A technique to construct symmetric variable-stepsize linear multistep methods for second-order systems

Some previous works show that symmetric fixed- and variable-stepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts, in such a way that the former have the same order as the latter. The order and symmetry of the integrators obtained is proved independently of the order of the underlying fixed-stepsize integrators. As this technique looks for efficiency, we concentrate on explicit linear multistep methods, which just make one function evaluation per step, and we offer some numerical comparisons with other one-step adaptive methods which also show a good long-term behaviour.

     

The Classification of Complex Factor-Representations of the Three-Dimensional Heisenberg Group over a Countable Group Field of Finite Characteristic

We consider a field F that is a direct limit of an increasing chain of finite fields, and describe the Bratteli diagram, complex factor-representations, and projective moduli of the Heisenberg group of 3 × 3 upper-triangular matrices with elements from F. Bibliography: 3 titles.     

Anti-Stokes Bands of Intrinsic Radiation in Undoped GaAs Crystals

It has been established that undoped gallium crystals exhibit anti-Stokes radiation with energy corresponding to the interband recombination of these crystals. Its appearance is most probably determined by EL2 defects, and its intensity depends on the product of the cross sections for photoionization of electrons and the holes from these defects.     

Penetration of radionuclides across the skin: Rat age dependent promethium permeation through skin in vitro

The composition and the permeation properties of the skin are dependent on age. In the animal models for permation studies, age affects the mechanical as well as the permeation properties significantly. The time dependence of permeation of ¹⁴⁷Pm³⁺ from aqueous solution was established by the animal skin model and the age dependence of promethium permeation through the skin was examined. The aim was to find the optimum rat skin age model for radionuclide permeation studies and to assess the relative importance of the main permeation pathways: transepidermal and transfollicular permeation. The skin from 5-day-old rats (5DR) was found to represent the optimum animal model to study transepidermal permeation of ions. The skin from 9-day-old rats (9DR) was selected to study transfollicular permeation of ions. Comparison of the permeated amounts of promethium through the skin without hairs (3 DR to 6 DR) and with hairs (7DR to 12DR) showed that the additional permation mode via follicles significantly contributed to the permeation rate and extent.     

EPR and optical absorption studies on VO ions in KZnClSO4·3H2O single crystals—an observation of superhyperfine structure

EPR spectra of VO²⁺ ions doped in KZnClSO₄·3H₂O single crystals have been studied at different temperatures. The EPR spectrum shows a well-resolved hyperfine and superhyperfine structure patterns. The angular variation of EPR spectra reveals the presence of more than three magnetic complexes, which correspond to distinct sites of VO²⁺ ion. From the angular variation EPR data, the spin-Hamiltonian parameters are evaluated and discussed. The optical absorption spectrum studied at room temperature shows bands corresponding to C_4v symmetry. From the EPR and optical data, the molecular-orbital bonding coefficient ε² and β² are evaluated and discussed. The observed five-line superhyperfine structure has been attributed to four protons (with I=1/2) from the surrounding water molecules of one of the vanadyl sites.     

Choquet-type Integral Representation of Invariant Functions for some Product Semigroups

We show that functions which are invariant for suitable product semigroups (one of which is a quasi-Poisson semigroup on a general state space) decompose into a singular eigen-function and a mixture of products of minimal eigen-functions.     

Preparation of Phosphoric-Carboxylic Cation Exchangers from Wood Cellulose

Phosphorus-containing cellulose cation exchangers were synthesized by reaction of wood cellulose with orthophosphoric acid and the ternary polymer from glycidylmethacrylate, styrene, and maleic anhydride. The effects of the ratio of reactants, temperature, and duration of the reaction on the phosphorylation and exchange capacity of the modified cellulose material were studied.     

On Dispersion in the Mathematical Model of Poroelastic Materials with the Balance Equation for Porosity

This article concerns the nonlinear asymptotic analysis of the mathematical model of a multi-component poroelastic medium with the porosity balance equation. It is proved that there exist soliton-like solutions for porosity and kink-like solutions for phase velocities under conditions similar to the entropy one. It is shown that solutions appear that describe a regime of stable displacement (so-called piston displacement) and a regime similar to the Saffman–Taylor instability. It is established that the diffusion force of interaction between phases of the inner friction type causes a decrease in the amplitudes of the discontinuities. This leads to the damping of initial perturbations of stable states. Such regimes have some properties similar to those of the pendulum model in the vicinity of a stable equilibrium point.     

Study of relaxor-like behaviour of laser ablated (Pb, La)Tio3 thin films

Lanthanum modified lead titanate (PLT) thin films are one of the potential candidates for the pyroelectric and memory applications due to their excellent dielectric, pyroelectric and ferroelectric properties. PLT thin films with 25 at.% of La were deposited on platinum coated Si substrates by the laser ablation technique. The phase transition studies were done in the temperature range of −40 to 150 °C as a function of frequency and ac field. A diffused phase transition with the shifting of the maximum dielectric permittivity (?_max) to higher temperatures with the increase of frequency and dielectric dispersion with frequency at the lower temperatures were observed. The variation of the temperature corresponding to maximum dielectric constant T_m, with frequency follows the Vogel-Fulcher relation, which is the characteristic of the relaxor-like behavior of the material. With the increase of ac drive, the T_max was shifted to lower value.