Domination inequality for martingale transforms of a Rademacher sequence

Letf _n = Σ _k=1 ⁿ v _k r _k ,n=1,…, be a martingale transform of a Rademacher sequence (r _n)and let (r _n ^′ ) be an independent copy of (r _n).The main result of this paper states that there exists an absolute constantK such that for allp, 1≤p<∞, the following inequality is true: In order to prove this result, we obtain some inequalities which may be of independent interest. In particular, we show that for every sequence of scalars (a _n)one has where is theK-interpolation norm between ℓ₁ and ℓ₂. We also derive a new exponential inequality for martingale transforms of a Rademacher sequence. This research was supported in part by an NSF grant and an FRPD grant at NCSU.     

Solvated electron in liquid methanol. An example of a statistical species in chemistry

The methods of analysis of the statistical ensembles of trapping sites, before and after electron localization, for electrons in disordered media are surveyed. The review covers the computer-search methods for pre-existing traps in polar matrices, random field theory of disordered polar matrices and the path integral simulations of solvated electron. The common picture provided by all these methods is emphasized: the solvated electron is a unique in chemistry statistical species characterized by statistical distributions of the structural parameters, energy states, reactivity, etc. The numerical examples are provided by the simulations of the trapping sites and the solvated electron in liquid methanol.     

Further studies on the chemistry and structure of n-oxides of sparteine and its derivatives—V: Synthesis and structure of 2-phenylsparteine-n16-oxide,a new case of “sponge” proton

The synthesis of 2-phenylsparteine-N₁₆-oxide (7) and its perchlorate salt (7-H⁺) was carried out. On the basis of spectral data, and by comparison with appropriate sparteine-N-oxides, the mechanism of formation and the structures of the two new compounds were proposed. It was found, the basicity of the new N-oxide is unexpectedly high and comparable to the basicity of quaternary ammonium hydroxides. The structure and the strength of intramolecular H-bond in 7-H⁺ makes 7 an excellent “catcher” proton or specific ”sponge” proton.     

Development of a capillary electrophoretic method for the analysis of amino acids containing tablets

Ketosteril is an enteral medicinal product indicated for prevention and therapy in chronic renal insufficiency in connection with a low protein diet. Tablets of Ketosteril contain five essential amino acids like: Lys, His, Thr, Trp, Tyr and another five amino acids in the form of their hydroxy and keto analogues as calcium salts, that are: alpha-ketoleucine, alpha-ketoisoleucine, alpha-ketovaline, alpha-ketophenylalanine and alpha-hydroxymethionine. The composition of Ketosteril tablets is routinely tested with three LC methods. Capillary electrophoretic method seems to be a good alternative for amino acids and their analogues determination in multicomponent pharmaceuticals because of short analysis time and the possibility to assay all components during a single run without any pretreatment. Electrophoresis was performed in 50 microm I.D. fused-silica capillaries with 65 cm distance to the detector. Capillaries were installed in Waters Quanta 4000 electrophoretic equipment with a positive power supply and on-line UV detection at 214 nm. Separations were done in a buffer containing 40 mM Tris and 160 mM boric acid titrated with NaOH to pH 10. The method developed allows the separation of all investigated analytes with an efficiency of n = 230,000 and 20 min analysis time. The method was applied for determination of all components of Ketosteril in commercial tablets.     

Electronic structure of octacyanides of molybdenum IV and V according to the SCCC MO method

The SCCC MO method has been used to calculate the electronic structure and spectrum of Mo(CN) ₈ ^4– and Mo(CN) ₈ ^3– ions of a D _4d symmetry. All metal-ligand and ligand-ligand interactions and all overlap integrals (over products of HF atomic orbitals) have been included within the SCCC MO scheme. Basing on these calculations a new assignment of some absorption bands is proposed. The overall agreement between the calculated and observed electronic spectrum is satisfactory.

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Zusammenfassung Elektronenstruktur und Spektrum der [Mo(CN)₈]^–4- und [Mo(CN)₈]^–3-Ionen in D _4d -Symmetrie wurden mit der SCCC-MO-Methode berechnet. Alle Metall-Ligand- und Ligand-Ligand-Wechsel-wirkungen und Überlappungsintegrale wurden berücksichtigt. Die Bandenzuordnung wurde neu vorgenommen. Die Übereinstimmung der berechneten und gemessenen Spektren ist befriedigend.

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Résumé Application à Mo(CN) ₈ ^4– et Mo(CN) ₈ ^3– de la méthode SCCC MO basée sur des orbitales atomiques HF approchées, en tenant compte du recouvrement et de toutes les interactions ligand-ligand. Dans la partie I on discute le cas de la symétrie D _4d . L'accord global avec l'expérience est satisfaisant en ce qui concerne les spectres. On montre aussi que toutes les attributions antérieures basées sur la théorie du champ cristallin semblent inadéquates.

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The authors are grateful to Prof. W. Jakób, Dr. Z. Stasicka and Dr. A. Samotus for many interesting discussions, to Prof. J. Chojnacki for providing us with new X-ray results before publication and to Dr. A. J. Sadlej for a help in dealing with the computer.     

