Convolution of Rayleigh functions with respect to the Bessel index

A convolution of Rayleigh functions with respect to the Bessel index can be treated as a special function in its own right. It appears in constructing global-in-time solutions for some semilinear evolution equations in circular domains and may control the smoothing effect due to nonlinearity. An explicit representation for it is derived which involves the special function ψ(x) (the logarithmic derivative of the Γ-function). The properties of the convolution in question are established. Asymptotic expansions for small and large values of the argument are obtained and the graph is presented.     

On Edgeworth expansions for dependency-neighborhoods chain structures and Stein's method

Let W be the sum of dependent random variables, and h(x) be a function. This paper provides an Edgeworth expansion of an arbitrary ``length' for %E{h(W)} in terms of certain characteristics of dependency, and of the smoothness of h and/or the distribution of W. The core of the class of dependency structures for which these characteristics are meaningful is the local dependency, but in fact, the class is essentially wider. The remainder is estimated in terms of Lyapunov's ratios. The proof is based on a Stein's method.Supported in part by NSF grant DMS-98-03623Supported in part by the Russian Foundation of Basic Research, grant # 00-01-00194, and by NSF grant DMS-98-03623Mathematics Subject Classification (2000):Primary 62E20; Secondary 60E05     

Application of Acoustic Spectroscopy to Investigation of Microinhomogeneous Media

Main mechanisms of absorption and dispersion of sound velocity in microinhomogeneous media are considered. Existing formulas for the velocity and absorption of sound in dispersion media is generalized to the case of continuos dispersed phase particle size distribution. The obtained relations were used for the analysis of the acoustic spectra of dodecane-based magnetic fluid measured in the 12–2000 MHz frequency range at temperatures varied from 0 to 80°C. The distribution of the volume fraction over particle sites in the examined magnetic fluid was described by a lognormal function. Parameters characterizing particle size distribution were determined. The analysis of the results of processing of the acoustic spectra of magnetic fluid indicated that the main contribution to the additional absorption (compared to absorption in the dispersion medium) originates from the friction and heat exchange between the particles and dispersion liquid. Absorption of sound due to scattering by the particles was negligibly small.     

Simulation of CPMAS Signals at High Spinning Speeds

The spin dynamics of anS( )I_Nsystem during the CP mixing time of continuous wave and variable amplitude cross-polarization magic angle spinning (CWCPMAS and VACPMAS) experiments is discussed. The signal enhancement of a low abundantSspin, coupled to a set ofN= 6 coupled spins withI= , is evaluated as a function of the length of the mixing time. For CWCPMAS this signal is first evaluated in the frequency domain and then transformed to the time domain. These calculations provide some additional insight into the CP spin dynamics and enable a practical approach toward the evaluation of CP signals of large spin systems. In addition the adiabatic character of the ramped VACPMAS experiments is discussed andS-spin signals of a spin system withN= 6 are simulated. Estimates of the upper bounds of the CP signals as a function of the number ofIspins in anS( )I_Nsystem are given and compared with the calculated values.     

Classification of metal ions according to their complexing properties: a data-driven approach

Factor, cluster and self-organizing map analyses were performed for the stability constants of complexes of 24 metal ions and hydrogen with 3960 ligands (15606 values of log K₁). Five factors reproduce 89% of data variability. Both direct clusterization and clusterization on the basis of factor analysis established the existence of six different classes of similar cations. The similarity series for metal ions and relative similarity of several ions are discussed and the Kohonen two-dimensional map, which visually represents the similarity, is presented.     

Ethylene polymerization over supported catalysts [2,6‐bis(imino)pyridyl iron dichloride/magnesium dichloride] with AlR3 as an activator

Data on ethylene polymerization over supported LFeCl₂/MgCl₂ catalysts {L = 2,6‐bis[1‐(2,6‐dimethylphenylimino)ethyl]pyridyl} containing AlR₃ (R = Me, Et, i‐Bu, or n‐Oct) as an activator are presented. These catalysts are highly active (100–300 kg of polyethylene/g of Fe h bar of C₂H₄) and stable in ethylene polymerization at 70–80 °C. Data on the effects of the iron content, AlR₃ type, Al(i‐Bu)₃ concentration, and hydrogen presence on the catalyst activity are presented. The molecular structure of polyethylene produced with these catalysts (including the molecular masses, molecular mass distribution, branching, and number of C?C bonds) has been studied; data on the effects of AlR₃ and hydrogen on the molecular structure are presented. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2128–2133, 2005     

New class of non-carbon AlP nanotubes: Structure and electronic properties

A new class of non-carbon nanotubes based on Group III and Group V elements (aluminum and phosphorus, respectively) is considered. The equilibrium geometry, energy characteristics, and electronic structure of the AlP nanotubes were calculated using the density functional theory. These calculations demonstrated that the AlP nanotubes are energetically stable structures. It was found that a low strain energy (approximately 0.01–0.07 eV) is required for rolling a two-dimensional hexagonal AlP structure into a tube. The AlP nanotubes are found to be wide-band-gap semiconductors with a band gap of 2.05–3.73 eV with direct (for the zigzag type) or indirect (for the armchair type) transitions between the top of the valence band and the bottom of the conduction band. The band gap of these nanotubes increases with the tube diameter, approaching the band gap of a two-dimensional hexagonal AlP layer.     

Anomalous reduction of the β-decay rate due to resonant energy absorption

The solvable model of a periodic array of quantum dots in a magnetic field is investigated. It is shown that in the case of square lattice and irrational flux the energy spectrum of a charged particle in the array has a fractal structure. In the case of honeycomb lattice the existence of an additional splitting of magnetic bands related with lattice geometry. The position of the Van Hove singularities is determined.     

The International Atomic Energy Agency's program on analytical quality control

For more than thirty years the International Atomic Energy Agency has been assisting laboratories in Member States in maintaining and improving the reliability, i.e. the quality of analyses of nuclear, industrial, environmental and biological materials, and materials of marine origin. Through the Analytical Quality Control Services (AQCS) the Agency initiates and supports improvements in the accuracy of analytical chemical and radiometric measurements and their traceability to basic standards. This is achieved by organizing worldwide and regional intercomparison exercises and by distributing reference materials. The latest biological and environmental reference and intercomparison materials are presented and general information is given on the preparation of materials, intercomparison runs, and the evaluation of reference data. Means to improve the quality of intercomparison results are presented and discussed.