Compound Binomial Approximations

We consider the approximation of the convolution product of not necessarily identical probability distributions q _j I + p _j F, (j=1,...,n), where, for all j, p _j =1−q _j ∈[0, 1], I is the Dirac measure at point zero, and F is a probability distribution on the real line. As an approximation, we use a compound binomial distribution, which is defined in a one-parametric way: the number of trials remains the same but the p _j are replaced with their mean or, more generally, with an arbitrary success probability p. We also consider approximations by finite signed measures derived from an expansion based on Krawtchouk polynomials. Bounds for the approximation error in different metrics are presented. If F is a symmetric distribution about zero or a suitably shifted distribution, the bounds have a better order than in the case of a general F. Asymptotic sharp bounds are given in the case, when F is symmetric and concentrated on two points. An erratum to this article can be found at     

Less toxic acetylacetonates as initiators of trimethylene carbonate and 2,2‐dimethyltrimethylene carbonate ring opening polymerization

This article presents the results of TMC and DMC polymerization with the use of acetylacetonates of low‐toxic metals: iron, zinc, and zirconium. Zinc (II) acetylacetonate proves to be a very good initiator of homopolymerization. The reaction carried out with the use of this initiator at 110 °C is very rapid and of high yield. Using both zinc and iron (III) acetylacetonates, as well as the zirconium (IV) one, in high temperatures it is possible to obtain PTMC possessing high molecular mass, thus ensuring optimization of the relation between the duration of the polymerization and its yield. A strong influence of thermal degradation on the course of the reaction has been observed, particularly at 160 °C, with the use of Fe(acac)₃ as the initiator. DMC polymerization proceeds much more slowly when initiated by iron and zinc acetylacetonates. A high conversion of the monomer is obtained in this case as well. The relation between the molecular mass of the obtained PDMC and the conversion of the monomer is directly proportional; however, those masses, determined on the basis of polystyrene standards, are much lower than those estimated theoretically. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1913–1922, 2005     

Application of radiochromic gel detector (FXG) for UVA dose measurements

Tissue equivalent radiochromic gel material containing ferrous ions, xylenol-orange ion indicator and gelatin as gelling agent (FXG) is known to be sensitive to γ- and X-rays; hence it has been used for ionizing radiation dosimetry. Changes in optical absorbance properties of FXG material over a wide region in the visible spectrum were found to be proportional to the radiation absorbed dose. An earlier study demonstrated the sensitivity of FXG gel detector to ultraviolet radiation and therefore that could give quantitative measure for UV exposure. This study focuses on the detection of UVA radiation (315–400 nm), which forms an important part (～97%) of the natural solar UV radiation reaching the earth surface. A solar UV simulator device was used to deliver UVA radiation to FXG samples. The beam was optically modified to irradiate gel samples at an exposure level about 58 W/m², which is comparable to the summer natural UVA radiation measured outside the laboratory building at midday (～60 W/m²). Experimental results were used to generate mathematical second order formulas that give the relationship between UVA dose and optical absorbance changes observed at two wavelengths in the visible region of the spectrum—430 and 560 nm.     

Initiation of the stereospecific polymerization of p-chlorophenylglycidyl and phenylglycidyl ethers by the Al(OiPr)3 + ZnEt2 (1:1) initiator system

The Al(OiPr)₃ + ZnEt₂ (1:1) system has been found to be an efficient initiator of the polymerization of phenylglycidyl ethers. About 40–60% of the polymer obtained was an isotactic polymer fraction (ca. 80% of iso diads). By using aluminum isopropoxide containing C¹⁴, the amount of linear polymer molecules terminated by isopropoxide groups was shown not to exceed 50%. IR spectrophotometric studies of the structure of the initiator system showed that its components form a complex compound by an exchange of substituents between the aluminum and zinc atoms.     

