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.     

Some results on fractionaln-factor-critical graphs

A simple graphG is said to be fractionaln-factor-critical if after deleting anyn vertices the remaining subgraph still has a fractional perfect matching. For fractionaln-factor-criticality, in this paper, one necessary and sufficient condition, and three sufficient conditions related to maximum matching, complete closure are given.     

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.     

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     

A parametric representation of linguistic hedges in Zadeh’s fuzzy logic

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced.     

Scientific heritage of Boris Lukich Laptev (4/23/05–1/15/89)

Biographical information on the eminent Soviet geometer Boris Lukich Laptev (4/23/05–1/15-89) is given as well as a survey of his research in the areas of differential geometry and history of mathematics.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp.27–42, 1989.