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.     

The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups

In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure .     

Neutronh 11/2 alignments in the triaxial nucleus133La

High spin states have been studied in¹³³La via the¹²²Sn (¹⁵N, 4ny) fusion evaporation reaction. Bands build on low lying h_11/2,g_7/2 and d_5/2 proton states have been identified. At higher spin a h_11/2 neutron alignment is observed. The softness with respect to the triaxial deformation makes the nuclear shape sensitive to the quasiparticle configurations and coexistence between states withy ≈ + 30°,y ≈ ? 30° andy ≦ ? 60° was found. The results have been interpreted using total routhian surface (TRS) model calculations.