On the moduli spaces of multipolygonal linkages in the plane

One can form a polygonal linkage by identifying initial and terminal points of two free linkages. Likewise, one can form a multipolygonal linkage by identifying initial and terminal points of three free linkages. The geometric and topological properties of moduli spaces of multipolygonal linkages in the plane are studied. These spaces are compact algebraic varieties. Some conditions under which these spaces are smooth manifolds, cross products or disjoint unions of moduli spaces of polygonal linkages, or connected, are determined. Dimensions in smooth manifold cases and some Euler characteristics are computed. A classification of generic multiquadrilateral linkages is also made.     

Separable subgroups of mapping class groups

We investigate separability questions for the mapping class group of a surface. While this group is not subgroup separable in general, we prove a large family of interesting subgroups are separable. This includes many classically studied subgroups such as solvable subgroups, Heegaard and Handlebody groups, geometric subgroups, and all the terms in the Johnson filtration.     

Nonminimal sets,their projections and integral representations of stable processes

New criteria are provided for determining whether an integral representation of a stable process is minimal. These criteria are based on various nonminimal sets and their projections, and have several advantages over and shed light on already available criteria. In particular, they naturally lead from a nonminimal representation to the one which is minimal. Several known examples are considered to illustrate the main results. The general approach is also adapted to show that the so-called mixed moving averages have a minimal integral representation of the mixed moving average type.     

Consolidation around a borehole embedded in media with double porosity under release of geostatic stresses

The paper deals with the stress, displacement, pore and fissure pressures fields induced by the drilling and/or the pressurization of a vertical borehole in a formation of water-saturated porous media with double porosity. The solution includes the boundary condition of non-hydrostatic in situ state of stress. The solid skeleton is assumed to behave as a linearly poroelastic material with compressible constituents. The analytical solution is derived in Laplace’s space and transformed to the time domain using a numerical inversion technique. The histories of pore and fissure pressures are illustrated to show the influence of permeabilities of the pore and fissure systems.     

Luminescence enhancement by hydrogenation of Si:Er,O

Erbium (Er)- and oxygen (O)-doped Cz–Si was additionally doped with hydrogen, using plasma enhanced chemical vapour deposition. Photoluminescence (PL) spectra show a large enhancement especially for samples treated with solid phase epitaxy before hydrogenation and annealing at 900°C later. Secondary ion mass spectroscopy measurements give evidence for an enhanced diffusion of O and Er at this temperature towards the surface. Etching shows that the PL does not stem from the heavily doped surface layer but from a deeper region with lower Er concentration. This conclusion is supported by the appearance of the so-called “cubic” centre with low solubility. Comparing the PL yield of the hydrogenated samples to that of samples with similar Er volume concentration but without hydrogenation still gives a large enhancement. We thus conclude that hydrogen can enhance the solubility of the cubic centre in Si:Er,O.     

Magnetic phases in Mn<Subscript>1</Subscript>_<Subscript>x</Subscript>Fe<Subscript>x</Subscript>WO<Subscript>4</Subscript> studied by neutron powder diffraction

The magnetic structures of Mn_1-xFe_xWO₄ with x = 0.0, 0.16, 0.21, 0.225, 0.232, 0.24, 0.27, 0.29, and 1.0 were refined from neutron powder diffraction data. The magnetic phase diagram could be completed in the coexistence range of different magnetic structures up to x = 0.29. For the magnetic state at 1.5 K a commensurate antiferromagnetic structure with a propagation vector = (±1/4, 1/2, 1/2) was found for x ⩽ 0.22 while the magnetic spins order with = (1/2, 0, 0) for x ≥ 0.22. In the latter phase, additionally, weak magnetic reflections indexed to an incommensurate ordering with = (- 0.214, 1/2, 0.457) occur in the diffraction pattern up to x = 0.29 indicating the occurence of a reentrant phase. For 0.12 ⩽ x ⩽ 0.29 the low temperature phases are separated from a magnetic high temperature phase showing only magnetic reflections indexed to a spin arrangement with = (1/2, 0, 0). The magnetic phase diagram is discussed qualitatively considering random superexchange between the statistically distributed Mn²⁺- and Fe²⁺-ions in the coexistence range 0.12 ⩽ x ⩽ 0.29 of different magnetic structures related to those of pure MnWO₄ and FeWO₄. Received 9 October 2002 Published online 14 March 2003     

Second harmonic generation in In2O3–SiON films doped by Al and Sn

Photoinduced optical and second-order non-linear optical effects in the interfaces separating In₂O₃–SiON (O/N ratio equals 1) films doped with A1, Sn and glass substrates were investigated using the photoinduced optical second harmonic generation. The photoinduced effective second-order optical susceptibility d_eff (at λ=1.76 μm) shows a good correlation with the linear optical susceptibility, particularly with the shift of the absorption edge. The maximal response of the photoinduced optical response signal was observed for the pump–probe delaying time of 34 ps. The performed experimental measurements indicate that the observed effects are mainly caused by the interface potential gradients on the border glass–In₂O₃–SiON film and by additional polarization due to insertion of the Al and Sn atoms. The observed phenomenon may be proposed as a sensitive tool for investigation of thin semiconducting interfacial layers and simultaneously such films may be used as materials for non-linear optical devices.     

Synthesis of β-phenyl-δ,ε-unsaturated amino acids and stereoselective introduction of side chain groups into [4,3,0]-bicyclic β-turn dipeptides

(2S,3S)- and (2R,3R)-2-amino-3-phenyl-5-hexenoic acids have been synthesized in large scale by using Ni(II)-complexes as a template. The amino acids were used in the synthesis of [4,3,0]-bicyclic β-turn mimetics by a convergent methodology. The unique advantage of this strategy is the convenience of introducing side chain groups with predetermined chiralities on both the five- and six-membered heterocyclic rings.