A normalization problem for a class of singular integral operators with carleman shift and unbounded coefficients

The solution to a normalization problem for singular integral operators with Carleman shift and degenerate and unbounded coefficients inL _p () is obtained, where is either the unit circle or the real line. The approach followed consists mainly in two steps: the reduction to a singular integral operator with bounded coefficients and the use of the solution to an abstract normalization problem.This research was supported by JNICT under the grant PBIC/C/CEN/1040/92.     

Field-induced reentrant novel phase and a ferroelectric-magnetic order coupling in HoMnO3

A reentrant novel phase is observed in the hexagonal ferroelectric HoMnO3 in the presence of magnetic fields in the temperature range defined by a plateau of the dielectric constant anomaly. The plateau evolves with fields from a narrow dielectric peak at the Mn-spin rotation transition at 32.8 K in zero field. The anomaly appears both as a function of temperature and as a function of magnetic field without detectable hysteresis. This is attributed to the indirect coupling between the ferroelectric (FE) and antiferromagnetic (AFM) orders, arising from an FE-AFM domain wall effect.     

Synthetic pores with sticky pi-clamps

In this report, we describe design, synthesis, evaluation and molecular dynamics simulations of synthetic multifunctional pores with pi-acidic naphthalenediimide clamps. Experimental evidence is provided for the formation of unstable but inert, heterogeneous and acid-insensitive dynamic tetrameric pores that are sensitive to base and ionic strength. Blockage experiments reveal that the introduction of aromatic electron donor-acceptor interactions provides access to the selective recognition of pi-basic intercalators within the pore. This breakthrough is important for the application of synthetic pores as multianalyte sensors.     

Electronic excitations and lattice dynamics of coordinatively "unsaturated" complex transition metal compounds

Single crystal polarized Raman and infrared spectra of the series Na(5)[MO(2)][X] with M = Co(I), Ni(I), and Cu(I) and X = S(2-) and CO(3)(2-), are reported. All phonon modes are assigned to the lattice eigenmodes based on the group theory analysis and first principles lattice dynamics calculations. The energies of the fundamental symmetric and asymmetric vibrations of the [MO(2)](3-) complex are discussed on the basis of their electronic structure and variation in M-O interatomic distances. Electronic Raman scattering and luminescence are observed for the magnetic members of the series (Co(I), d(8), and Ni(I), d(9)). Ligand field theory is employed to account for the electronic effects which originate from states split by spin-orbit coupling.     

Far-infrared spectroscopy of the supreconductor YBa2Cu4O8

The frequencies of allB _1u (z) phonon modes predicted by a group-theoretical analysis were measured and found to agree well with recent lattice dynamical calculations for this compound. We report also the determination of two superconducting gap values in YBa₂Cu₄O₈ through phonon self-energy effects in the normal and superconducting conducting state. The gap-to-T _c ratios obtained from an analysis of these effects are 2 ₁/kT _c 2.5 and 5.82 ₂/kT _c 9.2. This coincides with previous results of both phononic and electronic Raman scattering where values of 2.1 and 6.3 were found. We further find anomalous softenings of two phonon modes 40 Kabove T _c , which correlate with an observed deviation from the linear temperature dependence of the average plasma frequency _p (T).     

Pyrene fluorescence quenching by aromatic azides

Pyrene fluorescence quenching by phenylazide derivatives with donor and acceptor substituents has been studied by fluorescence spectroscopy and flash photolysis. The rate constants of quenching (k _q) in acetonitrile ((0.2–1.2) × 10¹⁰ l mol^?1 s^?1) are found to be close to a diffusion limit; the rate constants were somewhat higher for perfluoro-substituted arylazides. It is found that k _q does not depend on solvent polarity; the formation of the pyrene cation in the course of pyrene fluorescence quenching by tolylazide was not detected. Pyrene fluorescence quenching occurred by an energy-transfer mechanism; this is supported by the coincidence of the quantum yields of the direct and sensitized photodecomposition of tolylazide. As estimated, energy transfer in rigid media occurs at characteristic distances of about 10 Å.     

A bound of the exterior arcs for a univalent mapping

In this paper we consider the intersection of the circle ¦w|=x with the image of the disc ¦z|&#x2264;r, 0f(z)=z+c₂z²+... which is univalent analytic in ¦z|<1. Earlier I. E. Bazilevich proved that for xc^/er the measure of the above intersection does not exceed the measure of the intersection produced by the functionf ^*(z)=z/(1–z)², ¦=1. In this paper I. E. Bazilevich's ideas are used to strengthen some of his results.Translated from Matematicheskie Zametki, Vol. 18, No. 3, pp. 367–378, September, 1975.