On a Countable-Point Nonlinear Boundary-Value Problem on a Semiaxis for Ordinary Differential Equations in the Space of Bounded Numerical Sequences

We use the idea of the Samoilenko numerical-analytic method for the investigation of a nonlinear boundary-value problem with an unbounded countable set of boundary moments on the positive semiaxis in the case where the differential equation and boundary conditions are defined in the Banach space of bounded numerical sequences.     

The effect of high electric fields on the structure and dielectric properties of the B2 phase

Dielectric studies are presented of a banana-shaped compound that exhibits the antiferroelectric B₂ phase. Upon application and subsequent removal of strong electric fields the textures and dielectric properties of the phase drastically change. Most notable is the huge increase of the low frequency permittivity. This behaviour would suggest the induction of ferroelectricity by the electric field.     

Monodromy and irreducibility criteria with algorithmic applications in characteristic zero

Consider a projective algebraic variety V, which is the set of all common zeros of homogeneous polynomials of degrees less than d in n + 1 variables over a field of characteristic zero. We suggest an algorithm that decides whether two (or more) given points of V belong to the same irreducible component of V. We also show how to construct, for each s < n, an (s + 1)-dimensional plane in the projective space such that the intersection of every irreducible component of dimension n — s of V with the constructed plane is transversal and is an irreducible curve. These algorithms are deterministic and polynomial in dⁿ and the input size. Bibliography: 9 titles.Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 292, 2002, pp. 130–152.This revised version was published online in April 2005 with a corrected cover date and article title.     

Heavy metal ion uptake properties of polystyrene-supported chelating polymer resins

Metal ion uptake properties of polystyrene-supported chelating polymer resins functionalized with (i) glycine, (ii) hydroxy benzoic acid, (iii) Schiff base and (iv) diethanol amine have been investigated. The effects of pH, time and initial concentration on the uptake of metal ions have been studied. The uptake of metal ion depends on pH. The resins are more selective at pH 10 for Pb(II) and Hg(II), whereas at pH 6 they are found to be Cd(II) and Cr(VI) selective. Metal ion uptake properties of resins follow Freundlich’s equation. The resins are recyclable and are therefore employed for the removal of heavy metal pollutants from industrial waste water.     

Rod–coil block copolymers: An iterative synthetic approach via living free-radical procedures

A modular approach has been developed for the synthesis of rod–coil block copolymers involving the initial preparation of a macroinitiator based on the rod block followed by the growth of the coil segment with living free-radical procedures. The key feature of this strategy is the utilization of an alkoxyamine group from the beginning of the synthesis, which serves as a solubilizing group and ensures that each rod block contains a single initiating fragment. Using this approach permits block copolymers based on insoluble biphenyl ester oligomers to be conveniently prepared with coil segments that range from styrenes to acrylates to 1,3-dienes. The tendency of the rod segments to crystallize is strongly dependent on the weight fraction of the rod segment and the chemical nature of the coil segment. Rod–coil molecules containing at least 25–35 wt % polystyrene or poly(n-butyl acrylate) coil segments show a two-dimensional hexagonal arrangement of rod aggregates, as characterized by transmission electron microscopy and small-angle X-ray scattering. Polyisoprene block copolymers exhibit a lamellar microstructure with short rigid domains in which the rod units lie in an interdigitated smectic C arrangement. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3640–3656, 2003     

A Note about the Appearance of Non-Hyperbolic Solutions in a Mechanical Pendulum System

The investigation of the behavior of a nonlinear system consists in theanalysis of different stages of its motion, where the complexity varieswith the proximity of a resonance region. Near this region the stabilitydomain of the system undergoes sudden changes due basically tocompetition and interaction between periodic and saddle solutions insidethe phase portrait, leading to the occurrence of the most differentphenomena. Depending of the domain of the chosen control parameter,these events can reveal interesting geometric features of the system sothat the phase portrait is not capable to express all them, since theprojection of these solutions on the two-dimensional surface can hidesome aspects of these events. In this work we will investigate thenumerical solutions of a particular pendulum system close to a secondaryresonance region, where we vary the control parameter in a restrictdomain in order to draw a preliminary identification about what happenswith this system. This domain includes the appearance of non-hyperbolicsolutions where the basin of attraction in the center of the phaseportrait diminishes considerably, almost disappearing, and afterwardsits size increases with the direction of motion inverted. Thisphenomenon delimits a boundary between low and high frequency of theexternal excitation.