Pionic excitation of giant resonances in Y

Inelastic scattering of π⁺ and π⁻ exhibits strongly excited giant resonance structures. Besides the giant quadrupole resonance centered around 14 MeV, structures are observed at 16.8 MeV which can be fitted with a mixing of L=0 and L=1, and around 25 MeV (E_x = 110A^−1/3).     

The Cesàro Operator in Growth Banach Spaces of Analytic Functions

The Cesàro operator C, when acting in the classical growth Banach spaces \({A^{-\gamma}}\) and \({A_0^{-\gamma}}\), for \({\gamma} > 0\), of analytic functions on \({\mathbb{D}}\), is investigated. Based on a detailed knowledge of their spectra (due to A. Aleman and A.-M. Persson) we are able to determine the norms of these operators precisely. It is then possible to characterize the mean ergodic and related properties of C acting in these spaces. In addition, we determine the largest Banach space of analytic functions on \({\mathbb{D}}\) which C maps into \({A^{-\gamma}}\) (resp. into \({A_0^{-\gamma}}\)); this optimal domain space always contains \({A^{-\gamma}}\) (resp. \({A_0^{-\gamma}}\)) as a proper subspace.     

New Trends in Asymmetric Phase Transfer Catalysis

Phase Transfer Catalysis (PTC) is a powerful tool to perform reactions in a practical fashion, both in laboratory and industrial scale. Significant cost savings and major process improvements can be achieved in reactions performed under PTC conditions. In the last few years remarkable results in stereoselective reactions were achieved using chiral, non-racemic quaternary ammonium salts. Moreover, the use of bulky, chiral phosphate anions paired with achiral cations to generate lipophilic ion pairs allowed to design new avenues for the stereoselective construction of important building blocks. Hydrogen bond interactions were also shown to provide new pathways for asymmetric nucleophilic substitutions using insoluble reagents under PTC conditions. This Review will focus on recent advances in developing practical synthetic routes to construct molecules in a stereoselective fashion under PTC conditions.     

Localised solutions of Hartree equations for narrow-band crystals

We consider the Hartree equations for a system of an infinite number of electrons in a periodic potential consisting of a periodic array of wells. The filling fraction is assumed to be of one electron per well. We prove that if the wells are deep enough to admit a bound state and if they are separated by a distance large enough, then the Hartree equations have a solution in which all single particle wave functions decay exponentially.     

Perturbation theory for periodic orbits in a class of infinite dimensional Hamiltonian systems

We consider a class of Hamiltonian systems describing an infinite array of coupled anharmonic oscillators, and we study the bifurcation of periodic orbits off the equilibrium point. The family of orbits we construct can be parametrized by their periods which belong to Cantor sets of large measure containing certain periods of the linearized problem as accumulation points. The infinitely many holes forming a dense set on which the existence of a periodic orbit cannot be proven originate from a dense set of resonances that are present in the system. We also have a result concerning the existence of solutions of arbitrarily large amplitude.Address after September 1990     

On the global solvability in Gevrey classes on the n-dimensional torus

Let P be a linear partial differential operator with coefficients in the Gevrey class G^s(Tⁿ), where Tⁿ is the n-dimensional torus and s?1. We prove a necessary condition for the s-global solvability of P on Tⁿ. We also apply this result to give a complete characterization for the s-global solvability for a class of formally self-adjoint operators with nonconstant coefficients.     

On the critical problem of F. D. pressure treatment for laminar flows confined by permeable walls

In the present work the viscous (low Reynolds) flow in plane ducts confined by permeable walls has been studied. A simple model of the filtrating walls has been used, with the normal velocity component proportional to the pressure jump across the wall, resulting in a non-standard boundary value Navier-Stokes problem. A critical analysis of the appropriate boundary condition and pressure problem has led to the conclusions of employing a simple explicit finite volume approach, and of avoiding the use of higher order finite difference schemes. In this paper a special emphasis on the structure of the involved computational matrices has been given to illustrate the chosen algorithm. The latter yields a steady state solution that is second order accurate in space, and it has an accuracy in time of order ≤ Δt (the time step), due to the explicit treatment of the velocity boundary conditions along the membrane. The model has been tested to study the effects of the inlet/outlet conditions, Reynolds number and filtrating wall constant.     

Unitary dressing transformations and exponential decay below threshold for quantum spin systems. Parts III and IV

This is the continuation of a series of articles concerning a class of quantum spin systems with Hamiltonian operators of the form

Synthesis of 2,6-disubstituted morpholines through regioselective oxiranes ring opening by tosylamide under PTC conditions

Symmetric and non-symmetric 2,6-disubstituted morpholines were synthesized through regioselective nucleophilic ring opening of oxiranes with tosylamide under solid-liquid phase transfer catalysis (SL-PTC) conditions followed by cyclization of the tosylamido diols thus obtained and final deprotection of the corresponding N-tosyl morpholines. The morpholines prepared are interesting building blocks in the synthesis of pharmaceuticals and agrochemicals.