The elementary divisor theory over the Hurwitz order of integral quaternions

There exists a diagonal form with certain divisibility conditions for matrices over the Hurwitz order of integral quaternions under unimodular equivalence. The diagonal entries are uniquely determined up to similarity. Given two such diagonal forms, where the diagonal entries are similar by pairs, the matrices prove to be ummodularly equivalent, whenever the rank of the matrices is creater than one.     

Crystal Structure and Properties of Some Filled and Unfilled Skutterudites: GdFe4P12, SmFe4P12, NdFe4As12, Eu0.54Co4Sb12, Fe0.5Ni0.5P3, CoP3, and NiP3

The new cubic compound Fe_0.5Ni_0.5P₃ (a = 775.29(5) pm) as well as the known compounds CoP₃ and NiP₃ were synthesized from the elemental components using tin as a flux. Their skutterudite (CoAs₃) type structures were refined from single‐crystal X‐ray data. The new compound GdFe₄P₁₂ was prepared by reaction of an alloy Gd_1/3Fe_2/3 with phosphorus in a tin flux. Its cubic “filled” skutterudite (LaFe₄P₁₂ type) structure was refined from single‐crystal X‐ray data: a = 779.49(4) pm, R = 0.019 for 304 structure factors and 11 variable parameters. SmFe₄P₁₂ shows Van Vleck paramagnetism while GdFe₄P₁₂ is a soft ferromagnet with a Curie temperature of T_C = 22(5) K. Both are metallic conductors. The new isotypic polyarsenide NdFe₄As₁₂ (a = 830.9(1) pm) was obtained by reacting NdAs₂ with iron and arsenic in the presence of a NaCl/KCl flux. The new isotypic polyantimonide Eu_0.54(1)Co₄Sb₁₂ (a = 909.41(8) pm) was prepared by reaction of EuSb₂ with cobalt and antimony. Its structure was refined from single‐crystal X‐ray data to a residual of 0.024 (137 F values, 12 variables). A comparison of the Fe–P and P–P bond lengths in the compounds AFe₄P₁₂, where the A atoms (A = Ce, Eu, Gd, Th) have differing valencies, suggests that the Fermi level cuts through Fe–P bonding and P–P antibonding bands.     

Eine neue Reaction auf Coca?n

Ohne Zusammenfassung     

Clathrates of organic onium halides,V: preparation of new clathrates and structure of the 1-propanol inclusion of a bis-quinuclidinium salt

Organic onium salts (3–15) are prepared and their inclusion capacity towards solvent molecules is investigated. The crystal structure of the1·propanol·H₂O clathrate ofN,N-[5-tert-butyl-1,3-phenylenebis(methylene)]bis(quinuclidinium)dibromide (4) is reported and compared with the X-ray structures of related clathrates described earlier. Supplementary Data: Details of the crystal structure are available on request from the Fachinformationszentrum Energie-Physik-Mathematik, D-7517 Eggenstein, Leopoldshafen 2, by quoting the depository number CSD 50883, the names of the authors, and the journal citation.     

Ultrahigh Molecular mass Polyethylene/ Carbon Nanotube CompositesCrystallization and melting properties

Ultrahigh molecular mass polyethylene (UHMMPE) is filled with carbon nano-tubes (CNTs) by solution in the presence of maleic anhydride grafted styrene-(ethylene-co-butylene)-styrene copolymer (MA-SEBS) as a compatibilizer. The UHMMPE/CNT composites crystallized from melt were prepared at a cooling rate of 20°C min^-1. The melting and crystallization behaviors of UHMMPE/ CNT composites were investigated by differential scanning calorimetry. The results showed that onset melting temperature (T _m) and degree of crystallinity (X _c) of UHMMPE/CNT composites crystallized from solution are higher than those from melt due to the larger crystalline lamellar thickness. The onset crystallization temperature (T _c) of UHMMPE/CNT composites tends to shift to higher temperature region with increasing CNT content in the composites. Tm and Tc of UHMMPE phase in UHMMPE/CNT composites decrease with the addition of MA-SEBS. Moreover, the crystallization rate of UHMMPE phase in UHMMPE/CNT composite is increased due to the introduction of CNTs. MA-SEBS acts as compatilizer, enhances the dispersion of CNTs in the UHMMPE matrix. Thereby, the crystallization rate of UHMMPE phase in UHMMPE/CNT composite is further increased with the addition of MA-SEBS. This revised version was published online in August 2006 with corrections to the Cover Date.     

Peculiarities of polyacrylamide analysis by aqueous GPC

Various commercially available stationary phases of gel permeation chromatography (GPC) were tested to determine their effectiveness in aqueous exclusion chromatography. It was found that controlled pore glass (GPG) is the most suitable material for the separation of polyacrylamides and poly(acry1amide-co-sodium acrylate), dextrans, and poly(sodium styrene–sulfonates) in 0.1M aqueous Na₂S0₄ solutions of ionic strength 0.3. A calibration curve was established by using broad molecular weight distribution polyacrylamide standards in a trial and error procedure. To avoid artificial oscillations on the evaluated distribution curves a cubic B-spline representation of the calibration curve was used instead of the conventional polynomials. By applying this system the solution instability of polyacrylamides was observed by GPC and is discussed because of its general importance to the applicability of indirect molecular weight determination methods for polyacrylamides. The effectiveness of aqueous GPC was demonstrated in an evaluation of thermal degradation measurements of polyacrylamides. Finally, the feasibility of universal calibration of aqueous GPC by means of poly(sodium styrene–sulfonates) was investigated. It is apparent that in spite of some problems concerning adsorption of the polymer universal calibration is a successful tool for calibrating aqueous GPC.     

The singular modular forms on the 27-dimensional exceptional domain

Summary Due to a result of Resnikoff the non-constant singular modular forms on the 27-dimensional exceptional domain are exactly those of weight 4 and weight 8. They were constructed by Kim using analytic continuation of non-holomorphic Eisenstein series. In this paper a simpler construction is described. These modular forms arise from theta series on the Cayley half-plane of degree two, which is a 10-dimensional boundary component, by means of the Fourier-Jacobi expansion. This article was processed by the author using the IATEX style filecljour1 from Springer-Verlag.