On class numbers of algebraic function fields defined byy 2=x 5 +ax overGF(p)

Archiv der Mathematik -     

Error analysis for a potential problem on locally refined grids

Summary. For the simulation of biomolecular systems in an aqueous solvent a continuum model is often used for the solvent. The accurate evaluation of the so-called solvation energy coming from the electrostatic interaction between the solute and the surrounding water molecules is the main issue in this paper. In these simulations, we deal with a potential problem with jumping coefficients and with a known boundary condition at infinity. One of the advanced ways to solve the problem is to use a multigrid method on locally refined grids around the solute molecule. In this paper, we focus on the error analysis of the numerical solution and the numerical solvation energy obtained on the locally refined grids. Based on a rigorous error analysis via a discrete approximation of the Greens function, we show how to construct the composite grid, to discretize the discontinuity of the diffusion coefficient and to interpolate the solutions at interfaces between the fine and coarse grids. The error analysis developed is confirmed by numerical experiments. Received June 25, 1998 / Revised version received July 14, 1999 / Published online June 8, 2000     

Nano- and micro-fabrications of polystyrene having atactic and syndiotactic structures using focused ion beams lithography

Micro- and nano-fabrications of polystyrene (PS) having the atactic and syndiotactic structures were carried out with direct maskless etching using focused ion beam (FIB). Micro- and nano-scale structures were obtained with selective beam and material conditions avoiding the beam-heating and charge-up effects. The etching rates were different between atactic and syndiotactic PS. The rate of fabrication for syndiotactic PS shows higher than that of atactic one. Moreover, the direct etching was influenced by the molecular weight. The etching rate for the lower molecular weight became the faster. The FIB direct etching proceeds through the two steps (decomposition and desorption (outgas)). Both decomposition and desorption are influenced by both conformation (morphology) and configuration (stereoregularity). Furthermore, the beam profiles and fluence play the important roles to perform the nano-fabrication of PS.     

A new diarylheptanoid and a rare dammarane triterpenoid from <Emphasis Type="Italic">Alnus nepalensis</Emphasis>

A new diarylheptanoid, a rare dammarane triterpenoid, and centrolobol were isolated from the leaves of Alnus nepalensis D. Don (Betulaceae). Their structures were determined by using spectroscopic analysis.     

Three new flavonoid glycosides, byzantionoside B 6'-O-sulfate and xyloglucoside of (Z)-hex-3-en-1-ol from Ruellia patula

Three new flavonoid glycosides, demethoxycentaureidin 7-O-β-D-galacturonopyranoside, pectolinarigenin 7-O-α-L-rhamnopyranosyl-(1?→4″)-β-D-glucopyranoside and 7-O-α-L-rhamnopyranosyl-(1?→4″)-β-D-glucuronopyranoside, a new megastigmane glucoside, byzantionoside B 6'-O-sulfate, and a new (Z)-hex-3-en-1-ol O-β-D-xylopyranosyl-(1″→2')-β-D-glucopyranoside, were isolated from leaves of Ruellia patula JACQ., together with 12 known compounds, β-sitosterol glucoside, vanilloside, bioside (decaffeoyl verbascoside), acteoside (verbascoside), syringin, benzyl alcohol O-β-D-xylopyranosyl-(1″→2')-β-D-glucopyranoside, cistanoside E, roseoside, phenethyl alcohol O-β-D-xylopyranosyl-(1″→2')-β-D-glucopyranoside, (+)-lyoniresinol 3α-O-β-D-glucopyranoside, isoacteoside and 3,4,5-trimethoxyphenol O-α-L-rhamnopyranosyl-(1″→6')-β-D-glucopyranoside. Their structures were elucidated by means of spectroscopic analyses.     

Experimental evidence for violation of the fluctuation-dissipation theorem in a superspin glass

We present the experimental observation of the fluctuation-dissipation theorem violation in an assembly of interacting magnetic nanoparticles in the low temperature superspin-glass phase. The magnetic noise is measured with a two-dimension electron gas Hall probe and compared to the out of phase ac susceptibility of the same ferrofluid. For "intermediate" aging times of the order of 1 h, the ratio of the effective temperature T(eff) to the bath temperature T grows from 1 to 6.5 when T is lowered from T(g) to 0.3 T(g), regardless of the noise frequency. These values are comparable to those measured in an atomic spin glass as well as those calculated for a Heisenberg spin glass.     

On generators of ideals defining projective toric varieties

 For any ample line bundle L on a projective toric variety of dimension n, it is proved that the line bundle L ^⊗i is normally generated if i is greater than or equal to n−1, and examples showing that this estimate is best possible are given. Moreover we prove an estimate for the degree of the generators of the ideals defining projective toric varieties. In particular, when L is normally generated, the defining ideal of the variety embedded by the global sections of L has generators of degree at most n+1. When the variety is embedded by the global sections of L ^⊗(n−1) , then the defining ideal has generators of degree at most three. Received: 11 July 2001 / Revised version: 17 December 2001