Cantor exchange systems and renormalization

We prove a one-to-one correspondence between (i) C¹⁺ conjugacy classes of C^1+H Cantor exchange systems that are C^1+H fixed points of renormalization and (ii) C¹⁺ conjugacy classes of C^1+H diffeomorphisms f with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, we prove that there is no C^1+α Cantor exchange system, with bounded geometry, that is a C^1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set.     

Solving multiple-objective problems in the objective space

Projection and relaxation techniques are employed to decompose a multiobjective problem into a two-level structure. The basic manipulation consists in projecting the decision variables onto the space of the implicit tradeoffs, allowing the definition of a relaxed multiobjective master problem directly in the objective space. An additional subproblem tests the feasibility of the solution encountered by the relaxed problem. Some properties of the relaxed problem (linearity, small number of variables, etc.) render its solution efficient by a number of methods. Representatives of two different classes of multiobjective methods [the Geoffrion, Dyer, Feinberg (GDF) method and the fuzzy method of Baptistella and Ollero] are implemented and applied within this context to a water resources allocation problem. The results attest the computational viability of the overall procedure and its usefulness for the solution of multiobjective problems.This work was partially sponsored by grants from CNP_q and FAPESP, Brazil. The authors are indebted to the anonymous reviewers for their valuable comments.     

Yttrium aluminate crystals for slabs

The methods of growing YAG:Nd crystals with a flat interface and YAP:Nd crystals with a sharp conical interface are described. The form of the interface was controlled by the He and H₂O content in the reducing atmosphere composed mainly of Ar and H₂ as well as by axial temperature gradient above the melt level. The crystals of 120–180 mm in length were machined to the high-quality slabs.     

Silica hybrid nanocomposites

In this work we present experimental results about the formation, properties and structure of sol — gel silica based biocomposite containing Calcium alginate as an organic compound. Two different types of silicon precursors have been used in the synthesis: tetramethylortosilicate (TMOS) and ethyltrimethoxysilane (ETMS). The samples have been prepared at room temperature. The hybrids have been synthesized by replacing different quantitis of the inorganic precursor with alginate. The structure of the obtained hybrid materials has been studied by XRD, IR Spectroscopy, EDS, BET and AFM. The results proved that all samples are amorphous possessing a surface area from 70 to 290 m²/g. It has also been established by FT IR spectra that the hybrids containing TMOS display Van der Walls and Hydrogen bonding or electrostatic interactions between the organic and inorganic components. Strong chemical bonds between the inorganic and organic components in the samples with ETMS are present. A self-organized nanostructure has been observed by AFM. In the obtained hybrids the nanobuilding blocks average in size at about 8–14 nm for the particles.     

Electron transport in corona charged 12 μm teflon FEP with saturable deep traps

Surface-potential measurements carried out in negatively corona charged 12 m samples of fluorethylenepropylene (Teflon FEP) showed the following characteristics: 1) with a constant charging current, the potential initially rises linearly, and then sublinearly; 2) the potential saturates irrespectively of the charging process and 3) practically no potential decay is observed after switching off the corona. These results have been interpreted in terms of an usual model (field-independent trapping time) for charge transport in insulators, with saturable deep traps in both surface and bulk of the sample and a relatively high electron mobility in order to prevent free-space charge accumulation. The partial differential equations derived from the model are numerically solved and it was found that only the product of the mobility with the trapping time is relevant to the fitting of experimental results, provided that >10^–8 cm²/Vs. A field-dependent trapping time model leads to poorer fittings.     

Particle shape in thixotropic aluminium and thorium molybdates gels

Summary Electron microscope examination of thixotropic aluminium and thorium molybdate gels shows that one hour after formation they are constituted by short fibrils of small axial ratio. The fibrils of the aluminium molybdate gels, with ageing at room temperature or with boiling, increase in diameter and length; the fibrous shape of the particles is maintained after two and a half years of ageing; all fibrils are crystalline by electron diffraction. The fibrils of the thorium molybdate gels, except in the gels containing hydrochloric acid, change with ageing at room temperature or with boiling, into plates of hexagonal, elliptical or rectangular profile; the fibrils and plates are crystalline and have the same electron diffraction pattern as the fibrils.This work was aided, in part, by grants from Conselho Nacional de Pesquisas and the Rockefeller Foundation.     

Coordination modes of 2-hydroxynicotinic acid in second- and third-row transition metal complexes

The new Pd(II), Pt(II), Re(V), Mo(VI) and W(VI) complexes of 2-hydroxynicotinic acid (H₂nicO), trans-[PdCl(HnicO)(PPh₃)₂]·0.75CH₃CN (1), K[PdCl(HnicO)₂]·H₂O (2), [Pd(HnicO)₂(bipy)] (3), cis-[PtCl(HnicO)(PPh₃)₂]·0.75CH₃OH·0.5H₂O (4), [PtCl(HnicO)(bipy)] (5), cis-[ReOI₂(HnicO)(PPh₃)] (6), Na₂[Mo₂O₆(HnicO)₂]·5H₂O (7), Na₂[Mo₄O₁₂(HnicO)₂]·2H₂O (8) and Na₂[W₂O₆(HnicO)₂]·5H₂O (9) have been prepared. The crystal structures of 1 and 4, were determined by X-ray diffraction and show the HnicO⁻ ligand coordinated to palladium or platinum through the nitrogen atom only. Infrared, Raman, ¹H and ¹³C{¹H} NMR spectroscopic data for the complexes are presented and are in agreement with the crystallographic results.     

Kinetic model of a DC oxygen glow discharge

A simple kinetic model predicting the concentration of oxygen atoms, metastable singlet molecules O₂(a ¹) and negative ions O — in the positive column of a DC glow discharge is developed. The calculated O and O₂(a ¹) concentrations are compared to previously reported measurements for pressuresp=0.2–2 Torr and discharge currentsI=10–80 mA. The electron density calculated from the continuity equationj=n _e e v _d agrees well with experiment. The rate coefficients for electron impact processes used in the balance equations of O, O₂(a ¹), and O^– were taken from the literature as a function of the reduced electric fieldE/N forE/N=40–80 Td. A reasonable agreement is obtained between the model and the experiment with a set of 10 reactions for the production and destruction of the above-mentioned species