Ergodic properties of Poisson processes with almost periodic intensity

Summary We discuss in this paper a non-homogeneous Poisson process A driven by an almost periodic intensity function. We give the stationary version A ^* and the Palm version A ⁰ corresponding to A ^*. Let (T _i ,i) be the inter-point distance sequence in A and (T _i ⁰ ,i) in A ⁰. We prove that forj, the sequence (T _i+j,i) converges in distribution to (T _i ⁰ ,i). If the intensity function is periodic then the convergence is in variation.     

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.     

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.     

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).     

Bicyclic [b]-heteroannulated pyridazine derivatives. 4. Cyclization reactions of 4-aryltetrahydropyridazine-3,6-dione 3-hydrazones with some keto esters

Ethoxycarbonylalkylidene derivatives 2 and 6 of the title hydrazones were obtained in the reaction with ethyl pyruvate or ethyl aroylformate and ethyl acetoacetate, respectively, in methanol. Both compounds were mixtures of geometric isomers with high predominance of one of them. Nmr spectroscopy revealed an unexpected magnetic non-equivalence of the CH₂ protons in the ester ethyl group of the major isomer of 6 . On heating (?200°) in an inert medium or on refluxing in ethanolic sodium ethoxide 2 cyclized to the corresponding pyridazino[6,1-c]-triazines 4 , whereas 6 formed pyrazolylpyridazines 7 . The structure of the latter was unambigously established by X-ray analysis. Alkylation of 4a with benzyl bromide in the presence of tetrabutylammonium bromide occurred selectively on the pyridazine N atom.     

Inclusion-dependent mechanism of modification of cyclodextrins with heterocycles

Mono(6-deoxy-dimethylpyridinium)-β-cyclodextrins have been synthesized in reaction of mono (p-toluenesulfonyl) derivative of β cyclodextrin with the appropriate lutidine under microwave irradiation and conventional conditions. The results indicate that the mechanism consists of inclusion complex formation.