Polymerization of chlorophenyl glycidyl ethers. VIII. Initiation of the polymerization of p-chlorophenyl glycidyl ether and phenyl glycidyl ether by the system aluminum isopropoxide and zinc chloride (1:1)

Labeled aluminum alcoholate was used to determine the content of end groups of polyethers formed in polymerization reactions initiated by the system Al(OiPr)₃ + ZnCl₂ (1:1). The polymerization process proceeded in several successive stages. Polymerization initiation and propagation mechanisms were proposed.     

A shorter proof of Kanter’s Bessel function concentration bound

We give a shorter proof of Kanter’s (J. Multivariate Anal. 6, 222–236, 1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide sharp upper bounds for the sum of modified Bessel functions I₀(x) + I₁(x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent random variables due to Čekanavičius & Roos (Lith. Math. J. 46, 54–91, 2006); Roos (Bernoulli, 11, 533–557, 2005), Barbour & Xia (ESAIM Probab. Stat. 3, 131–150, 1999), and Le Cam (Asymptotic Methods in Statistical Decision Theory. Springer, Berlin Heidelberg New York, 1986).      

Poisson type approximations for the Markov binomial distribution

The Markov binomial distribution is approximated by the Poisson distribution with the same mean, by a translated Poisson distribution and by two-parametric Poisson type signed measures. Using an adaptation of Le Cam’s operator technique, estimates of accuracy are proved for the total variation, local and Wasserstein norms. In a special case, asymptotically sharp constants are obtained. For some auxiliary results, we used Stein’s method.     

Volume-dependent rate processes in an epoxy resin

Results for four different volume-dependent rate processes of an epoxy resin, Epon 1001F, fully cured with a stoichiometric amount of 4,4′-diamino diphenyl sulfone are presented: (1) specific volume measurements at constant rates of cooling; (2) time-dependent volume measurements after rapid temperature changes; (3) elongational creep compliance measurements; and (4) shear creep compliance measurements. Voluminal and shear retardation spectra are compared as are the temperature time scale shift factors, a_T obtained from the four processes. Volume–temperature cooling curves show the decreasing glass temperature with decreasing rate of cooling, but appear to reach the glass line at a constant temperature regardless of the rate of cooling. This narrowing of the “transition range” is not predicted by the Kovacs, Aklonis, Hutchinson, and Ramos (KAHR) multiparameter model, which assumes thermorheological simplicity.     

Investigation of the quantitative properties of the quadrupole orthogonal acceleration time-of-flight mass spectrometer with electrospray ionisation using 3,4-methylenedioxymethamphetamine

This paper describes the investigation of the potential of a quadrupole orthogonal acceleration time-of-flight mass spectrometer (Q-TOF) equipped with an atmospheric pressure ionisation interface for quantitative measurements of small molecules separated by reversed phase liquid chromatography. To this end, the detection limits and linear dynamic range in particular were studied in an LC/MS/MS experiment using 3,4-methylenedioxymethamphetamine standards and 3,4-methylenedioxyethylamphetamine for internal standardisation. In a second phase, the experiment was repeated with real biological extracts (whole blood, serum, and vitreous humour). A calibration for 3,4-methylenedioxymethamphetamine and its metabolite 3,4-methylenedioxyamphetamine was prepared in each of these matrices again using 3,4-methylenedioxyethylamphetamine as internal standard. The resulting quantitative data were compared with those obtained by liquid chromatography with fluorescence detection for the same extracts. The Q-TOF results revealed excellent sensitivity and a linear dynamic range of nearly four decades (2-10 000 pg on-column, r(2) = 0.9998, 1/x weighting). Furthermore, all the calibration curves prepared in biological material were superimposable, LC/MS/MS and LC-fluorescence, and the quantitative results for actual samples compared very favourably. It was concluded that the Q-TOF achieves a linear dynamic range for quantitative LC/MS/MS work exceeding that of fluorescence detection and at much better absolute sensitivity. Copyright 1999 John Wiley & Sons, Ltd.