Some uniform stability and convergence results for integral equations on the real line and projection methods for their solution

The paper considers second kind equations of the form (abbreviated x=y + K2x) in which and the factor z is bounded but otherwise arbitrary so that equations of Wiener-Hopf type are included as a special case. Conditions on a set are obtained such that a generalized Fredholm alternative is valid: if W satisfies these conditions and I − Kz, is injective for each z ε W then I − Kz is invertible for each z ε W and the operators (I − Kz)−1 are uniformly bounded. As a special case some classical results relating to Wiener-Hopf operators are reproduced. A finite section version of the above equation (with the range of integration reduced to [−a, a]) is considered, as are projection and iterated projection methods for its solution. The operators (where denotes the finite section version of Kz) are shown uniformly bounded (in z and a) for all a sufficiently large. Uniform stability and convergence results, for the projection and iterated projection methods, are obtained. The argument generalizes an idea in collectively compact operator theory. Some new results in this theory are obtained and applied to the analysis of projection methods for the above equation when z is compactly supported and k(s − t) replaced by the general kernel k(s,t). A boundary integral equation of the above type, which models outdoor sound propagation over inhomogeneous level terrain, illustrates the application of the theoretical results developed.

The real value of equality

This paper investigates how political theorists and philosophers should understand egalitarian political demands in light of the increasingly important realist critique of much of contemporary political theory and philosophy. It suggests, first, that what Martin O'Neill has called non-intrinsic egalitarianism is, in one form at least, a potentially realistic egalitarian political project and second, that realists may be compelled to impose an egalitarian threshold on state claims to legitimacy under certain circumstances. Non-intrinsic egalitarianism can meet realism’s methodological requirements because it does not have to assume an unavailable moral consensus since it can focus on widely acknowledged bads rather than contentious claims about the good. Further, an appropriately formulated non-intrinsic egalitarianism may be a minimum requirement of an appropriately realistic claim by a political order to authoritatively structure some of its members' lives. Without at least a threshold set of egalitarian commitments, a political order seems unable to be transparent to many of its worse off members under a plausible construal of contemporary conditions.

Immersive Projection for biochemical pattern matching

In all biological processes, protein molecules and other small molecules interact to function and form transient macromolecular complexes. This interaction of two or more molecules can be described by a docking event. Docking is an important phase for structure-based drug design strategies, as it can be used as a method to simulate protein-ligand interactions. Various docking programs exist that allow automated docking, but most of them have limited visualization and user interaction. It would be advantageous if scientists could visualize the molecules participating in the docking process, manipulate their structures and manually dock them before submitting the new conformations to an automated docking process in an immersive environment, which can help stimulate the design/docking process. This also could greatly reduce docking time and resources. To achieve this, we propose a new virtual modelling/docking program, whereby the advantages of virtual modelling programs and the efficiency of the algorithms in existing docking programs will be merged.

A new set of orthogonal patterns in weather and climate: Optimally interpolated patterns.

A new spectral-based approach is presented to find orthogonal patterns from gridded weather/climate data. The method is based on optimizing the interpolation error variance. The optimally interpolated patterns (OIP) are then given by the eigenvectors of the interpolation error covariance matrix, obtained using the cross-spectral matrix. The formulation of the approach is presented, and the application to low-dimension stochastic toy models and to various reanalyses datasets is performed. In particular, it is found that the lowest-frequency patterns correspond to largest eigenvalues, that is, variances, of the interpolation error matrix. The approach has been applied to the Northern Hemispheric (NH) and tropical sea level pressure (SLP) and to the Indian Ocean sea surface temperature (SST). Two main OIP patterns are found for the NH SLP representing respectively the North Atlantic Oscillation and the North Pacific pattern. The leading tropical SLP OIP represents the Southern Oscillation. For the Indian Ocean SST, the leading OIP pattern shows a tripole-like structure having one sign over the eastern and north- and southwestern parts and an opposite sign in the remaining parts of the basin. The pattern is also found to have a high lagged correlation with the Niño-3 index with 6-months lag.

On the evolution of the solar wind between 1 and 5 AU at the time of the Cassini Jupiter flyby: Multispacecraft observations of interplanetary coronal mass ejections including the formation of a merged interaction region

The Cassini flyby of Jupiter occurred at a time near solar maximum. Consequently, the pre-Jupiter data set reveals clear and numerous transient perturbations to the Parker Spiral solar wind structure. Limited plasma data are available at Cassini for this period due to pointing restrictions imposed on the instrument. This renders the identification of the nature of such structures ambiguous, as determinations based on the magnetic field data alone are unreliable. However, a fortuitous alignment of the planets during this encounter allowed us to trace these structures back to those observed previously by the Wind spacecraft near the Earth. Of the phenomena that we are satisfactorily able to trace back to their manifestation at 1 AU, two are identified as being due to interplanetary coronal mass ejections. One event at Cassini is shown to be a merged interaction region, which is formed from the compression of a magnetic cloud by two anomalously fast solar wind streams. The flux-rope structure associated with this magnetic cloud is not as apparent at Cassini and has most likely been compressed and deformed. Confirmation of the validity of the ballistic projections used here is provided by results obtained from a one-dimensional magnetohydrodynamic projection of solar wind parameters measured upstream near the Earth. It is found that when the Earth and Cassini are within a few tens of degrees in heliospheric longitude, the results of this one-dimensional model predict the actual conditions measured at 5 AU to an impressive degree. Finally, the validity of the use of such one-dimensional projections in obtaining quasi-solar wind parameters at the outer planets is discussed.

Effects of patch size and density on flower visitation and seed set of wild plants: a pan-European approach

1. Habitat fragmentation can affect pollinator and plant population structure in terms of species composition, abundance, area covered and density of flowering plants. This, in turn, may affect pollinator visitation frequency, pollen deposition, seed set and plant fitness. 2. A reduction in the quantity of flower visits can be coupled with a reduction in the quality of pollination service and hence the plants’ overall reproductive success and long-term survival. Understanding the relationship between plant population size and⁄ or isolation and pollination limitation is of fundamental importance for plant conservation. 3. Weexamined flower visitation and seed set of 10 different plant species fromfive European countries to investigate the general effects of plant populations size and density, both within (patch level) and between populations (population level), on seed set and pollination limitation. 4. Wefound evidence that the effects of area and density of flowering plant assemblages were generally more pronounced at the patch level than at the population level. We also found that patch and population level together influenced flower visitation and seed set, and the latter increased with increasing patch area and density, but this effect was only apparent in small populations. 5. Synthesis. By using an extensive pan-European data set on flower visitation and seed set we have identified a general pattern in the interplay between the attractiveness of flowering plant patches for pollinators and density dependence of flower visitation, and also a strong plant species-specific response to habitat fragmentation effects. This can guide efforts to conserve plant–pollinator interactions, ecosystem functioning and plant fitness in fragmented habitats.