A Novel Dimeric Eremophilane from Ligularia virgaurea spp. oligocephala

A novel dimeric eremophilane, ligulolide B, was isolated from the alcoholic extract of the whole plant of Ligularia virgaurea spp. oligocephala. The structure was elucidated by various spectroscopic methods including intensive 2D NMR techniques （^1H-^1H COSY, gHMQC, gHMBC and ^1H-^1H NOESY） and HR-ESI-MS.     

一类齐次对称多项式上的切比雪夫不等式

本文借助于控制不等式及数学归纳法，将著名的切比雪夫不等式推广到m次一般齐次对称多项式上(如文中定理及引理7)，并将此结果用于对称平均等．旨在展示证明解析不等式的一些有效的方法和技巧，同时为数学研究特别是高维几何研究提供一些新的有趣而有用的解析不等式．     

Beugung elektromagnetischer Wellen in Braunbekscher Näherung. I

An approximation method proposed by Braunbek for the diffraction of scalar waves by plane obstacles, or apertures in a plane screen, is extended to the diffraction of electromagnetic waves. As an example, the diffraction of a linearly polarized plane electromagnetic wave normally incident on a circular aperture in a perfectly conducting plane screen and on a perfectly conducting plane circular disk is considered in detail. The results are compared with those obtained from the exact solution ofMeixner andAndrejewski and with the results ofKirchhoff's approximations. It is shown that, in contrast to theKirchhoff approximations,Braunbek's method leads in all cases to the correct ‘optical’ limits and represents a good approximation even for wavelengths comparable with the size of the obstacle. After a general formulation ofBraunbek's method in the electromagnetic diffraction problem, we calculate in the present paper the far field of the circular aperture and the transmission coefficient by means of the cross section theorem. The near field of the circular aperture and the circular disk will be considered in a subsequent paper.     

Generalized fresnel model for very heavy ion scattering: (II). Relation to the optical model

The generalized Fresnel model presented in part I as a simplified method for analyzing angular distributions of very heavy ion scattering is used here with an alternative parameterization of the partial-wave S-matrix. Its form is suggested by analytic expressions for the reflection function and nuclear phase shifts derived by Kauffmann from conventional optical potentials. This enables us to formulate explicitly the relationships between the l-space and r-space properties of the elastic heavy ion interaction, in particular the continuous ambiguities and other features found empirically from optical model calculations.     

Investigation of the quantitative properties of the quadrupole orthogonal acceleration time-of-flight mass spectrometer with electrospray ionisation using 3,4-methylenedioxymethamphetamine

This paper describes the investigation of the potential of a quadrupole orthogonal acceleration time-of-flight mass spectrometer (Q-TOF) equipped with an atmospheric pressure ionisation interface for quantitative measurements of small molecules separated by reversed phase liquid chromatography. To this end, the detection limits and linear dynamic range in particular were studied in an LC/MS/MS experiment using 3,4-methylenedioxymethamphetamine standards and 3,4-methylenedioxyethylamphetamine for internal standardisation. In a second phase, the experiment was repeated with real biological extracts (whole blood, serum, and vitreous humour). A calibration for 3,4-methylenedioxymethamphetamine and its metabolite 3,4-methylenedioxyamphetamine was prepared in each of these matrices again using 3,4-methylenedioxyethylamphetamine as internal standard. The resulting quantitative data were compared with those obtained by liquid chromatography with fluorescence detection for the same extracts. The Q-TOF results revealed excellent sensitivity and a linear dynamic range of nearly four decades (2-10 000 pg on-column, r(2) = 0.9998, 1/x weighting). Furthermore, all the calibration curves prepared in biological material were superimposable, LC/MS/MS and LC-fluorescence, and the quantitative results for actual samples compared very favourably. It was concluded that the Q-TOF achieves a linear dynamic range for quantitative LC/MS/MS work exceeding that of fluorescence detection and at much better absolute sensitivity. Copyright 1999 John Wiley & Sons, Ltd.     

Generalized fresnel model for very heavy ion scattering: (III). Dynamic polarization effects

It is shown that the large deviations from the typical Fresnel shape of heavy ion angular distributions, observed recently in the elastic scattering from deformed nuclei, can be described quite adequately by a very simple modification of the closed formulae for the differential cross section ratio $\text{gs(θ)}\text{σ}{}_{\mathrm{R}}\text{(θ)}$ of the generalized Fresnel model presented in parts I and II of this work. Our treatment rests basically on the relatively long range of the dynamic polarization potential that describes the Coulomb excitation to which the large deviations from the normal Fresnel pattern are attributed. We also calculate the effects of nuclear coupling in an adiabatic approximation and show that these lead to another modification, this time of the damping function F(z), which is however much smaller than that for Coulomb excitation and hardly discernible in angular distributions for very heavy ion scattering.     

Noncommutative Differential Calculus Approach to Discrete Symplectic Schemes on Regular Lattice

By means of a noncommutative differential calculus on function space of discrete Abelian groups and that of the regular lattice with equal spacing as well as the discrete symplectic geometry and a kind of classical mechanical systems with separable Hamiltonian of the type H(p, q) = T(p) + V(q) on regular lattice, we introduce the discrete symplectic algorithm, i.e., the phase-space discrete counterpart of the symplectic algorithm including original symplectic schemes and the jet-symplectic schemes in terms of the discrete time jet bundle formalism, on the regular lattice. We show some numerical calculation examples and compare the results of different schemes.