The measure of a translated ball in uniformly convex spaces

Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r ^q , whereq depends on the properties of the norm. We specify it in the case ofL spaces, >1.     

Relationships between characteristics in periodic Poisson queues

We study single server periodic queues in the day equilibrium conditions. The following characteristics of interest are considered at time of dayt: V^p(t)-the work load, L^p(t)-the number of customers and u^p(t)-the departure rate. We give relationships between E[V^p(t)], E[L^p(t)] and u^p(t). We also prove that E[V^p(t)] < and E[L^p(t)] < provided the second moment of the service time is finite.     

Nuclear spin relaxation study of aqueous raffinose solution in the presence of a gadolinium contrast agent

Paramagnetic enhancement of nuclear spin-lattice relaxation rates (PREs) was measured in aqueous solution of the trisaccharide raffinose in the presence of a gadolinium(III) complex, GdDTPA-BMA, used as a magnetic resonance imaging contrast agent. The relaxation enhancement of aqueous protons was measured over a broad range of magnetic fields, using field-cycling apparatus in addition to conventional spectrometers. The nuclear magnetic relaxation dispersion profile thus obtained was interpreted with a recently developed model, allowing for both inner- and outer-sphere relaxation. The relaxation enhancement for the carbon-13 nuclei in raffinose was studied under high-resolution conditions at three magnetic fields, whereas the sugar proton PRE was measured at two fields. The PRE of the sugar nuclei could be interpreted in a consistent way, assuming that it was caused by the outer-sphere mechanism. The electron spin relaxation was found to be a less important source of modulation of the electron-nuclear dipole-dipole interaction than the mutual translational diffusion.     

Determination of organotin compounds in biological samples using accelerated solvent extraction,sodium tetraethylborate ethylation,and multicapillary gas chromatography–flame photometric detection

A method has been developed for species-selective analysis of organotin compounds in solid, biological samples. The procedure is based on accelerated solvent extraction (ASE) of analytes and includes extraction of the tin species with a methanol–water (90% methanol) solution of acetic acid/sodium acetate containing tropolone (0.03% w/v), their ethylation with NaBEt₄, and separation and detection by GC–FPD. The analytical procedure was optimized with an unspiked sample of harbor porpoise (Phocoena phocoena) liver. Effects of ASE operational variables (extraction temperature and pressure, solvent composition, number of static extraction steps) are discussed. Method detection limits (MDL) were in the range 6–10 ng(Sn) g^–1 dry weight and 7–17 ng(Sn) g^–1 dry weight for butyl- and phenyltin compounds, respectively. Recoveries were comparable with or better than those obtained by use of other procedures reported in the literature. The analytical procedure was validated by analysis of NIES No. 11 (fish tissue) certified reference material.     

Large configuration interaction calculations of nuclear spin-spin coupling constants: III. Vibrational effects in ammonia

Large configuration interaction calculations of the proton—proton coupling constant for several geometrical configurations of the ammonia molecules are reported. The analytical expressions for the energy surface and the coupling constant as functions of two cartesian displacement coordinates are fitted to the calculated values. The potential is used for the calculation of the vibrational wavefunctions for ¹⁵NH₃ and ¹⁵ND₃ species and the vibrational averaging of the coupling constant is carried out using these functions. Though the value of the coupling constants shows a very strong geometry dependence, the vibrational corrections are found to be small. A possible correlation of the proton—proton coupling constant with an angular parameter in the NH₂ group in RNH₂ compounds is indicated.     

Unusual reactivity of ortho-carbonylphenylboronic acids with diethanolamine

The reaction of carbonyl-substituted phenylboronic acids with diethanolamine has been investigated. For compounds containing carbonyl groups at the meta or para positions the reaction occurs exclusively at the boronic acid. Different reactivities were observed for ortho-substituted acetyl- and formylphenylboronic acids where the reaction occurred at both the boronic acid and at the carbonyl group. X-ray studies revealed the presence of a polycyclic structure with tetravalent boron and nitrogen atoms.     

Synthesis of novel tri-podal mesogenic alkenes and side-chain polysiloxanes

Low molecular weight tri-podal biphenyl- and benzoate-type mesogens [C₆H₅C₆H₄O(CH₂)₅SiMe₂CH₂CH₂SiMe₂]₃CH (4), [C₁₁H₂₃O(C₆H₄)₂O(CH₂)₅SiMe₂]₃CH (5) and [MeOC₆H₄OC(O)C₆H₄O(CH₂)₅SiMe₂]₃CH (6) (C₆H₄ = 1,4-phenylene) were obtained, from branched silyl substituted methane precursors [CH₂CH(Me)₂Si]₃CH (1) and (HMe₂Si)₃CH (2). The biphenyl-containing ones (4) and (5) were converted into terminal alkenes, which were subsequently hydrosilylated with poly(methylsiloxanes). The polymer derived from (5) exhibited mesomorphic properties. Such systems have the potential to significantly increase the density of liquid crystal rod-like structures in side chains of linear polymers (or dendritic liquid crystal polymers).