Matrix Lax Polynomials, Geometry of Prym Varieties and Systems of Hess–Appel’rot Type

We consider a four-dimensional generalization of Hess–Appel’rot system and costruct its Lax pair. Both classical and algebro-geometric integration procedure are proceeded. The algebro-geometric integration is based on deep facts from geometry of Prym varieties such as the Mumford relation and Mumford-Dalalyan theory. The integration is similar to the integration of Lagrange bitop which has recetly been performed by the authors.     

XRR and GISAXS study of silicon oxynitride films

Thin films of silicon oxynitride have largely replaced pure silicon oxide films as gate and tunnel oxide films in modern technology due to their superior properties in terms of efficiency as boron barrier, resistance to electrical stress and high dielectric strength. A single chamber system for plasma enhanced chemical vapor deposition was employed to deposit different films of SiO_xN_yH_z with 0.85 < x < 1.91. All films were previously characterized by Rutherford back-scattering and infrared spectroscopy to determine the stoichiometry and the presence of various bonding configurations of constituent atoms. We used X-ray reflectivity to determine the electron density profile across the depth, and we showed that the top layer is densified. Moreover, grazing incidence small-angle X-ray scattering was used to study inhomogeneities (clustering) in the films, and it is shown that plate-like inhomogeneities exist in the top and sphere-like particles at the bottom part of the film. Their shape and size depend on the stoichiometry of the films.     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

The temperature and pressure in the plasma parallel plate accelerator

This paper presents the results of plasma temperature and pressure calculations in the parallel plate accelerator during the accelerating process. The plasma pressure is calculated by means in Dalton's law.     

Chlorokomplexe von Cu2+ und Ni2+ in Dimethylformamid

Zusammenfassung Durch spektrophotometrische Messungen in Dimethylformamid (DMF) werden die Koordinationsformen [CuCl]⁺ und [CuCl₃]^– sowie [NiCl]⁺, [NiCl₃]^– und [NiCl₄]^2– nachgewiesen. Bei Nickel(II)-chlorid und Kupfer(II)-chlorid wird Autokomplexbildung diskutiert. Die Solvate [Cu(DMF)₄] (ClO₄)₂ und [Ni(DMF)₆] (ClO₄)₂ werden isoliert.Im Zuge der Untersuchungen über Chlorokomplexe von Ionen der Übergangsmetalle^{1, 2} in nichtwäßrigen Lösungsmitteln wurden die Spektren der Lösungen von Kupfer(II)- und Nikkel(II)-perchlorat inDMF in Gegenwart verschiedener Mengen Tetraäthylammoniumchlorid aufgenommen.Mit 5 Abbildungen     

Finitely additive states and completeness of inner product spaces

For any unit vector in an inner product space S, we define a mapping on the system of all -closed subspaces of S, F(S), whose restriction on the system of all splitting subspaces of S, E(S), is always a finitely additive state. We show that S is complete iff at least one such mapping is a finitely additive state on F(S). Moreover, we give a completeness criterion via the existence of a regular finitely additive state on appropriate systems of subspaces. Finally, the result will be generalized to general inner product spaces.     

Crystal structure and vibrational spectra of hydrazinium (2+) tri-μ-fluoro bis[pentafluorozirconate (IV)] fluoride and vibrational spectra of its hafnium analogue

Monoclinic (N₂H₆)₃Zr₂F₁₃·F crystallizes in space group P2₁-C ₂ ² (No. 4) with unit cell dimensionsa=5.670(1),b=10.984(2),c=10.601(2) Å,=93.88(1)°,V=658.7(4) ų andZ=2. Two different types of N₂H₆ ²⁺ ions are present. One is involved in strong H-bonds to F^– ions in infinite chains running along the a axis (the shortest N-F distance is 2.437(5) Å), and the other links the structure through weaker bi- and trifurcated H-bonds to fluorine ligands of the Zr₂F₁₃ ^5– ions. The N-N bond lengths range from 1.430(5) to 1.446(5) Å with apparently no meaningful correlation to the type of N₂H₂ ²⁺ ions. The Zr₂F₁₃ ^5– ions have very nearly C₂ point symmetry and are formed by joining two distorted bicapped trigonal prisms of ZrF₈-units through a common face. Distances of Zr-F terminal bonds range from 2.015(2) to 2.112(2) Å and of bridging bonds from 2.133(2) to 2.212(2) Å. (N₂H₆)₃Hf₂F₁₃·F is isomorphous. The vibrational spectra of the two compounds are nearly identical, with the exception of a strong infrared band, which is assigned to a stretching mode with the moving central atom within the anion. The anion part of the spectrum is simple, showing broad unresolved bands. The cation part shows two types of N₂H₆ ^– ions. H-Bonding is strongly present in the spectra, but no simple correlations with the H-bond strength is evident.     

Some Landau's type inequalities for infinitesimal generators

Summary Lett T(t) be a strongly continuous contraction semigroup on a complex Banach space and letA be its infinitesimal generator. We prove that, forx D(A ³), the following inequalities hold true: Ax³ 243/8 x²A ³ x, A ² x 24 xA ³ x². Ift T(t) is a contraction group (resp. cosine function) we get the analogous but better inequalities with constants 9/8 and 3 (resp. 81/40 and 72/25) instead of 243/8 and 24. We consider also uniformly bounded semigroups, groups and cosine functions.