The sum of the squares of degrees: Sharp asymptotics

Let f(n,m) be the maximum of the sum of the squares of degrees of a graph with n vertices and m edges. Summarizing earlier research, we present a concise, asymptotically sharp upper bound on f(n,m), better than the bound of de Caen for almost all n and m.     

Long-wavelength dynamics of the two-dimensional antiferromagnet

We perform the long-wavelength reduction of the two-dimensional quantum lattice rotator model. An intermediate scale is introduced and the short-wavelength antiferromagnetic spin fluctuations are integrated out. The saddle-point solution for the generalized continuous sigma-model in terms of parameters of the initial model is constructed.     

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.     

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     

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.