the pyrrolylbenzotriazinone 7 afforded the pyrrolylbenzamides 10 and 11 . By thermal rearrangement instead, the first fully aromatic derivative of the pyrrolo[3,4-c]isoquinoline ring system 9 was obtained.     

Chemical mechanisms in C3F8-H2 radiofrequency discharges

Discharges fed with C₃F₈-H₂ mixtures have been studied by means of mass spectrometry in a tubular reactor operated at 0.5 torr and 50 W. Comparison of the results with those obtained with emission actinometry give additional evidence that emission actinometry and mass spectrometry are powerful diagnostic tools to monitor stable and unstable species in discharges utilized for dry etching and polymer depositions. Mechanisms for end product formation and polymer deposition are also discussed.