Sticks and clubs

We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side by-side product of partial orderings which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with ¬CH and Martin's axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club principle for every stationary subset of limits of ω₁ together with ¬CH and Martin's axiom for countable p.o.-sets.     

Radical cyclization of sugar-derived beta-(alkynyloxy)acrylates: synthesis of novel fused ethers

[formula: see text] Tributyltin radical mediated cyclization of carbohydrate-derived beta-(alkynyloxy)acrylates leading to highly functionalized cis- and trans-fused bicyclic ethers of various ring sizes is described. The efficacy of the radical cyclization is nicely illustrated in the iterative construction of a trans-fused tricyclic tetrahydropyran.     

Technische Verfahren zur Synthese von Carotinoiden und verwandten Verbindungen aus 6-Oxo-isophoron. VI. Synthese Von Rhodoxanthin und (3-RS, 3′RS)-Zeaxanthin; Zugänge zur C15-Ringkomponente über 3-Oxo-jonon-Derivate

Technical Procedures for the Synthesis of Carotenoids and Related Compounds from 6-Oxo-isophorone, VI. Synthesis of Rhodoxanthin and (3RS, 3′RS)-Zeaxanthin; Routes to the C₁₅-Ring Component via 3-Oxo-ionone Derivatives The C₁₅-ring component 4 , key intermediate of a new scheme for the synthesis of rhodoxanthin ( 1 ) and (3RS, 3RS)-zeaxanthin ( 3 ), has been synthesized starting from 6-oxo-isophorone ( 7 ) via 3-oxo-cyclocitral and 3-oxo-ionone derivatives.     

Comparing weak versions of separability

Our aim is to investigate spaces with σ-discrete and meager dense sets, as well as selective versions of these properties. We construct numerous examples to point out the differences between these classes while answering questions of Tkachuk [22], Hutchison [13] and the authors of [7].     

Redoxkinetik von Metallkomplexen in nichtwäßrigen Lösungen,XI. Die Reduktion von Thallium(III)oxinat mit Eisen(II) in schwach koordinierenden Lösungsmitteln

The kinetics of the iron(II) reduction of thallium(III) oxinate does not differ essentially from that of the oxinate-transfer from thallium(III)-oxinate to iron(III), described before: formation of a binuclear intermediate, rearrangements within, and subsequent reaction with the excess reactant to the final products. As for the redox process, these intermediates are binuclear Tl(II)-Fe(III) complexes which, with initial reactants, form further complexes in which the second electron is transferred. In the cases of excess Tl(ox)₃ and of equimolar reactants, disproportionations are likely involved.     

Contribution to the application of the langmuir probe technique for plasma monitoring in the Ar and n-hexane mixture plasma during the polymerisation process

In the present paper the Langmuir probe technique was applied for plasma monitoring in the Ar and n-hexane mixture plasma during the polymerisation process. The experiments were performed in a stainless steel DC magnetron reactor with a planar magnetron cathode. Within the investigated range of the gas pressure, no time-stable condition of the discharge was found. The regular oscillations, of a frequency of approximately 32 kHz, were observed in the Ar and 20% n-hexane mixture at the total pressure of 10 Pa and the discharge current of 8 mA. The experimentally obtained probe characteristics were used to determine the density and the average energy of electrons. In the DC magnetron stainless steel reactor the electron average energy in the Ar and n-hexane mixture plasma was about one order of magnitude smaller than in the case in which the working gas inside the reactor was the pure Ar. The probe measurements in the magnetron reactor were supplemented by the experiment in the customary glass discharge tube with a hollow cathode. In the glass discharge tube and in the Ar and 10% n-hexane mixture plasma a region of plasma parameters was found, in which the plasma was stable and no instabilities were observed. At such conditions the experiments in the glass discharge tube were used for the study of the efficiency of the probe surface cleaning methods used. This report was financially supported by grant 202/97/1011, 202/98/0116 and 202/98/0666 of the Grant Agency of Czech Republic, by the grant 75/98 of the Grant Agency of Charles University and by project COST 516. This work has been done within the framework of Association for Education, Research and Application in Plasma Chemistry.     

Accurate and stable numerical Hartree–Fock calculations for atoms. I. The 1s2 ground state of H−, He,Li+, and Be++

New techniques have been developed for atomic self-consistent-field calculations by numerical integration. For the origin and tail regions we present analytical expansions which can represent the solutions to high accuracy. For the numerical integration in the central region a five-point generalization of the Numerov formula is used; the error term is of the order h¹⁰. While this formula is unstable if used in the customary way, stability is achieved by using a Gaussian elimination technique. The new procedures are tested on the ground state of the helium isoelectronic series; with 251 integration points all quantities are calculated with an inherent accuracy of better than 10^–11.