Convergence acceleration of the doubly periodic Green's function for the analysis of thin wire arrays

A method is proposed to accelerate the evaluation of the Green's function of an infinite double periodic array of thin wire antennas. The method is based on the expansion of the Green's function into series corresponding to the propagating and evanescent waves and the use of Poisson and Kummer transformations enhanced with the analytic summation of the slowly convergent asymptotic terms. Unlike existing techniques the procedure reported here provides uniform convergence regardless of the geometrical parameters of the problem or plane wave excitation wavelength. In addition, it is numerically stable and does not require numerical integration or internal tuning parameters, since all necessary series are directly calculated in terms of analytical functions. This means that for nonlinear problem scenarios that the algorithm can be deployed without run time intervention or recursive adjustment within a harmonic balance engine. Numerical examples are provided to illustrate the efficiency and accuracy of the developed approach as compared with the Ewald method for which these classes of problems requires run time splitting parameter adaptation.

Convergence and tracking analysis of a variable normalised LMF (XE-NLMF) algorithm

The least-mean-fourth (LMF) algorithm is known for its fast convergence and lower steady state error, especially in sub-Gaussian noise environments. Recent work on normalised versions of the LMF algorithm has further enhanced its stability and performance in both Gaussian and sub-Gaussian noise environments. For example, the recently developed normalised LMF (XE-NLMF) algorithm is normalised by the mixed signal and error powers, and weighted by a fixed mixed-power parameter. Unfortunately, this algorithm depends on the selection of this mixing parameter. In this work, a time-varying mixed-power parameter technique is introduced to overcome this dependency. A convergence analysis, transient analysis, and steady-state behaviour of the proposed algorithm are derived and verified through simulations. An enhancement in performance is obtained through the use of this technique in two different scenarios. Moreover, the tracking analysis of the proposed algorithm is carried out in the presence of two sources of nonstationarities: (1) carrier frequency offset between transmitter and receiver and (2) random variations in the environment. Close agreement between analysis and simulation results is obtained. The results show that, unlike in the stationary case, the steady-state excess mean-square error is not a monotonically increasing function of the step size. (c) 2007 Elsevier B.V. All rights reserved.

The main-sequence rotation-colour relation in the Coma Berenices open cluster

We present the results of a photometric survey of rotation rates in the Coma Berenices (Melotte 111) open cluster, using data obtained as part of the SuperWASP exoplanetary transit-search programme. The goal of the Coma survey was to measure precise rotation periods for main-sequence F, G and K dwarfs in this intermediate-age (~600 Myr) cluster, and to determine the extent to which magnetic braking has caused the stellar spin periods to converge. We find a tight, almost linear relationship between rotation period and J - K colour with an rms scatter of only 2 per cent. The relation is similar to that seen among F, G and K stars in the Hyades. Such strong convergence can only be explained if angular momentum is not at present being transferred from a reservoir in the deep stellar interiors to the surface layers. We conclude that the coupling time-scale for angular momentum transport from a rapidly spinning radiative core to the outer convective zone must be substantially shorter than the cluster age, and that from the age of Coma onwards stars rotate effectively as solid bodies. The existence of a tight relationship between stellar mass and rotation period at a given age supports the use of stellar rotation period as an age indicator in F, G and K stars of Hyades age and older. We demonstrate that individual stellar ages can be determined within the Coma population with an internal precision of the order of 9 per cent (rms), using a standard magnetic braking law in which rotation period increases with the square root of stellar age. We find that a slight modification to the magnetic-braking power law, P ~ t0.56, yields rotational and asteroseismological ages in good agreement for the Sun and other stars of solar age for which p-mode studies and photometric rotation periods have been published.

Convergence of partial-wave expansions for energies, scattering amplitudes and positron annihilation rates

We use many-body theory to find the asymptotic behaviour of second-order correlation corrections to the energies and positron annihilation rates in many- electron systems with respect to the angular momenta l of the single-particle orbitals included. The energy corrections decrease as 1/(l+1/2)4, in agreement with the result of Schwartz, whereas the positron annihilation rate has a slower 1/(l+1/2)2 convergence rate. We illustrate these results by numerical calculations of the energies of Ne and Kr and by examining results from extensive con?guration-interaction calculations of PsH binding and annihilation.

Ireland's Innovation Performance: 1991-2005

In this paper we use data from the five waves of the Irish Innovation Panel (IIP) to profile the innovation performance of manufacturing plants in Ireland and Northern Ireland over the period 1991 to 2005. Despite considerable public sector investment on both sides of the border levels of innovation activity have remained broadly similar throughout this period although somewhat different trends are evident in Ireland and Northern Ireland. In terms of product innovation for example, the proportion of manufacturing plants making product changes has increased 5 per cent in Ireland and just over 7 per cent in Northern Ireland. In terms of process innovation a decline of almost 7 per cent in Ireland has been accompanied by a 7 per cent increase in Northern Ireland. These trends provide some evidence of convergence in innovation performance over the 1991 to 2005 period. This is evident in the narrowing gap between the proportion of product innovators in Ireland and Northern Ireland, convergence in the proportion of plants undertaking process innovation and in terms of the increasingly similar proportions of sales derived from innovative products. Looking in more detail at the determinants of manufacturing innovation emphasises the importance of R&D and backwards supply chain linkages as sources of new knowledge for innovation. Other external linkages prove less important suggesting the value of policy initiatives designed to promote knowledge sharing. We also find a significant negative innovation effect from legislative restrictions on plants’ product innovation. Public support for both product and process innovation are having positive effects on innovation outputs at the level of the individual plant. Future research interest centres on the contrast between this strong positive result at firm level and the more modest increases in innovation among the population of firms in Ireland and Northern Ireland.

Positive almost Dunford-Pettis operators and their duality

We study some properties of almost Dunford-Pettis operators and we characterize pairs of Banach lattices for which the adjoint of an almost Dunford-Pettis operator inherits the same property and look at conditions under which an operator is almost Dunford-Pettis whenever its adjoint is.

Convergence of bimodules over maximal abelian selfadjoint algebras

We prove a continuity result for the map sending a masa-bimodule to its support. We characterise the convergence of a net of weakly closed convex hulls of bilattices in terms of the convergence of the corresponding supports, and establish a lower-semicontinuity result for the map sending a support to the corresponding masa-bimodule.