Phase liquid-crystalline transitions in hydroxypropylcellulose-ethanol and hydroxypropylcellulose-acetic acid systems under deformation

The phase transitions and phase state of hydroxypropylcellulose mixtures with ethanol and acetic acid under static conditions and in the shear field have been studied by the turbidity-point method and polarization microscopy with the use of a polarization-photoelectric setup and a modified plastoviscometer. The deformation of solutions leads to a decrease in the temperature of mesomorphic phase formation and to a change in the type of liquid crystals from cholesteric to nematic.     

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.     

On the Rolewicz theorem for evolution operators

We give a short proof of a generalization of the Rolewicz theorem based on the uniform boundedness principle.

     

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.     

Microlocal analysis of seismic inverse scattering in anisotropic elastic media

Seismic data is modeled in the high‐frequency approximation, using the techniques of microlocal analysis. We consider general, anisotropic elastic media. Our methods are designed to allow for the formation of caustics. The data is modeled in two ways. First, we give a microlocal treatment of the Kirchhoff approximation, where the medium is assumed to be piecewise smooth, and reflection and transmission occur at interfaces. Second, we give a refined view on the Born approximation based upon a linearization of the scattering process in the medium parameters around a smooth background medium. The joint formulation of Born and Kirchhoff scattering allows us to take into account general scatterers as well as the nonlinear dependence of reflection coefficients on the medium parameters. The latter allows the treatment of scattering up to grazing angles. The outcome of the analysis is a characterization of the singular part of seismic data. We obtain a set of pseudodifferential operators that annihilate the data. In the process we construct a Fourier integral operator and a reflectivity function such that the data can be represented by this operator acting on the reflectivity function. In our construction this Fourier integral operator becomes invertible. We give the conditions for invertibility for general acquisition geometry. The result is also of interest for inverse scattering in acoustic media. © 2002 John Wiley & Sons, Inc.     

Estimates for Elements of Inverse Matrices for a Class of Operators with Matrices of Special Structure

In this paper, we consider questions related to the structure of inverse matrices of linear bounded operators acting in infinite-dimensional complex Banach spaces. We obtain specific estimates of elements of inverse matrices for bounded operators whose matrices have a special structure. Matrices are introduced as special operator-valued functions on an index set. The matrix structure is described by the behavior of the given function on elements of a special partition of the index set. The method used for deriving the estimates is based on an analysis of Fourier series of strongly continuous periodic functions.