A relation-algebraic approach to simple games

Simple games are a powerful tool to analyze decision-making and coalition formation in social and political life. In this paper, we present relation-algebraic models of simple games and develop relational specifications for solving some basic problems of them. In particular, we test certain fundamental properties of simple games and compute specific players and coalitions. We also apply relation algebra to determine power indices. This leads to relation-algebraic specifications, which can be evaluated with the help of the BDD-based tool Rel View after a simple translation into the tool’s programming language. In order to demonstrate the visualization facilities of Rel View we consider an example of the Catalonian Parliament after the 2003 election.     

Evolution of massive scalar fields in the spacetime of a tense brane black hole

In the spacetime of a d-dimensional static tense brane black hole we elaborate the mechanism by which massive scalar fields decay. The metric of a six-dimensional black hole pierced by a topological defect is especially interesting. It corresponds to a black hole residing on a tensional 3-brane embedded in a six-dimensional spacetime, and this solution has gained importance due to the planned accelerator experiments. It happened that the intermediate asymptotic behaviour of the fields in question was determined by an oscillatory inverse power-law. We confirm our investigations by numerical calculations for five- and six-dimensional cases. It turned out that the greater the brane tension is, the faster massive scalar field decay in the considered spacetimes.     

On the Locally Polynomial Complexity of the Projection-Gradient Method for Solving Piecewise Quadratic Optimisation Problems

This paper proposes a method for solving optimisation problems involving piecewise quadratic functions. The method provides a solution in a finite number of iterations, and the computational complexity of the proposed method is locally polynomial of the problem dimension, i.e., if the initial point belongs to the sufficiently small neighbourhood of the solution set. Proposed method could be applied for solving large systems of linear inequalities.     

EPR and XPS measurements of polymeric catalysts doped with hereopolyacids in oxygen adsorption studies

The goal of our studies was to determine the nature of interactions between catalytic active samples, such as polypyrrole (PPy) doped with: chloride anions, heteropolyacids such as H₅PMo₁₀V₂O₄₀, or H₄SiW₁₂O₄₀, and oxygen particles. In order to reveal the mechanism of the linkage between the catalysts and oxygen we provided the electron paramagnetic resonance (EPR) measurements of synthesized samples in O₂ and N₂ flow. Moreover, the X-ray photoelectron spectroscopy (XPS) measurements were performed to show the properties of doped heteropolyacids and the state of nitrogen in polypyrrole matrix. The results of EPR studies of PPy(Cl), PPy(H₄SiW₁₂O₄₀), PPy(H₅PMo₁₀V₂O₄₀) samples, show that the polypyrrole doped with chloride anions interacts much easier with oxygen than polypyrrole doped with heteropolyacids (in the above given order, of preference with the most active polypyrrole system first). It correlates with XPS results, which show that a molybdenium-vanadium anion is more reduced than a silicon-tungsten one. The redox reactions of heteropolyacids involve the oxidation-reduction of the conjugated polymer chain, leaving no or little place for interactions with oxygen. Polypyrrole doped with H₄SiW₁₂O₄₀ shows some oxygen sensitivity as observed in the EPR studies, as opposed to polypyrrole doped with H₅PMo₁₀V₂O₄₀, which is in line with the XPS results.     

Wave optics of Liesegang rings

Liesegang rings refract and reflect at the interface between the regions of the same gel but of different thickness. The incident and the refracted rings obey a refraction law analogous to the Snell's law of classical optics, with a reverse of the spacing coefficient being a counterpart of the refraction index. The wavelike behavior of the rings at the interface is explained by geometrical arguments derived from the Jablczynski's spacing principle, and is reproduced in numerical simulations based on a three-dimensional minimalistic version of the nucleation-growth model.     

Fluorescence probes based on 9‐acridyl derivatives of aromatic amines for monitoring free‐radical polymerization

The series of 9‐acridyl derivatives of aromatic amines have been investigated as fluorescent probes for monitoring the progress of free‐radical polymerization. This study on the changes in the fluorescence intensity and spectroscopic shift of specific compounds was carried out during thermally initiated polymerization of methyl methacrylate and photoinitiated polymerization of 2‐ethyl‐2‐(hydroxymethyl)‐1,3‐propanediol triacrylate‐1‐methyl‐2‐pyrrolidonone mixture. The purpose of this investigation was to find a relationship between the changes in the shape and intensity of fluorescent probes and the degree of monomer conversion into a polymer. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3481–3488, 2002     

Synthesis,Characterization and Biological Investigations of Half-Sandwich Ruthenium(II) Complexes Containing Benzimidazole Moiety

Half-sandwich Ru(II) complexes belong to group of biologically active metallo-compounds with promising antimicrobial and anticancer activity. Herein, we report the synthesis and characterization of arene ruthenium complexes containing benzimidazole moiety, namely, [(η⁶-p-cymene)RuCl(bimCOO)] (1) and [(η⁶-p-cymene)RuCl₂(bim)] (2) (where bimCOO = benzimidazole-2-carboxylate and bim = 1-H-benzimidazole). The compounds were characterized by ¹H NMR, ¹³C NMR, IR, UV–vis and CV. Molecular structures of the complexes were determined by SC-XRD analysis, and the results indicated the presence of a pseudo-tetrahedral (piano stool) geometry. Interactions in the crystals of the Ru complexes using the Hirshfeld surface analysis were also examined. In addition, the biological studies of the complexes, such as antimicrobial assays (against planktonic and adherent microbes), cytotoxicity and lipophilicity, were performed. Antibacterial activity of the complexes was evaluated against S. aureus, E. coli, P. aeruginosa PAO1 and LES B58. Cytotoxic activity was tested against primary human fibroblasts and adenocarcinoma human alveolar basal epithelial cells. Obtained biological results show that the ruthenium compounds have bacteriostatic activity toward Pseudomonas aeruginosa PAO1 strain and are not toxic to normal cells. A molecular docking study was applied as a predictive source of information about the plausibility of examined structures binding with HSA as a transporting system.     

