Rigidity and flexibility of virtual polytopes

All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.     

1,3-dihalo-5,5-dimethylhydantoin/NaNO2 as an efficient heterogeneous system for the N-nitrosation of N,N-dialkylamines under mild conditions

A combination of 1,3-dihalo-5,5-dimethylhydantoin (X = Br, Cl) and sodium nitrite in the presence of wet SiO₂ was used as an effective nitrosating agent for the nitrosation of N,N-dialkyl amines to their corresponding nitroso derivatives under mild and heterogeneous conditions in good to excellent yields.     

Character of the thermal motion of water molecules according to the data on quasielastic incoherent scattering of slow neutrons

The paper discusses the applicability of quasi-crystalline approximation to describing the thermal motion of water molecules in their normal and supercooled states. The problem is subjected to the critical analysis of experimental data on incoherent scattering of slow neutrons based on theories developed by Singwi-Sjolander [1] and Oskotsky [2] modified to duly take into account the limited applicability range of diffusion approximation. The applicability conditions of quasi-crystalline approximation are shown to be consistently satisfied only when water is in supercooled state and within a narrow temperature range above the melting temperature.     

Lagrangian for the t–J Model Constructed from the Generators of the Supersymmetric Hubbard Algebra

In order to describe the dynamics of the t–J model, two different families of first-order Lagrangians in terms of the generators of the Hubbard algebra are found. Such families correspond to different dynamical second-class constrained systems. The quantization is carried out by using the path-integral formalism. In this context the introduction of proper ghost fields is needed to render the model renormalizable. In each case the standard Feynman diagrammatics is obtained and the renormalized physical quantities are computed and analyzed. In the first case a nonperturbative large-N expansion is considered with the purpose of studying the generalized Hubbard model describing N-fold-degenerate correlated bands. In this case the 1/N correction to the renormalized boson propagator is computed. In the second case the perturbative Lagrangian formalism is developed and it is shown how propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator coming from our formalism is studied in details. As an example the thermal softening of the magnon frequency is computed. The antiferromagnetic case is also analyzed, and the results are confronted with previous one obtained by means of the spin-polaron theories.     

Viscoelastic properties of amorphous polymers 3: low molecular weight poly(methylphenylsiloxane)

By making creep and recoverable creep measurements of a nearly monodisperse low molecular weight poly(methyl phenyl siloxane) sample, we have found on decreasing temperature towardsT _g that there is continuously a change in the viscoelastic spectrum concomitant with a decrease of the steadystate recoverable compliance. This behavior is exactly the same as previously observed in low molecular weight poly(styrene), proving that this spectacular anomaly in the viscoelasticity of low molecular weight polymers is general and deserves an explanation. Photon correlation spectroscopic measurements performed on the same sample have extended the observation of the viscoelastic response to shorter times and the result corroborates the trend of variation established by the creep data.Dedicated to Prof.Dr. E. W. Fischer on his 65th Birthday. Prof.Dr. Fischer is known for his valuable contribution to fosterine, international collaboration of research in polymer science. This work is an example of his contribution because it would not be possible without him bringing us together. One of us (KLN) would like to take this opportunity to thank Prof. Dr. Fischer for his unwaiving support of the 1st (Crete) and the 2nd (Alicante) International Discussion Meeting on Relaxations in Complex Systems     

Effect of phonon scattering from neutral and charged impurity centers on the lattice heat conductivity of PbTe:(Tl, Na)

Experimental data on the effect of thallium and sodium impurities on the lattice heat conductivity of PbTe at room temperature are reported. Because the lattice of lead chalcogenides is strongly polarized near charged impurities, the effect of impurities on the lattice heat conductivity depends substantially on their charge state. This property of the material has been used to determine the charge state of the thallium impurity in PbTe. The results obtained argue for a model of quasi-local thallium-impurity states which assumes low electron-correlation energy at an impurity center. Fiz. Tverd. Tela (St. Petersburg) 40, 1206–1208 (July 1998)     

Laser spectroscopy of the 1s HFS of H-like ions at a bunched beam in the storage ring ESR

The investigation of the 1s HFS provides a good possibility for testing QED effects in a combination of a strong electric and magnetic field. Here, we report about the laserspectroscopic measurements of the ground state hyperfine splitting in ²⁰⁷Pb⁸¹⁺. To handle this M1-transition in the infrared optical regime with its long lifetime, we developed a new detection technique using a bunched ion beam. For the observation of fluorescence light, a new mirror system is adapted to the emission characteristics from an ion beam at relativistic velocities. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mössbauer study of Martian regolith analogues

Terrestrial basalt rocks considered to be a good analogues of the Martian regolith were studied by using the Mössbauer spectroscopy and X-ray diffraction. The weathering of basalts was followed by the changes of the Fe²⁺/Fe³⁺ ratio. The basalt rock undergoes alteration from primary mineral composition (olivine+pyroxene+plagioclase) through smectite to kaolinite clay with oxides and hydroxides with the increase of the Fe²⁺/Fe³⁺ ratio.