A sharper decay rate for a viscoelastic wave equation with power nonlinearity

We consider a viscoelastic wave equation with power nonlinearity. First, we construct a local solution by the Faedo-Galerkin approximation scheme and contraction mapping theorem. Next, we continue the local solution to the global one by a priori estimates obtained from a decreasing energy. Finally, we discuss the decay rate of the global solution by assuming that the kernel function is convex.     

An alternative scheme for calculating the unrestricted Hartree–Fock equation: Application to the boron and neon atoms

We present an alternative scheme for calculating the unrestricted Hartree–Fock (HF) equation. The scheme is based on the variational method utilizing the sophisticated basis functions that include no adjustable parameters. The validity of the present scheme is confirmed by actual calculations of the boron and neon atoms. The total energy of the present scheme is lower than that of the conventional restrictive HF equation, but higher than that of the CI method. Also, the resultant wave function satisfies the electron–nucleus cusp condition.     

Arsenobetaine-decomposing Ability of Marine Microorganisms Occurring in Particles Collected at Depths of 1100 and 3500 Meters

The arsenobetaine-decomposing ability of microorganisms occurring in sinking particles, which play a main role in the vertical transport of organic substances produced in the photic zone, was investigated. The microorganisms in particles collected in the deep sea, 1100 and 3500 m in depth, clearly showed decomposing ability. With the particles from 1100 m, the degradation products were the same as those produced by microorganisms occurring in sources in the photic zone, i.e. trimethylarsine oxide (TMAO), dimethylarsinic acid (DMA) and inorganic arsenic(V). At 3500 m, the degradation activity was diminished, smalls amount of DMA and TMAO being produced. These results suggest that arsenobetaine contained in the animals starts to degrade immediately after the death of the animals and their transformation to particles. The degradation of arsenobetaine to inorganic arsenic in our tentative arsenic cycle in marine ecosystems (inorganic arsenic to inorganic arsenic via the biosynthesis of arsenobetaine) may apply to the deep sea as well as to the photic zone. © 1997 by John Wiley & Sons, Ltd.     

On inconsistency of the common rate difference estimators from sparse follow-up data

It has been shown that the unconditional maximum likelihood estimator of the common odds ratio, risk ratio and risk difference parameters are inconsistent in sparse statification. Under a Poisson sparse-data model, the maximum likelihood estimator for the rate difference, which is the difference of the disease incidence rates among the exposed and the unexposed, is also shown to be biased. The sparse-data asymptotic bias of the maximum likelihood estimator is evaluated numerically and compared with that of the weighted least squares estimators.     

Touchdown and related problems in electrostatic MEMS device equation

We study the electrostatic MEMS-device equation, , with Dirichlet boundary condition. First, we describe the touchdown of non-stationary solution in accordance with the total set of stationary solutions. Then, we classify radially symmetric stationary solutions and their radial Morse indices. Finally, we show the Morse-Smale property for radially symmetric non-stationary solutions. On leave to Department of Statistics and Actuarial Science, University of the Aegean, current email address:nkaval@aegean.gr