A note on the Percus-Yevick and hypernetted chain theories of adsorption: The second and third virial coefficients for a hard-sphere gas in contact with a wall with a soft surface layer

The first three virial coefficients of a new type in the density expansion of the adsorption isotherm for hard spheres in contact with a wall with a soft surface layer are calculated. The results are compared with those for hard spheres in contact with a hard wall.     

Black hole uniqueness from a hidden symmetry of Einstein's gravity

A theorem is proven that the only possible exterior solution for a pseudostationary, rotating, electrovacuum black hole with nondegenerate event horizon is the Kerr-Newman solution withM ²-J²/M²-Q²>0. A special role played in the proof of this theorem by the hidden symmetry groupSU(1, 2) of Einstein's equations is established.This essay received the third award from the Gravity Research Foundation for the year 1983 [Ed.].     

Dynamical dark energy models – dynamical system approach

We study the Friedmann-Robertson-Walker model with dynamical dark energy modelled in terms of the equation of state p _X = w _X (a(z)) ρ _X in which the coefficient w _X is parameterized by the scale factor a or redshift z. We use methods of qualitative analysis of differential equations to investigate the space of all admissible solutions for all initial conditions on the two-dimensional phase plane. We show advantages of representing this dynamics as a motion of a particle in the one-dimensional potential V(a). One of the features of this reduction is the possibility of investigating how typical big rip singularities are in the future evolution of the model. The properties of potential function V can serve as a tool for qualitative classification of all evolution paths. Some important features like resolution of the acceleration problem can be simply visualized as domains on the phase plane. Then one is able to see how large is the class of solutions (labelled by the inset of the initial conditions) leading to the desired property.     

Vortex fluctuations in underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) crystals

Vortex thermal fluctuations in heavily underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) (T(c)=69.4 K) are studied using Josephson plasma resonance. From the zero-field data, we obtain the c-axis penetration depth lambda(L,c)(0)=230+/-10 micrometer and the anisotropy ratio gamma(T). The low plasma frequency allows us to study phase correlations over the whole vortex solid state and to extract a wandering length r(w) of vortex pancakes. The temperature dependence of r(w) as well as its increase with dc magnetic field is explained by the renormalization of the vortex line tension by the fluctuations, suggesting that this softening is responsible for the dissociation of the vortices at the first order transition.     

Antioxidant Activities of Some New Chromonyl-2,4-Thiazolidinediones and Chromonyl-2,4-Imidazolidinediones Having Chromone Cores

The antioxidant properties of 11 new synthesized chromonyl-2,4-thiazolidinediones and chromonyl-2,4-imidazolidinediones (CBs) were investigated. The antioxidant activities and mechanisms of the CBs interaction with reactive oxygen species (ROS) were clarified using various in vitro antioxidant assay methods including superoxide anion radical ( $ \mathrm{O}\overline{{}_2^{\bullet }} $ ), hydroxyl radical (HO^?), 1,1-diphenyl-2-picryl-hydrazyl free radical (DPPH^?) scavenging activity and the iron (II)-ferrozine complex formation. The potassium superoxide/18-crown-6 ether dissolved in dimethylsulfoxide (DMSO) was applied as a source of superoxide anion radical. Hydroxyl radicals were produced in the Fenton-like reaction Fe(II)+H₂O₂. Chemiluminescence, spectrophotometry, and electron paramagnetic resonance (EPR) spectroscopy using 5,5-dimethyl-1-pyrroline-1-oxide (DMPO) as spin trap were applied as the measurement techniques. The CBs examined that exhibited good free radical scavenging activity also showed strong total antioxidant power capacity. Possible mechanisms of antioxidation are proposed to explain the differences in the experimental results between the chromone derivatives with imidazolidine-2,4-dione ring and those with thiazolidine-2,4-dione ring. In conclusion, some of the new CBs are promising to be applied as inhibitors of free radicals.     

