On theK-property of some planar hyperbolic billiards

TheK-property is demonstrated for a class of planar billiards satisfying Wojtkowski's principles. Their boundary may consist of convex-scattering, concave and linear pieces. Earlier Wojtkowski showed that these billards had non-zero Lyapunov exponents.     

Thermal degradation of copolymers of styrene and methyl-vinyl-silane by pyrolysis gas chromatography

Pyrolysis gas chromatographic investigations have been carried out on copolymers of styrene with trimethyl-vinyl-silane and of styrene with dimethyl-phenyl-vinyl-silane, in order to study the mechansims of thermal degradation and the copolymer structures. We have identified the pyrolysis products and measured their relative amounts. The experiments show that the controlling factor in the mechanism of the degradation is the nature of the side-group attached to the carbon atom at which chain scission occurs. If this side-group is phenyl, the main degradation process is depropagation; if it is if it is trimethyl-silyl or dimethyl-phenyl-silyl, intramolecular hydrogen abstraction followed by β scission becomes more important than depropagation. From the point of view of degradation mechanism, the nature of the side-group attached to the carbon atom from which the hydrogen is abstracted is of minor importance.We estimated the average copolymer block length from the amounts of products containing both comonomers as well as from the amounts of trimer composed of the same monomer.     

Selective liquid adsorption and structural properties of montmorillonite and its hexadecylpyridinium derivatives

Summary An X-ray diffraction method was used to study the structures of montmorillonites, the surfaces of which were covered to a systematically increasing extent with hexadecylpyridinium (HDP) cations. It was found that, depending on the degree of cover of the surface, the HDP cations form a mono- or bimolecular layer in the interlayer space. A detailed investigation was made of the selective sorption of binary mixtures on montmorillonite and on HDP-montmorillonites with different surface coverages. The adsorption excess isotherms were determined, as were the adsorption capacities from analysis of the isotherms, and also the equivalent specific surface areas.It was established that from benzene-n-heptane mixtures the benzene is adsorbed only on the external surface of montmorillonite, while in the case of organocomplexes it causes moderate disaggregation.From benzene, alcohols with different numbers of carbon atoms are also preferentially adsorbed on the internal surfaces of montmorillonite; with the rise in the number of carbon atoms, the extent of interlamellar adsorption decreases. In the case of HDP-montmorillonites in methanol-benzene mixtures, the adsorption capacity exhibits a monotonous increase with the degree of organopbility in the range under consideration. In the event of optimum organophility the disaggregation of the organocomplex is complete, and the equivalent specific surface area is 764-778 m² · g^–1. The swelling of the organocomplex, which can be characterized by X-ray diffraction measurement, is in close correlation with the interlamellar liquid adsorption. The results show modification of the surface of montmorillonite with HDP cations fundamentally determines the nature and extent of the selective liquid adsorption.

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Zusammenfassung Die Struktur von mit Hexadecyl-pyridinium(HDP)-Kationen im systematisch gesteigerten Maße bedeckten Montmorilloniten wurde mit der Röntgendiffraktions-Methode untersucht. Es wurde festgestellt, daß die HDP-Kationen, von der Bedeckung der Oberfläche abhängend, im Schichtzwischenraum eine mono- bzw. bimolekulare Schicht bilden. Die selektive Sorption binärer Gemische wurde an Montmorilloniten und an HDP-Montmorilloniten verschiedener Bedeckung eingehend untersucht. Es wurden die Adsorptionsisothermen von Flüssigkeitsgemischen und aus deren Analyse die Adsorptionskapazitäten und die äquivalenten spezifischen Oberflächen bestimmt.Es wurde festgestellt, daß aus Benzol-n-Heptan-Gemischen das Benzol nur an der äußeren Montmorillonite-Oberfläche adsorbiert wird, während es bei Organokomplexen eine mäßige Desaggregation verursacht. Die Adsorption von Alkoholen verschiedener Kohlenstoffzahl aus Benzol erscheint auch an inneren Montmorillonit-Oberflächen bevorzugt; mit zunehmender Kohlenstoffzahl nimmt das Ausmaß der interlamellaren Adsorption ab. Bei HDP-Montmorilloniten zeigt die Adsorptionskapazität aus Methanol-Benzol-Gemischen mit zunehmender Organophilität im untersuchten Gebiet eine monotone Steigerung. Im Falle optimaler Organophilität ist die Desaggregation vollständig, die äquivalente spezifische Oberfläche beträgt 764-778 m²/g. Die durch Röntgenn-diffraktionsmessung charakterisierbare Quellung des Organokomplexes steht mit der interlamellaren Flüssig-keitsadsorption in engern Zusammenhang. Unsere Ergebnisse zeigen, daß Charakter und Ausmaß der selektiven Flüssigkeitsadsorption durch die Modifizierung der Montmorillonit-Oberfläche mit HDP-Kationen grundlegend verändert wird.

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With 14 figures and 4 tables     

Beitrag zur Kenntnis der Pt(II)-Verbindungen mit Acetoxim

Zusammenfassung Es wurde die thermische Zersetzung dercis-undtrans-Isomeren des [PtAox ₂Cl₂] sowie des [PtAox ₃Cl]Cl mit Hilfe derTG-undTD-Kurven im Falle des reinen Komplexes sowie im Falle einer Mischung mit Al₂O₃ (1:3) geklärt. Dietrans-Form ist stabiler als diecis-Form, die Zersetzung wird durch Al₂O₃ nicht beeinflu\t. [PtAox ₃Cl]Cl wird infolge der Erhitzung in die stabileretrans-Form [PtAox ₂Cl₂] umgewandelt und verhält sich auch weiterhin wie diese.