The Role of Singlet Oxygen in Photoreactivity and Phototoxicity of Curcumin

Curcumin is a plant-derived yellow-orange compound widely used as a spice, dye and food additive. It is also believed to have therapeutic effects against different disorders. On the other hand, there are data showing its phototoxicity against bacteria, fungi and various mammalian cells. Since the mechanism of its phototoxic action is not fully understood, we investigated here the phototoxic potential of curcumin in liposomal model membranes and in HaCaT cells. First, detection of singlet oxygen (¹O₂) luminescence proved that curcumin generates ¹O₂ upon blue light irradiation in organic solvent and in liposomes. Then, HPLC-EC(Hg) measurements revealed that liposomal and cellular cholesterol is oxidized by ¹O₂ photogenerated by curcumin. Enrichment of liposome membranes with curcumin significantly increased the oxygen photo-consumption rate compared to the control liposomes as determined by EPR oximetry. Cytotoxicity measurements, mitochondrial membrane potential analyses and protein hydroperoxides detection confirmed strong phototoxic effects of curcumin in irradiated HaCaT cells. These data show that since curcumin is advertised as a valuable dietary supplement, or a component of cosmetics for topical use, caution should be recommended especially when skin is exposed to light.     

Poly(vinylbenzyl Pyridinium Salts) as Novel Sorbents for Hazardous Metals Ions Removal

Novel efficient complexing resins—poly(vinylbenzyl pyridinium salts) fabricated through poly(vinylbenzyl halogene-co-divinylbenzene) quaternization of N-decyloxy-1-(pyridin-3-yl)ethaneimine and N-decyloxy-1-(pyridin-4-yl)ethaneimine—were tested as adsorbents of Pb(II), Cd(II), Cu(II), Zn(II), and Ni(II) from aqueous solutions. The structure of these materials was established by ¹³C CP-MAS NMR, X-ray photoelectron spectroscopy, elemental analysis, and Fourier transform infrared spectroscopy, as well as thermogravimetric and differential thermal analyses. The textural properties were determined using scanning electron microscopy and low-temperature N₂ sorption. Based on the conducted sorption studies, it was shown that the uptake behavior of the metal ions towards novel resins depended on the type of functionalities, contact time, pH, metal concentrations, and the resin dosage. The Langmuir model was investigated to be the best one for fitting isothermal adsorption equilibrium data, and the corresponding adsorption capacities were predicted to be 296.4, 201.8, 83.8, 38.1, and 39.3 mg/g for Pb(II), Zn(II), Cd(II), Cu(II), and Ni(II), respectively. These results confirmed that owing to the presence of the functional pyridinium groups, the resins demonstrated proficient metal ion removal capacities. Furthermore, VBBr-D4EI could be successfully used for the selective uptake of Pb(II) from wastewater. It was also shown that the novel resins can be regenerated without significant loss of their sorption capacity.     

Manganese(II), cobalt(II), nickel(II), copper(II) and zinc(II) complexes with 4-oxo-4H-1-benzopyran-3-carboxaldehyde

The complexes Mn(II), Co(II), Ni(II) and Zn(II) with 4-oxo-4H-1-benzopyran-3-carboxaldehyde were synthesized and characterized by elemental analysis, infrared and UV spectroscopy, X-ray diffraction patterns, magnetic susceptibility, thermal gravimetric analysis, conductivity and also solubility measurements in water, methanol and DMF solution at 298 K. They are polycrystalline compounds with various formula and different ratio of metal ion:ligand. Their formula are following: [MnL₂(H₂O)](NO₃)₂·2H₂O, [CoL₂](NO₃)₂·3H₂O, [NiL₂](NO₃)₂·3H₂O, [CuL₂](NO₃)₂·H₂O and [ZnL₃](NO₃)₂, where L = C₁₀H₆O₃. The coordination of metal ions is through oxygen atoms present in 4-position of γ-pyrone ring and of aldehyde group of ligand. Chelates of Mn(II), Co(II), Ni(II) and Cu(II) obey Curie–Weiss law and they are high-spin complexes with the weak ligand fields. The thermal stability of analyzed complexes was studied in air at 293–1,173 K. On the basis of the thermoanalytical curves, it appears that thermal stability of anhydrous analysed chelates changed following: Cu (423 K) < Zn (438 K) ~ Co (440 K) < Ni (468 K). The gaseous products of thermal decomposition of those compounds in air atmosphere are following: CO₂, CO, NO₂, N₂O, hydrocarbons and in case of hydrates also water. The molar conductance data confirm that the all studied complexes are 1:2 electrolytes in DMF solution.