On the growth of meromorphic functions of infinite order

Letf be a meromorphic function of infinite order,T(r, f) its Nevanlinna (or Ahlfors-Shimizu) characteristic, andM(r, f) its maximum modulus. It is proved that $$\mathop {\lim \inf }\limits_{r \to \infty } \frac{{\log M(r,f)}}{{rT'(r,f)}} \leqslant \pi and\mathop {\lim \inf }\limits_{r \to \infty } \frac{{\log M(r,f)}}{{T(r,f)\psi (log T(r,f))}} = 0$$ . if ? (x)/x is non-decreasing, ?′(x)<-√?(x) and ∝^∞ dx/?(x) < ∞.     

Electron-cluster interactions

Beam depletion spectroscopy has been used to measure absolute total inelastic electron-sodium cluster collision cross sections in the energy range fromE0.1 toE6 eV. The investigation focused on the closed shell clusters Na₈, Na₂₀, and Na₄₀. The measured cross sections show an increase for the lowest collision energies where electron attachment is the primary scattering channel. The electron attachment cross section can be understood in terms of Langevin scattering, connecting this measurement with the polarizability of the cluster. For energies above the dissociation energy the measured electron-cluster cross section is energy independent, thus defining an electron-cluster interaction range. This interaction range increases with the cluster size.     

Near melting point flow injection: a drastic enhancement in FAAS detection limits

The described technique is based on segregation phenomena taking place in solids near their melting point. High impurity concentration occurs in a liquid phase at the grain boundaries. A continuous flow of an adequate solvent is used in far from equilibrium conditions to reach high extraction efficiency of the analyte. As an example, the determination of trace amounts of caesium in metallic sodium is described. The 5 mg/kg detection limit of conventional FAAS is thus lowered to a few g/kg.     

Newton's method and periodic solutions of nonlinear wave equations

We prove the existence of periodic solutions of the nonlinear wave equation satisfying either Dirichlet or periodic boundary conditions on the interval [O, π]. The coefficients of the eigenfunction expansion of this equation satisfy a nonlinear functional equation. Using a version of Newton's method, we show that this equation has solutions provided the nonlinearity g(x, u) satisfies certain generic conditions of nonresonance and genuine nonlinearity. © 1993 John Wiley & Sons, Inc.     

Synthesis of vinca alkaloids and related compounds. 100. Stereoselective oxidation reactions of compounds with the aspidospermane and quebrachamine ring system. First synthesis of some alkaloids containing the epoxy ring

The first syntheses of the alkaloids (-)-mehranine (3), (+)-voaphylline/conoflorine (4), (+)-N(a)-methylvoaphylline/hecubine (5), and (-)-lochnericine (2) were achieved by stereoselective epoxidation starting from (-)-tabersonine (1), through intermediates with the aspidospermane and quebrachamine skeleton.     

Structure and diffusion in amorphous aluminum silicate: a molecular dynamics computer simulation

The amorphous aluminum silicate (Al2O3)2(SiO2) [AS2] is investigated by means of large scale molecular dynamics computer simulations. We consider fully equilibrated melts in the temperature range 6100 K> or =T> or =2300 K as well as glass configurations that were obtained from cooling runs from T=2300 to 300 K with a cooling rate of about 10(12) K/s. Already at temperatures as high as 4000 K, most of the Al and Si atoms are fourfold coordinated by oxygen atoms. Thus, the structure of AS2 is that of a disordered tetrahedral network. The packing of AlO4 tetrahedra is very different from that of SiO4 tetrahedra in that Al is involved with a relatively high probability in small-membered rings and in triclusters in which an O atom is surrounded by four cations. We find as typical configurations two-membered rings with two Al atoms in which the shared O atoms form a tricluster. On larger length scales, the system shows a microphase separation in which the Al-rich network structure percolates through the SiO2 network. The latter structure gives rise to a prepeak in the static structure factor at a wave number q=0.5 A(-1). A comparison of experimental x-ray data with the results from the simulation shows good agreement for the structure function. The diffusion dynamics in AS2 is found to be much faster than in SiO2. We show that the self-diffusion constants for O and Al are very similar and that they are by a factor of 2-3 larger than the one for Si.