Infinite Patterns that can be Avoided by Measure

A set A of real numbers is called universal (in measure) ifevery measurable set of positive measure necessarily containsan affine copy of A. All finite sets are universal, but no infiniteuniversal sets are known. Here we prove some results relatedto a conjecture of Erds that there is no infinite universalset. For every infinite set A, there is a set E of positivemeasure such that (x + tA)E fails for almost all (Lebesgue)pairs (x, t). Also, the exceptional set of pairs (x, t) (forwhich (x + tA)E) can be taken to project to a null set on thet-axis. Finally, if the set A contains large subsets whose minimumgap is large (in a scale-invariant way), then there is ER ofpositive measure which contains no affine copy of A. 1991 MathematicsSubject Classification 28A12.     

Designing Zn(II) and Cu(II) derivatives as probes for in vitro fluorescence imaging

New M(II) bis(thiosemicarbazonato) complexes (M = Ni(II), Cu(II) and Zn(II)) featuring allyl groups at the exocyclic nitrogens have been synthesised. The complexes were characterised in solution by spectroscopic methods and their solid state structures determined by single crystal X-ray diffraction using synchrotron radiation. The Zn(II) complex was found to be intrinsically fluorescent and soluble in biocompatible media. The uptake of this Zn(II) complex in HeLa, MCF-7 and IGROV cancer cells was monitored by fluorescence microscopies (epi- and confocal fluorescence imaging). The radiolabelling to (64)Cu(II) bis(thiosemicarbazonato) complex was performed cleanly by transmetallation from the corresponding Zn(II) species using (64)Cu(OAc)(2).     

Computing the flow around a moving profile by numerically integrating the Navier–Stokes equations

A vorticity velocity formulation is proposed for the solution of the equations for viscous flow around a moving profile. A non-inertial reference frame is used and the velocities are computed from a Poincaré integral formula. The studies are directed towards the need to understand helicopter blade aerodynamics. Worked examples are given which validate the method and programme for laminar flows, at least for low Reynolds numbers. © 1998 John Wiley & Sons, Ltd.     

Bulk titanium for structural and biomedical applications obtaining by spark plasma sintering (SPS) from titanium hydride powder

Titanium is a low density element with excellent mechanical properties, and is an attractive material for structural and biomedical applications. In recent years, a new process technology is emerging by which titanium and titanium alloys can be obtained by using titanium hydride (TiH₂) as a precursor for Ti and its mixture with alloying elements. The feasibility of this manufacturing approach has been fully demonstrated from powder to sintering and from microstructure to mechanical properties. In this paper, a study concerning powder metallurgy processing of Ti by spark plasma sintering (SPS) route is presented. The influence of the technological parameters on the hardness and microstructures change during SPS has been studied. The experimental results are related to microscopic, thermal, and mechanical analysis.     

Elaboration,characterization and study of a new hybrid chitosan/ceramic membrane for affinity membrane chromatography

A new kind of metal affinity membrane based on a ceramic support was prepared. It was elaborated in four steps: (i) deposition of a chitosan layer in order to functionalize the ceramic support, (ii) cross-linking with epichlorohydrin to stabilise the polymer layer and to enable the grafting, (iii) iminodiacetic acid grafting, (iv) Cu²⁺ adsorption. Due to the ceramic support, this membrane is highly resistant and the chitosan layer brings its biocompatibility properties. Each step of the membrane elaboration was studied and the membrane structure was characterized. Both thin coating of the polymer on the alumina grains of the support and the chemical modification of the membrane were proved. Then, bovine serum albumin (BSA) was used as a model protein to test protein retention of the affinity membrane. The protein/membrane interactions were investigated showing that some non-specific ones are involved. Finally, the effect of buffer concentration was checked and it appears that, in the studied range, an increase of the buffer concentration entailed a limitation of the non-specific interactions inducing a better BSA recovering and a higher selectivity.     

Ferromagnetic coupling through spin polarization in the hexanuclear [MnII(3)CuII(3)] complex

A novel Cu(II)-Mn(II) hexanuclear complex of formula [[MnCuL](3)(tma)](ClO(4))(3).8H(2)O [H(2)L = macrocyclic Robson proligand; H(3)tma = trimesic acid] has been obtained by connecting three heterobinuclear [Cu(II)Mn(II)L](2+) cationic species through the trimesate anion. The complex exhibits a C(3) rotational symmetry, imposed by the geometry of the bridging ligand. The interaction within each Mn(II)-Cu(II) pair is antiferromagnetic (J = -16.7 cm(-1)). A weak ferromagnetic coupling among the three S = 2 resulting spins through the tricarboxylato bridge leads to a S = 6 ground spin state, for which the spin polarization mechanism is responsible.     

Dynamic chemical devices: modulation of photophysical properties by reversible, ion-triggered, and proton-fuelled nanomechanical shape-flipping molecular motions

The terpy-derived (terpy=terpyridine) ligand 1 has an extended W shape in which the two appended photoactive pyrenyl groups are held apart. On binding of a zinc(II) ion with a terpy group, ligand 1 is converted into complex 2 whereby it adopts a U shape, thus stacking the aromatic units. This structural modification leads to a very pronounced change in photophysical properties: from a highly fluorescent free ligand to a very weakly emitting complex. The W/U structural switching can be reversibly induced by the addition of a competitive tren ligand, which binds and releases a zinc(II) ion under protonation/deprotonation cycles, thus leading to oscillations in light emission. Therefore, the present system performs periodic modulation of optical output through a nanomechanical shape-flipping motion, triggered by metal ion binding and fuelled by acid-base neutralisation energy. Overall, it represents an ion-triggered opto-mechanical supramolecular device.     

Accurate double many-body expansion potential energy surface for triplet H3+. II. The upper adiabatic sheet (2(3)A')

We report on a global potential energy hypersurface for the upper sheet of the lowest triplet state of H3+. The analytic representation is based on the double many-body expansion theory. The ab initio data points, calculated with a large cc-pV5Z basis, are represented with a root mean square deviation of only 5.54 cm(-1) in the energy region below the H(+)+2H(2S) dissociation threshold. The quasi-bound vibronic states supported by this surface have also been calculated.