Ergodic properties of Markov maps inR d

Summary For domainsIR ^d (bounded or not) the notion of a Markov map fromI into itself is developed. It is shown that under a condition of Rényi type and the assumption that the map is Markov, any probability density tends inL ¹-norm to a unique invariant measure under the action of the Perron-Frobenius operatorP . The smoothness and ergodic properties of that invariant measure are studied. The paper generalizes results of Lasota and Yorke from dimension one to higher dimension.     

The influence of reverse energy transport on emission anisotropy in two-component viscous solutions

The effect of nonradiative reverse energy transport (NRET) in two donor-acceptor systems was studied experimentally. It was found that the NRET occurring in system I; rhodamine 6G (donor) and rhodamine B (acceptor), considerably lowers the emission anisotropy at medium and high concentrations. These results qualitatively confirm the predictions of the approximate theoretical approach of L. Kulak and C. Bojarski (see the preceding paper). In system II; rhodamine 6G (donor) and Nile Blue (acceptor), for which the NRET process does not occur, a good agreement with no-back-transport theory was obtained.     

Invariant measures ofC 2-diffeomorphisms of Markov type inR d

A class of uniformly expanding, piecewiseC ²-diffeomorphisms from domainsIR ^d (bounded or not) into themselves is considered. It is shown that the number of the extreme points of Fix (P )={gG:Pg=g} whereP is the Frobenius-Perron operator associated with andG={gL ¹: g0 g=1}, can be determined in an effective way. Moreover, it is shown that the sequence {P ^j g} is convergent inL ¹ for anygG, and in the topology of uniform convergence for anygG(1). The limit is a linear projectionR inL ¹ (defined by (3.1)) which mapsG onto Fix (P ) (see Th. 3.1).Dedicated to professor A. Lasota on the occasion of his 60th birthday     

The classification of differential structures on quantum 2-spheres

Exterior algebras of differential forms on quantum 2-spheresS _qc ² ,q[–1, 1]/{0},c[0, ] (c=0 forq=±1), are classified. In the definition of exterior algebras we assume the invariance w.r.t. the action of the quantumSU(2) group and dimensionality conditions (which imply that we deal with two-dimensional manifolds). The exterior algebras exist only forc=0 and are unique in that case. The corresponding generalized directional derivatives are provided.     

Non-smoothness of event horizons of Robinson-Trautman black holes

It is shown that generic small data Robinson-Trautman space-times cannot beC ¹²³ extended beyond the r=2m Schwarzschild-like event horizon. This implies that an observer living in such a space-time can determine by local measurements whether or not he has crossed the event-horizon of the black-hole.     

Novel C60 Fullerenol-Gentamicin Conjugate–Physicochemical Characterization and Evaluation of Antibacterial and Cytotoxic Properties

This study aimed to develop, characterize, and evaluate antibacterial and cytotoxic properties of novel fullerene derivative composed of C₆₀ fullerenol and standard aminoglycoside antibiotic–gentamicin (C₆₀ fullerenol-gentamicin conjugate). The successful introduction of gentamicin to fullerenol was confirmed by X-ray photoelectron spectroscopy which together with thermogravimetric and spectroscopic analysis revealing the formula of the composition as C₆₀(OH)₁₂(GLYMO)₁₁(Gentamicin)_0.8. The dynamic light scattering (DLS) revealed that conjugate possessed ability to form agglomerates in water (size around 115 nm), while Zeta potential measurements demonstrated that such agglomerates possessed neutral character. In vitro biological assays indicated that obtained C₆₀ fullerenol-gentamicin conjugate possessed the same antibacterial activity as standard gentamicin against Staphylococcus aureus, Staphylococcus epidermidis, Pseudomonas aeruginosa, and Escherichia coli, which proves that combination of fullerenol with gentamicin does not cause the loss of antibacterial activity of antibiotic. Moreover, cytotoxicity assessment demonstrated that obtained fullerenol-gentamicin derivative did not decrease viability of normal human fibroblasts (model eukaryotic cells) compared to control fibroblasts. Thus, taking into account all of the results, it can be stated that this research presents effective method to fabricate C₆₀ fullerenol-gentamicin conjugate and proves that such derivative possesses desired antibacterial properties without unfavorable cytotoxic effects towards eukaryotic cells in vitro. These promising preliminary results indicate that obtained C₆₀ fullerenol-gentamicin conjugate could have biomedical potential. It may be presumed that obtained fullerenol may be used as an effective carrier for antibiotic, and developed fullerenol-gentamicin conjugate may be apply locally (i.e., at the wound site). Moreover, in future we will evaluate possibility of its applications in inter alia tissue engineering, namely as a component of wound dressings and implantable biomaterials.     