Propagating transverse electric and transverse magnetic modes in liquid crystal-clad planar waveguides

ABSTRACT

In a planar dielectric waveguide, weak confinement of a propagating mode in a high index core leads to a measurable evanescent interaction with the cladding. In this work, we study the effect of a reorientable anisotropic cladding on the behaviour of Transverse Electric (TE) and Transverse Magnetic (TM) mode polarisations using a liquid crystal (LC)-clad waveguide architecture. The polarised evanescent field of a guided mode interacts with a voltage-tunable birefringent LC cladding to deflect an out-coupled beam. Experimental measurements are coupled with a theoretical framework and show good consistency with simulation results. We isolate the effect of mode confinement by changing the thickness of the high index core. Interactions between the LC index ellipsoid and the mode polarisation are probed by changing the initial alignment of the LC. Finally, we examine the difference in deflection between TE and TM modes, which incorporates both a change in mode confinement and a difference in LC index components.     

Solvent extraction and bulk liquid membrane transport of Co(II) and Ni(II) ammine cations by proton-ionizable crown ethers

Separation efficiencies and selectivities in solvent extraction of Co(II) and Ni(H) ammine cations from aqueous solutions into chloroform and toluene and in transport through bulk toluene membranes by proton-ionizable crown ethers have been determined. Six proton-ionizable crown ethers with differing lipophilicities, polyether cavity sizes and ionizable groups (carboxylic and sulfonic acid functions) were examined. Higher selectivity and efficiency for Co(II) ammine cation extraction was observed for the more lipophilic, proton-ionizable crown ethers. Highly lipophilic crown carboxylic acids provided effective and selective transport of Co(II) ammine cations through bulk toluene membranes.Presented in part at the 6th International Symposium on High Purity Materials in Science and Technology: Preparation, Characterization and Application of Well-Defined Materials, Dresden, GDR, May 1985, Poster D91, Poster Abstracts, pp. 144, 145.All extraction and transport experiments were conducted at this location.     

Solvent-generated HPLC systems with β-cyclodextrin derivatives as chiral additives

It is shown that enantioselective solvent-generated liquid-liquid and liquid-solid Chromatographic systems with -cyclodextrin derivatives can be realized. The liquid-liquid systems are based on ternary solvent systems of limited miscibility, containing chiral additives; the chiral stationary phase is spontaneously generated on the porous microparticulate silica used as a solid support. In the solvent-generated adsorption systems a very small proportion of -cyclodextrin derivatives is added to the mobile phase. These components act as column activators, since they are strongly adsorbed on the RP solid support where they form new stereoselective adsorption sites. It is demonstrated that dynamically generated systems with -cyclodextrin derivatives as chiral agents are powerful and versatile tools for enantioseparation of different types of compounds. This technique creates not only a new type of selectivity but also leads to very stable and reproducible Chromatographic columns.Dedicated to Professor J. F. K. Huber on the occasion of his 65th birthday     

Silicate Xerogels with Dopant-Induced Chirality

A series of silicate xerogels with entrapped chiral amino acids have been obtained via sol-gel technology. The transparent, glassy samples obtained exhibit chirality in the bulk due to the presence of the entrapped asymmetric molecules. Measurements of the optical activity of the doped xerogel samples revealed that the entrapment did not significantly influence the optical activity observed for liquid solutions of the amino acids. Thus, the sol-gel method enables the preparation of amorphous optical materials exhibiting properties of strictly spatially defined molecular systems. Apart from the obvious optical applications, such porous materials with asymmetric centers might find interesting applications in chiral chemical syntheses and separations.     

Thermal decomposition of Cr(III) dithiocarbamates

The thermal stability of chromium(III) complexes with dithiocarbamate acid derivatives was studied. The general formula of these complexes is (RCS₂)₃Cr where: The thermal stability of these complexes was found to depend on the kind ofR and the decomposition occur in several stages.The final product of the decomposition of the complexes in the 20–600 temperature range investigated is chromium sulphide, Cr₂S₃ or with incomplete combusted sulfur atoms.

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Zusammenfassung Die Thermostabilität von Chrom(III)-Komplexen mit sauren Derivaten von Dithiocarbamat wurde untersucht. Die allgemeine Formel dieser Komplexe ist (RCS₂)₃Cr. Es wurde festgestellt, da\ die Thermostabilität dieser Komplexe von der Art von R abhängt und die Zersetzung in mehreren Stufen verläuft.Das Endprodukt der Zersetzung der Komplexe im untersuchten Temperaturbereich von 20 bis 600 ist Chromsulfid, Cr₂S₃, oder solches mit überschüssigem Schwefel.

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Résumé On a étudié la stabilité thermique des complexes du chrome(III) avec les dérivés de l'acide dithiocarbamique. La formule générale de ces complexes est (RCS₂)₃Cr où: On a trouvé que la stabilité thermique de ces complexes dépendait de la nature du radical et que la décomposition se déroulait en plusieurs étapes.Dans l'intervalle de température étudié, de 20 à 600, le produit final de la décomposition des complexes est le sulfure de chrome, Cr₂S₃, éventuellement accompagné de soufre résultant d'une combustion incomplÊte.

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(III) - . — (RCS₂)₃ Cr, , R . 20–600 Cr₂S₃ .

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The autors would like to thank Doc. dr h. J. F. Biernat for valuable discussions.