Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

Electromagnetic wave diffraction from an infinite array of complex-shaped microstrip reflectors

A numerical-analytical method is developed for solving surface integral equations (IEs) describing electromagnetic wave diffraction from arrays of complex-shaped planar reflectors. Solutions to these equations are regularized via analytical transformation of the separated singular part of the matrix kernel. Basis functions satisfying the metal-edge condition are determined on the entire surface of the complex region. The amplitude and phase responses of arrays consisting of polygonal reflectors are numerically investigated.

Nematode neuropeptides: Localization, isolation and functions

Historically, peptidergic substances (in the form of neurosecretions) were linked to moulting in nematodes. More recently, there has been a renewal of interest in nematode neurobiology, initially triggered by studies demonstrating the localization of peptide immunoreactivities to the nervous system. Here, David Brownlee, Ian Fairweather, Lindy Holden-Dye and Robert Walker will review progress on the isolation of nematode neuropeptides and efforts to unravel their physiological actions and inactivation mechanisms. Future avenues for research are suggested and the potential exploitation of peptidergic pathways in future therapeutic strategies highlighted.

Structure observed in measured electron energy distribution functions in capacitively coupled radio frequency hydrogen plasmas

Electron energy probability functions measured with a passively compensated Langmuir probe in asymmetric capacitively coupled hydrogen and deuterium plasmas exhibit structure. The otherwise relatively continuous distribution appears to have an abrupt peak in electron density near 5 eV. This structure occurs at a higher energy in deuterium than hydrogen and there is a correlation between floating potential and the voltage at which the structure is observed in the second derivative of the I(V) characteristic. While the cause of the structure has yet to be clarified, spectroscopic observations and computer-based hydrogen models indicate that the high energy tail of the distribution is strongly modulated during the radio frequency cycle. The effect of this modulation on plasma properties and probe measurements has yet to be explored. (C) 1999 American Institute of Physics. [S0003-6951(99)00819-0].

A COMPARISON OF EXPERIMENTAL AND THEORETICAL ELECTRON-ENERGY DISTRIBUTION-FUNCTIONS IN A MULTICUSP ION-SOURCE

Experimental and theoretical electron energy distribution functions (EEDFS) measured in and calculated for the driver of a multicusp ion source operating in hydrogen are compared. The results show that atomic physics based theoretical models can accurately predict the EEDF in such discharges if some appropriate experimentally determined quantities are used as input parameters. The magnitude and shape of the EEDF is found to be particularly sensitive to the effective surface area to volume ratio for electrons.

ELECTRON-ENERGY DISTRIBUTION-FUNCTIONS AND NEGATIVE-ION CONCENTRATIONS IN TANDEM AND HYBRID MULTICUSP NEGATIVE HYDROGEN-ION SOURCES

The second derivative of a Langmuir probe characteristic is used to establish the electron energy distribution function (EEDF) in both a tandem and hybrid multicusp H- ion source. Moveable probes are used to establish the spatial variation of the EEDF. The negative ion density is measured by laser induced photo-detachment. In the case of the hybrid source the EEDF consists of a cold Maxwellian in the central region of the source; the electron temperature increases with increasing discharge current (rising from 0.3 eV at 1 A to 1.2 eV at 50 A when the pressure is 0.4 Pa). A hot-electron tail exists in the EEDF of the driver region adjacent to each filament which is shown to consist of a distinct group of primary electrons at low pressure (0.08 Pa) but becomes degraded mainly through inelastic collisions at higher pressures (0.27 Pa). The tandem source, on the other hand, has a single driver region which extends throughout the central region. The primary electron confinement times are much longer so that even at the lowest pressure considered (0.07 Pa) the primaries are degraded. In both cases the measured EEDF at specific locations and values of discharge operating parameters are used to establish the rate coefficients for the processes of importance in H- production and destruction.