Theoretical study of the influence of laser-induced defects on the adsorption of gases on solid surfaces

Laser treatment of a solid surface was modeled by applying an analytical theory as well as by using Monte Carlo simulations. The crystalline surface was assumed to be initially smooth and chemically uniform, that is free of impurities built into the structure. Creation of surface defects by a laser beam was assumed to have entirely random nature. In particular, the surface was assumed to have been scanned by the beam focused successively on randomly chosen points. In the course of the ablation process, the beam produces a pyramidal crater whose dimensions are proportional to the applied laser power. According to the assumed nature of the scanning procedure, the craters formed by the beam are allowed to overlap. The influence of the number of laser pulses and the crater dimensions on the structural and adsorptive properties of the surface were examined by analysis of the variation of the mean surface depth and the surface width. Changes in the adsorptive properties were also estimated by the calculation of the thermally programmed desorption (TPD) spectra of monomolecular adsorbates desorbed from laser-treated surfaces. Additionally, equilibrium adsorption isotherms were calculated for the obtained surfaces.     

Prime ideals and radicals of centred extensions and tensor products

In this paper, we study prime ideals and radicals of centred extensions of rings. Obtained results are applied to tensor products of algebras over commutative rings. This research was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. The second-named author was also supported by KBN grant 2 P301 035 06.     

Applicability of medium-size basis sets in calculations of molecular dynamic polarisabilities

Static and dynamic average polarisabilities and polarisability anisotropies of seven linear non-polar and polar molecules are calculated within the CCS, CC2, and CC3 approximations using a range of medium-sized basis sets: the polarised LPol-n (n = ds, dl, fs, fl), the aug-pc-n (n = 1, 2), the def2-SVPD, and -TZVPD basis sets. Reference values are obtained using a hierarchy of Dunning's (d-)aug-cc-pVXZ (X = D, T, Q, 5) basis sets. The results are discussed together with the available CCSD values in terms of basis set and correlation method errors, and their ratio. Detailed analysis shows that already the def2-SVPD basis set can be used in CCS polarisability calculations. When affordable, the slightly larger aug-pc-1 basis set is recommended, as it leads to significant reduction of basis set error. The def2-TZVPD, LPol-ds, and aug-pc-2 basis sets are optimal choice within the CC2 approximation, with the latter allowing to approach the CC2 basis set limit. The LPol-ds, -dl, and def2-TZVPD sets outperform the aug-cc-pVTZ set in average polarisability CCSD calculations, with the def2-TZVPD being competitive to other reduced-size sets also in determination of polarisability anisotropy. The aug-pc-2 basis is a particularly attractive choice for CCSD, giving the accuracy of aug-cc-pVQZ at a significantly reduced computational cost. The polarisability anisotropy is shown to be more computationally demanding than the average polarisability, in particular with respect to the accuracy of the correlation method and an accurate evaluation of this property requires at least the CCSD model.     

MR microscopy of water diffusion tensor in biological systems

Diffusion tensor imaging (DTI) of the control and mechanically injured spinal cord of a ratin vitro andin vivo are reported.In vitro experiments were done on a home-built 6.4 T magnetic resonance microscope. Results for formaline-fixed samples show significant differences in diffusion tensor components between gray matter and white matter of the control spinal cord. Moreover, it is shown that already 6–10 min after the injury DTI can detect changes in water diffusion in areas extending far beyond the region of primary tissue damage.In vivo experiments were performed using a 9.4 T Magnex magnet and Bruker Medspec imaging system. Good-quality DTI images, free from motion artifacts were obtained. Results from control samples confirm differences in water diffusion between white matter and gray matter, observedin vitro. In vivo experiments show that characteristic changes in water diffusion observedin vitro 6–10 min after injury are preserved 60–360 min after injury, without significant alteration during this time.     

Chemical reactions at surfaces: Application of the reaction ensamble monte carlo method

The Monte Carlo simulation method introduced by Smith and Triska [J. Chem. Phys.100 (1994) 3019] is extended to the case of a reacting fluid in contact with a hard wall. The fluid structure for both spherical and nonspherical reaction products is discussed for simple models of reacting hard spheres near a hard wall and near a wall interacting via Lennard-Jones (9,3) potential. In the latter case the investigated model assumes that the probability of a chemical reaction changes with a distance from the surface. It is shown that the applied technique is suitable for the study of reacting nonuniform fluids. This work is supported by KBN under the Grant No. 3 T09A 062 10.