Spectre negatif d'un operateur elliptique avec des conditions au bords de Robin

In this article we discuss some estimates of the number of the negative eigenvalues and their moments of energy for an elliptic operator L = L0 - V(x) defined in Hm(Rn+) with the Robin boundary conditions containing a potential W(x), in terms of some integrals of V and W

Ion Association Effects of Lipophilic Quaternary Ammonium Salts in Ion-Exchange and Potentiometric Selectivity

Strong effects of ion association on the anion-exchange selectivity in systems water -solutions of high quaternary ammonium salts (QAS) in organic solvents as well as on the potentiometric selectivity of plasticized polyvinylchloride (PVC) membranes containing QAS as ion exchangers have been established experimen¬tally and substantiated theoretically. Based on the linear Gibbs energy relations (LGER) and ion association theory by Eigen-Denison-Ramsey-Fuoss, an approach to separate estimation of the parts played by the solvation and ion association fac¬tors in ion-exchange and potentiometric selectivity has been proposed. The results obtained serve as the basis for revision of the formed notions about QAS as of «nonselective» ion exchangers and enable the development of methods for the con¬trol of ion-exchange and potentiometric selectivity using the factor of ion associa¬tion. Specifically, it has been demonstrated that variation of steric accessibility of the QAS exchange center is a powerful means to control the selectivity. It has been found experimentally that due to varying steric accessibility of the QAS exchange center the selectivity values have changed by 3 orders of magnitu¬de in case of single- charged anions exchanged for single-charged ones and by more than 7 orders - in case of double-charged anions exchanged for the sing¬le-charged ones. The above-mentioned effects revealed also in the potentiometric selectivity of QAS-based PVC membranes and to some extent - in the potentiometric selectivity of the membranes based on neutral anion carriers, doped with QAS for provision of anion permselectivity, are of great practical importance for the development of ISE with improved selectivity

Direct Observation of Condon Domains in Silver by Hall Probes

Using a set of micro Hall probes for the detection of the local induction, the inhomogeneous Condon domain structure has been directly observed at the surface of a pure silver single crystal under strong Landau quantization in magnetic fields up to 10 T. The inhomogeneous induction occurs in the theoretically predicted part of the H-T Condon domain phase diagram. Information about size, shape and orientation of the domains is obtained by analyzing Hall probes placed along and across the long sample axis and by tilting the sample. On a beryllium surface the induction inhomogeneity is almost absent although the expected induction splitting here is at least ten times higher than in silver.Comment: 4 pages, 6 figures, submitted to PR

Hysteresis in the de Haas-van Alphen Effect

A hysteresis loop is observed for the first time in the de Haas-van Alphen (dHvA) effect of beryllium at low temperatures and quantizing magnetic field applied parallel to the hexagonal axis of the single crystal. The irreversible behavior of the magnetization occurs at the paramagnetic part of the dHvA period in conditions of Condon domain formation arising by strong enough dHvA amplitude. The resulting extremely nonlinear response to a very small modulation field offers the possibility to find in a simple way the Condon domain phase diagram. From a harmonic analysis, the shape and size of the hysteresis loop is constructed.Comment: 4 pages, 5 figures, submitted to PR

Spatial polarimetry of inhomogeneous surfaces under laser illumination

A study aimed at improving the methods of remote laser polarimetry of inhomogeneous surfaces using complex probe signals with a combined amplitude-phase and polarization modulation has been performed. It is shown that the informative properties of probe signals can be improved that potentially allows for carrying out some operations of forming and processing polarization images of objects in the probe stage. The efficiency of application of the proposed probe signals for recognizing various types of materials is experimentally confirme