On classification of conformally flat spaces

Classification of conformally flat n-dimensional pseudo-Riemannian spaces via Plebanski's method is discussed. It is based on embedding these spaces into a flat (n + 2)-dimensional space and on finding their minimal isometry groups which are subgroups of the conformal group. In particular, the case n = 4 is given in full detail and compared with incomplete results known in the literature. The found conformally flat spacetimes are identified with the associated solutions of the Einstein equations and with the spacetimes used in various cosmological considerations.     

In vitro screening of the action of non-steroidal anti-inflammatory drugs on hypochlorous acid-induced hyaluronan degradation

The antioxidative effect of two non-steroidal anti-inflammatory drugs was studied in vitro by measuring the kinetics of degradation of high-molecular weight hyaluronan (HA) in a system comprising hypochlorous acid + CuCl₂ + ascorbic acid using a Brookfield rotational viscometer equipped with a Teflon cup and spindle of coaxial cylindrical geometry. The changes in HA chemical structure were investigated by chemiluminometry. When sodium naproxen was added to the system during a running degradative process its inhibitory effect was clearly shown. The inhibition was dependent on the drug concentration. However, when this drug was added to the system before the initiation of HA degradation, no inhibition was seen even at the highest drug concentration tested. The inhibitory effect of acetylsalicylic acid was achieved with a relatively low concentration of the drug and was independent of the experimental model used.     

A model for dynamic relaxations in amorphous polymers. I. Conceptual framework,formal implementation of simplest version,and application to poly(ester carbonates)

A new model for the dynamic relaxations occurring below the glass transition temperature in amorphous polymers is introduced. This model combines ideas from theoretical solidstate physics, thermodynamics, and statistical mechanics. Formal analogies are made between the dynamic relaxations and phase transitions. The concepts of percolation theory are briefly discussed. The molecular level motions which might be giving rise to each dynamic relaxation are incorporated within this framework. The simplest version of the model is then formally implemented within the context of bisphenol-A polycarbonate (BPAPC) and its poly (ester carbonates) (PEC). The following results are calculated: (1) Characteristic temperatures (T_c) for BPAPC, similar to γ₁, and γ₂ relaxation temperatures observed by dynamic mechanical spectroscopy (DMS) at commonly used measurement frequencies. (2) T_c for the β₂ relaxation in tetrabromo-BPAPC much higher than the T_c in BPAPC. (3) A slow and monotonic increase in both the intensity and the T_cof the γ₂ relaxation with an increasing fraction of terephthalate comonomer in PEC copolymers. It is hoped that this model, which is admittedly tentative at this time, will be useful as a working hypothesis. The next paper of this series will provide extensions and generalizations of the model, and its application to the poly (alkyl methacrylates).     

Scattering and bound states of a nonrelativistic neutral spin-1/2 particle in a magnetic field

We have investigated the scattering and bound states of a nonrelativistic spin-1/2 particle in the system ofN magnetic barriers (or magnetic wells) andN magnetic delta functions. We have studied three types of problems: tunnelling with spin, band structure and change of polarization during transmission and reflection.     

EPR investigation of cell membrane fluidity upon external oxidative stimulus

The perturbation of the physical state of cell membranes triggered by an external oxidative stimulus has been studied with sperm cells which were chosen as a model system. Electron paramagnetic resonance (EPR) spectroscopy was applied and three different nitroxides bearing a paramagnetic group on the 5th, 7th and 13th carbon of the stearic acid acyl chain were used to probe different regions of the membrane. The theoretical simulations of the experimental spectra indicate distinct domains in the intact cell plasma membrane where local steric constraints impose different degrees of motional averaging experienced by the reporter group. Upon the external oxidative stimulus the spectral changes were proportional to the accumulated oxidation products and were detected only for the reporter group residing close to the lipid-water interface. The EPR spectra reveal that the motion of the reporter group has slowed down in the oxidized cells and that the oxidatively modified membrane shows up as a more rigid structure as compared with the native state. The results also indicate that the oxidation-induced spectral changes are supressed in the presence of gangliosides.     

On the Seneta Sequences

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.     

Separation of vibrational-electronic Hamiltonian in crude representation

A separation of the vibrational-electronic Hamiltonian in crude representation is presented. The separation is done in the following way: first we quantize only the electronic states on the unperturbed Hamiltonian level, then using the perturbation theory, we treat the terms where we have electronic operators to obtain new harmonic potential energy. Then we quantize a-posteriori the nuclear motion and as a result the only perturbation term is due to anharmonicity.     

A census of semisymmetric cubic graphs on up to 768 vertices

A list is given of all semisymmetric (edge- but not vertex-transitive) connected finite cubic graphs of order up to 768. This list was determined by the authors using Goldschmidt's classification of finite primitive amalgams of index (3,3), and a computer algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several previously undiscovered graphs. For each graph in the list, a significant amount of information is provided, including its girth and diameter, the order of its automorphism group, the order and structure of a minimal edge-transitive group of automorphisms, its Goldschmidt type, stabiliser partitions, and other details about its quotients and covers. A summary of all known infinite families of semisymmetric cubic graphs is also given, together with explicit rules for their construction, and members of the list are identified with these. The special case of those graphs having K_1,3 as a normal quotient is investigated in detail. Supported in part by N.Z. Marsden Fund (grant no. UOA 124) and N.Z. Centres of Research Excellence Fund (grant no. UOA 201) Supported in part by “Ministrstvo za šolstvo, znanost in šport Slovenije”, research program no. 101-506. Supported in part by research projects no. Z1-4186-0101 and no. Z1-3124-0101. The fourth author would like to thank the University of Auckland for hospitality during his visit there in 2003.     

Problems of an additional experiment

In some situations estimates of unknown parameters must be corrected by additional measurements. It is in principle no problem to calculate the corrected estimates, however, it is of more interest to find formulae for correction itself. The formulae enable us to design an additional experiment and to judge its usefulness. The aim of the paper is to find such formulae for several situations. Supported by the grant of the Council of Czech Government MSM 6 198 959 214.