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A contribution to the study of the compounds of Pt(II) with acetoxime

The thermal decomposition ofcis- andtrans-[PtAox ₂Cl₂] and of [PtAox ₃Cl]Cl was studied by means ofTGA andTDA on pure substances as well as on mixtures with Al₂O₃ (1:3). Thetrans form is more stable then thecis form, the presence of Al₂O₃ has no influence on its decomposition. The [PtAox ₃Cl]Cl is transformed by heating into the more stabletrans-isomer and its further behaviour is identical with that of thetrans isomer.

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Mit 4 Abbildung     

Investigation on the chemistry of berbans—VII: Synthesis of 10,11-dimethoxy(depyrrolo)raunescine stereoisomers

Acyloxy-ketone rearrangement, proceeding by the action of base, has been observed in the case of ketone 2. By the reduction of ketones 2 and 3 with sodium boron hydride, new 10, 11-dimethoxy(depyrrolo)raunescine stereoisomers (5a–7a) have been prepared. Previously known alcohols with alloberban skeleton (12,13) have been similarly converted into tetracyclic raunescine stereoisomers (8a,9) by the oxido-reductive method. The stereochemistry of these compounds has been investigated by physical (¹H NMR, IR) and by chemical methods.     

Comparative study on separation of diastereomers by HPLC

Summary Reversed (RP-HPLC) and normal phase chromatographic (NP-HPLC) separations have been developed for diastereomers ofN-acyl-1-methyl-1,2,3,4-tetrahydo-β-carbolines which are acylated derivatives of simple natural β-carboline alkaloids. Separations of derivatives having different acyl moieties in theO,O-diacyl-tartaric acid ester subtituent differed remarkably. Little or no resolution in either NP-HPLC or RP-HPLC could be achieved with the diacetyl-tartrate derivative. Base-line separation by RP-HPLC but no separation by NP-HPLC was possible with the bulkier and more apolar dipivaloyl derivative. Retention order of the bis-benzoylated diastereomers was reversed and separation time increased dramatically by RP-HPLC. Good separation of the medium polarity, but rigid,N-camphanyl derivative by NP-HPLC has been achieved, whereas RP-HPLC could not be used for separation of these diastereomers. Separability of different diastereomers was highly dependent on polarity and rigidity of the derivatizingN-acyl moieties. Conformational analysis by molecular mechanics and comparison of the lowest energy conformational states of the diastereomers was applied to rationalise separation-retention behaviour of stereoisomers by RP-HPLC. Presented at Balaton Symposium '01 on High-Performance Separation Methods, Siófok, Hungary, September 2–4, 2001     

On Strassen's law of the iterated logarithm

Summary Kolmogorov's law of the iterated logarithm has been sharpened by Strassen who proved a more refined theorem by using tools from functional analysis. The present paper gives a classical proof of Strassen's theorem, using a method along the lines of Kolmogorov's original approach. At the same time the result proved here is more general since a) the random variables involved need not have the same distributions, b) the condition of independence is weakened and c) instead of Kolmogorov's growth condition on the random variables, only a mild restriction on their moments of order l3 is needed.     

Study of the gas-phase parameters affecting the silicon-oxide film deposition induced by an ArF laser

A study of the gas-phase parameters involved in ArF laser induced chemical vapour deposition of silicon-oxide thin films is presented. A complete set of experiments has been performed showing the influence of the concentration of the precursor gases, N₂O and SiH₄, and their influence on total and partial pressures on film growth and properties. In this paper we demonstrate the ability of this LCVD method to deposit silicon oxide films of different compositions and densities by appropriate control of gas composition and total pressure. Moreover, a material specific calibration plot comprising data obtained using different preparation techniques is presented, allowing determination of the stoichiometry of SiO _x films by using FTIR spectroscopy independently of the deposition method. For the range of processing conditions examined, the experimental results suggest that chemical processes governing deposition take place mainly in the gas phase.     

Direct Images,Fields of Hilbert Spaces,and Geometric Quantization

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H _s of Hilbert spaces, and the question arises if the spaces H _s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787–902, 1991) and Hitchin (Commun. Math. Phys. 131:347–380, 1990) suggest viewing H _s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle ${E \to Y}$ along a non–proper map ${Y \to S}$ . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Sz?ke (Bull. Lond. Math. Soc. 44:367–374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.     

Unambiguous identification of three beta-decaying isomers in 70Cu

Using resonant laser ionization, beta-decay studies, and for the first time mass measurements, three beta-decaying states have been unambiguously identified in 70Cu. A mass excess of -62 976.1(1.6) keV and a half-life of 44.5(2) s for the (6-) ground state have been determined. The level energies of the (3-) isomer at 101.1(3) keV with T(1/2)=33(2) s and the 1+ isomer at 242.4(3) keV with T(1/2)=6.6(2) s are confirmed by high-precision mass measurements. The low-lying levels of 70Cu populated in the decay of 70Ni and in transfer reactions compare well with large-scale shell-model calculations, and the wave functions appear to be dominated by one proton-one neutron configurations outside the closed Z=28 shell and N=40 subshell. This does not apply to the 1+ state at 1980 keV which exhibits a particular feeding and deexcitation pattern not reproduced by the shell-model calculations.