Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach

The characteristic exponent α of a Lévy-stable law S _α (σ, β, μ) was thoroughly studied as the extreme value index of a heavy tailed distribution. For 1 < α < 2, Peng (Statist. Probab. Lett. 52: 255–264, 2001) has proposed, via the extreme value approach, an asymptotically normal estimator for the location parameter μ. In this paper, we derive by the same approach, an estimator for the scale parameter σ and we discuss its limiting behavior.      

Structural-morphological and biological properties of selenium nanoparticles stabilized by bovine serum albumin

Nanostructures formed during the reduction of ionic selenium in the selenite-ascorbate redox system in an aqueous solution of bovine serum albumin (BSA) were studied using static and dynamic light scattering and flow birefringence. It was established that this process results in the formation of stable aggregates of selenium nanoparticles that adsorb BSA molecules. It was found that highly-ordered superhigh-molecular-weight spherical nanostructures with high density and unique morphology are formed. Experiments with a cell culture of promyelocytic leukemia HL-60 showed that BSA adsorbed on selenium nanoparticles can inhibit the growth of tumor cells and deactivate free radicals with an efficiency comparable with that of sodium selenite.     

A Lower Bound for the Differences of Powers of Linear Operators

Let T be a bounded linear operator in a Banach space, with σ（T）={1}. In 1983, Esterle-Berkani＇ s conjecture was proposed for the decay of differences （I - T） T^n as follows： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.     

Zinc-Containing Polymers and Their Latexes: Structure and Properties

This work deals with the polymer latexes synthesized using zinc-containing monomers. The effect of the ligand environment of the zinc-containing monomers on the colloidal and rheological properties of the latexes, as well as on mechanical properties of their films is studied. Mixed zinc salts containing the residues of saturated and unsaturated carboxylic acids are shown to be more efficient cross-linking agents than the symmetric salts of this metal.     

Complex backflow dynamics in nematic liquid crystals

Received December 31, 2001 / Published online May 21, 2002     

The Laplacian and Dirac operators on critical planar graphs

On a periodic planar graph whose edge weights satisfy a certain simple geometric condition, the discrete Laplacian and Dirac operators have the property that their determinants and inverses only depend on the local geometry of the graph. We obtain explicit expressions for the logarithms of the (normalized) determinants, as well as the inverses of these operators. We relate the logarithm of the determinants to the volume plus mean curvature of an associated hyperbolic ideal polyhedron. In the associated dimer and spanning tree models, for which the determinants of the Dirac operator and the Laplacian respectively play the role of the partition function, this allows us to compute the entropy and correlations in terms of the local geometry. In addition, we define a continuous family of special discrete holomorphic functions which, via convolutions, gives a general process for constructing discrete holomorphic functions and discrete harmonic functions on critical planar graphs. Oblatum 6-III-2002 & 12-VI-2002?Published online: 6 August 2002     

On Pairs of Diagonal Quintic Forms

We demonstrate that a pair of additive quintic equations in at least 34 variables has a nontrivial integral solution, subject only to an 11-adic solubility hypothesis. This is achieved by an application of the Hardy–Littlewood method, for which we require a sharp estimate for a 33.998th moment of quintic exponential sums. We are able to employ p-adic iteration in a form that allows the estimation of such a mean value over a complete unit square, thereby providing an approach that is technically simpler than those of previous workers and flexible enough to be applied to related problems.