Biochemical and Molecular Investigation of the Effect of Saponins and Terpenoids Derived from Leaves of Ilex aquifolium on Lipid Metabolism of Obese Zucker Rats

Ilex paraguariensis, the holly tree, is a plant with recognized biological properties, whose aqueous infusions are known as “Yerba mate”, that regulate lipid metabolism, reduce obesity, and improve brain stimulation. In the present study, the effect of standardized saponin and terpenoid fractions of a European taxon, Ilex aquifolium, on blood biochemical parameters in a rat model of metabolic disorder, (fa/fa) Zucker, are presented. The profiles of the volatile fractions of two species and six European varieties of Ilex were investigated. After selecting the best variety, the saponin and terpenoid fractions were isolated and standardized, and animals were fed 10 mg kg⁻¹ b.w. for 8 weeks. A statistically significant decrease in liver adiposity was observed, confirmed by histology and quantitative identification (gas chromatography–mass spectrometry analyses of hepatic lipids. RT-qPCR analysis of gene expression in the aorta revealed that the administration of the terpenoid fraction downregulated LOX-1, suggesting a reduction in atherosclerotic stimuli. In addition, a statistically significant reduction (p < 0.05) in PPARγ for the saponin fraction was observed in the liver. The expression of the ACAT-1 gene in the liver, responsible for the formation of cholesterol esters, increased significantly in the group receiving the terpenoid fraction compared to the control, which was also confirmed by the analysis of individual blood biochemical parameters. The opposite effect was observed for saponins. Taking the above into account, it is shown for the first time that Ilex aquifolium can be a source of compounds that positively influence lipid metabolism.     

Effect of Ion and Binding Site on the Conformation of Chosen Glycosaminoglycans at the Albumin Surface

Albumin is one of the major components of synovial fluid. Due to its negative surface charge, it plays an essential role in many physiological processes, including the ability to form molecular complexes. In addition, glycosaminoglycans such as hyaluronic acid and chondroitin sulfate are crucial components of synovial fluid involved in the boundary lubrication regime. This study presents the influence of Na+, Mg2+ and Ca2+ ions on human serum albumin–hyaluronan/chondroitin-6-sulfate interactions examined using molecular docking followed by molecular dynamics simulations. We analyze chosen glycosaminoglycans binding by employing a conformational entropy approach. In addition, several protein–polymer complexes have been studied to check how the binding site and presence of ions influence affinity. The presence of divalent cations contributes to the decrease of conformational entropy near carboxyl and sulfate groups. This observation can indicate the higher affinity between glycosaminoglycans and albumin. Moreover, domains IIIA and IIIB of albumin have the highest affinity as those are two domains that show a positive net charge that allows for binding with negatively charged glycosaminoglycans. Finally, in discussion, we suggest some research path to find particular features that would carry information about the dynamics of the particular type of polymers or ions.     

Comparison of Volatile Profiles of Meads and Related Unifloral Honeys: Traceability Markers

Volatile profiles of unifloral honeys and meads prepared in different ways (boiled-saturated, not boiled-unsaturated) were investigated by headspace solid-phase micro extraction (HS-SPME) and dehydration homogeneous liquid–liquid extraction (DHLLE) followed by GC-FID/MS analyses. The obtained data were analyzed by principal component analysis (PCA) to evaluate the differences between the investigated products. The volatile profiles of honey as well as the boiled and the not boiled meads prepared from it showed significant discrepancies. The meads contained more aliphatic acids and esters but fewer monoterpenes and aliphatic hydrocarbons than the honey. Significant/substantial differences were found between the boiled (more aliphatic alcohols and acids) and the not boiled meads (more aliphatic hydrocarbons and esters). Some compounds related to yeast metabolism, such as tryptophol, may be considered markers of honey fermentation. This research allowed us to identify chemical markers of botanical origin, retained and detectable in the meads: 4-isopropenylcyclohexa-1,3-diene-1-carboxylic acid and 4-(1-hydroxy-2-propanyl)cyclohexa-1,3-diene-1-carboxylic acid for linden; valeric acid, γ-valerolactone, p-hydroxybenzoic acid for buckwheat; 4-hydroxybenzeneacetic acid, homovanillic acid and trans-coniferyl alcohol for honeydew; and methyl syringate for canola.