On the geometry of infinite cyclic subgroups

In this paper we construct an example of a word metric on an infinite cyclic subgroup. This example shows that subexponential distortion does not obstruct non-trivial growth of connected radii. This answers a question of Gromov [6]. The constructed metric has other pathological properies. Specifically, its asymptotic cone depends on the choice of ultrafilter and scaling sequence. The work has been partially supported by the Swiss National Science Foundation.     

New universality classes in “Percolative” dynamics

We study a site analogue of directed percolation. Random trajectories are generated and their critical behavior is studied. The critical behavior corresponds to that of simple percolation in some of the parameter space, but elsewhere the exponents reveal new universality classes. As a byproduct, we use the model to make an improved estimate of the percolation hull exponents and to calculate the site percolation probability for the square lattice.     

The plasticity of the Cu(H2O) 6 2+ Jahn-Teller complex affected by lattice strains and cooperative interactions

The EPR spectra evolution of Cs₂Zn_1?x Cu_x(ZrF₆)₂ · 6H₂O (x=0.01, 0.6, 0.8, and 1.0) in the temperature range 4.2–330 K and the x-ray structure analysis of the compound with x=1.0 in the range 150–327 K show that the Jahn-Teller (JT) complex Cu(H₂O)₆ coordination sphere undergoes a plastic deformation. The observed effect is due to the combined influence of small lattice strains existing in the paraphase and a new one appearing as a result of a ferroelastic phase transition and increasing with decreasing temperature below T _c . It is proved that both cooperative interactions between JT complexes and ferroelastic strain stabilize a certain JT configuration. The problem of instability of a JT configuration compressed at T ～ 265 K is discussed.     

Symplectically asystatic actions of compact Lie groups

In this paper we introduce the notion of symplectically asystatic Hamiltonian action on a Kahler manifold. In the algebraic setting we prove that if a complex linear group G acts on a Kahler manifold in a symplectically asystatic fashion, then the G-orbits are spherical. Finally, we give the complete classification of symplectically asystatic irreducible representations.     

Convexity of Domains of Riemannian Manifolds

In this paper the problem of the geodesic connectedness and convexity ofincomplete Riemannian manifolds is analyzed. To this aim, a detailedstudy of the notion of convexity for the associated Cauchy boundary iscarried out. In particular, under widely discussed hypotheses,we prove the convexity of open domains (whose boundaries may benondifferentiable) of a complete Riemannian manifold. Variationalmethods are mainly used. Examples and applications are provided,including a result for dynamical systems on the existence oftrajectories with fixed energy.     

LocalH-theorem for a kinetic variational theory

A localH-theorem is derived for a recently proposed extension of Enskog kinetic theory to a dense model fluid composed of particles with interactions extending beyond a hard core.On leave from: Katedra Fizyki, Uniwersytetu Szczecinskiego, 70-451 Szczecin, Poland.     

Thermal analysis of glasses for proecological applications

Thermal behaviour and biochemical activity of potassium-silicate-phosphate glasses modified by addition of Ca, Mg, acting as ecological fertilisers of controlled release rate of the nutrients for plants were studied. It has been found that the biochemical activity of silicate-phosphate glasses depends on the nature and the number of components forming the glassy framework and is related to the thermal stability of glass demonstrated by the formation of new compounds during the process of crystallisation. It is proved that these seemingly different properties are determined by the same parameters which are the strengths bonds of glass network-formers and modifiers as well as their chemical affinity. This revised version was published online in July 2006 with corrections to the Cover Date.     

Development in Synthesis,Electrochemistry, LB Moieties of Phenothiazine Based Units

A convenient and higher yielding synthetic route to N‐alkyl‐bis(thiophene)phenothiazine derivatives is reported and their aggregation, electrochemical properties and polymerization are characterized. The key step in the synthesis of this group of compounds has been the Stille type coupling reaction between the N‐alkyldibromophenothiazine and tin derivatives of thiophene as the best way for preparation of conjugated N‐alkylphenothiazine derivatives. For this group of compounds we also present an electrochemical polymerization effect and widely adopted approach to prepare structurally ordered thin, electroconducting films by Langmuir–Blodgett technique.     

Evidences of phase separation in moisture‐cured poly(urethane urea)s by means of temperature modulated differential scanning calorimetry

The degree of phase separation in several moisture‐cured poly(urethane urea)s (PUUs) was studied by FTIR spectroscopy, wide angle X‐ray diffraction (WAXD), and temperature‐modulated differential scanning calorimetry (TMDSC). This latter technique was shown to be particularly useful in analysing the degree of phase separation in PUU polymers. Both phase mixing and phase segregation coexisted in the PUUs and the degree of phase separation increased as the urea hard segment (HS) content in the PUU increased. The maximum solubility of urea HSs into the polyol soft segments (SSs) was achieved for 50 wt % urea HS content in diol‐based PUUs, whereas for triol‐based PUUs the highest solubility between HS and SS was reached for lower urea HS amount. Finally, the higher the urea HS content the higher the extent of phase separation in the PUU. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 3034–3045, 2007