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.     

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.     

Regioselective synthesis of polysubstituted benzenes from Baylis-Hillman adducts via [4+2] annulation protocol

A new and regioselective [4+2] benzannulation protocol toward polysubstituted benzenes was developed. A nitroalkane derivative, which was prepared from Baylis-Hillman adduct, served as the four-carbon unit and a Michael acceptor as a two-carbon unit. Vinyltriphenylphosphonium salt could also be used as a Michael acceptor efficiently.     

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.     

Mononuclear nonheme ferric-peroxo complex in aldehyde deformylation

A mononuclear nonheme ferric-peroxo complex bearing a macrocyclic tetradentate N4 ligand, [(TMC)Fe(III)-O2]+, was prepared and used in mechanistic studies of aldehyde deformylation; a catalytic aldehyde deformylation by a nonheme iron(II) complex, [Fe(II)(TMC)]2+, and molecular oxygen is reported as well.     

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     

Optimization,validation and comparison of various extraction techniques for the trace determination of polycyclic aromatic hydrocarbons in sewage sludges by liquid chromatography coupled to diode-array and fluorescence detection

There is a need for a better characterization of sludges from wastewater treatment plants which are destined to be spread on agricultural lands. Inorganic pollutants are regularly controlled but organic pollutants have received few attention up to now. On this paper, we have been interested on the analysis of the 16 polycyclic aromatic hydrocarbons (PAHs) listed in the US Environmental Protection Agency (US EPA) priority list and more particularly of the six PAHs listed in the European community list (fluoranthene, benzo[b and k]fluoranthene, benzo[a]pyrene, benzo[ghi]perylene, indeno[1,2,3-cd]pyrene). The analysis step consists on liquid chromatography with both fluorescence and UV detections as described in the EPA Method 8310. As for the extraction step, several techniques such as supercritical fluid extraction, pressurized liquid extraction, focused microwave extraction in open vessels, Soxhlet and ultrasonic extractions are compared after optimization of the experimental conditions (solvent nature and quantity, temperature, pressure, duration, ... ) and validation with certified sludges. When optimized, these five extraction techniques are as much efficient with similar relative standard deviation. Whatever the extraction techniques used, the whole analysis protocol permits to quantify PAHs in the range of 0.09 to 0.9 mg/kg of dried sludges.     

(2E,4E)-3-苯基-2-[2-(N-乙氧羰基甲基氨基)-苯硫基]-2,4-己二烯酸乙酯——一个新的分子内重排反应产物

２，３－二氢－２－甲基－４－苯基－１，５－苯并硫氮杂卓与重氮乙酸乙酯反应，得到非预期的分子内重排的开环产物。通过元素分析、ＩＲ，１ＨＮＭＲ，ＭＳ及Ｘ－晶体衍射分析确定了它的结构，并根据产物的结构，对这一新反应的反应机理进行了探讨和研究。