On Mobility and Einstein Relation for Tracers in Time-Mixing Random Environments

In this paper we rigorously establish the existence of the mobility coefficient for a tagged particle in a simple symmetric exclusion process with adsorption/desorption of particles, in a presence of an external force field interacting with the particle. The proof is obtained using a perturbative argument. In addition, we show that, for a constant external field, the mobility of a particle equals to the self-diffusivity coefficient, the so-called Einstein relation. The method can be applied to any system where the environment has a Markovian evolution with a fast convergence to equilibrium (spectral gap property). In this context we find a necessary relation between forward and backward velocity for the validity of the Einstein relation. This relation is always satisfied by reversible systems. We provide an example of a non-reversible system, where the Einstein relation is valid.This revised version was published online in March 2005 with corrections to the page numbers.     

On the existence of an invariant measure for Markov-Feller operators

Let X be a Polish space and P a Markov operator acting on the space of Borel measures on X. We will prove the existence of an invariant measure with respect to P, provided that P satisfies some condition of a Prokhorov type and that the family of functions is equi-continuous with respect to the Prokhorov distance at some point of the space X. Moreover, we will construct a counterexample which show that the above equi-continuity condition cannot be dropped.     

3D MR imaging of dental cavities-an in vitro study

A 3D spin-echo (3D SE) pulse sequence was used on a 4.7 T research MRI system to produce images of extracted human first molar tooth placed in CuSO4 water solution. The maximal resolution achieved was 35 x 63 x 300 microm3 in read and two phase directions, respectively. The high-intensity signal from water in solution together with the lack of signal from mineralized tooth tissue produce very good contrast allowing to visualize topography of outer and inner surfaces of the tooth. The 3D MR data were median filtered, binarized and then divided into separate segments corresponding to the inner tooth cavities and the hard tooth tissue. The topography of the root canals was visualized and the canals volume was calculated. The presented technique may be used for quantitative analysis of the root canal cavities shape and volume. The results of such an analysis may be applied for estimation of the quality of the impressional mapping methods in restorative dentistry or as an alternative non-impressional 3D mapping method.     

Application of chemiluminescence for the detection of peroxy compounds in high-performance liquid chromatography

The possibility of applying post-column reaction and chemiluminescence to determine organic peroxy compounds by RP-HPLC was investigated. Conditions of qualitative and quantitative analyses have been established. The applicability of the method has been demonstrated for a series of compounds representative of the most important groups of peroxy-type compounds, that is, hydroperoxides, dialkyl peroxides, diacyl peroxides, peroxyesters, and peroxyacids.     

Reductive activation of mitomycin A by thiols

[reaction: see text]. Mitomycin C is unchanged upon exposure to thiols under physiological conditions. Its more toxic variant, mitomycin A (MA), undergoes elimination of methanol to give a variety of mitosene derivatives, diagnostic of its activation to a reactive electrophile. Evidence is presented for a novel reductive mechanism, characterized by the transient addition of a thiol to the quinone of MA, followed by intramolecular electron transfer, leading to reduced quinone and oxidized thiol.     

Effect of Polythiophene Content on Thermomechanical Properties of Electroconductive Composites

The thermal, mechanical and electrical properties of polymeric composites combined using polythiophene (PT) dopped by FeCl₃ and polyamide 6 (PA), in the aspect of conductive constructive elements for organic solar cells, depend on the molecular structure and morphology of materials as well as the method of preparing the species. This study was focused on disclosing the impact of the polythiophene content on properties of electrospun fibers. The elements for investigation were prepared using electrospinning applying two substrates. The study revealed the impact of the substrate on the conductive properties of composites. In this study composites exhibited good thermal stability, with T₅ values in the range of 230–268 °C that increased with increasing PT content. The prepared composites exhibited comparable PA T_g values, which indicates their suitability for processing. Instrumental analysis of polymers and composites was carried out using Fourier Transform Infrared spectroscopy (FT-IR), thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), dynamic mechanical thermal analysis (DMTA) and scanning electron microscopy (SEM).     

Explicit Formulas of the Bergman Kernel for Some Reinhardt Domains

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for Reinhardt domains \(\{|z_3|^{\lambda } < |z_1|^{2p} + |z_2|^2, \ |z_1|^{2p} + |z_2|^2 < |z_1|^{p} \}\) and \(\{|z_4|^{\lambda } < (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2, \ (|z_1|^2 + |z_2|^2)^{p} + |z_3|^2 < (|z_1|^2 + |z_2|^2 )^{p/2} \}\).