Non-weakly supercyclic operators

Several methods based on an easy geometric argument are provided to prove that a given operator is not weakly supercyclic. The methods apply to different kinds of operators like composition operators or bilateral weighted shifts. In particular, it is shown that the classical Volterra operator is not weakly supercyclic on any of the LP [0, 1] spaces, 1

New results on a classical operator

It is remarkable how the classical Volterra integral operator, which was one of the first operators which attracted mathematicians' attention, is still worth of being studied. In this essentially survey work, by collecting some of the very recent results related to the Volterra operator, we show that there are new (and not so new) concepts that are becoming known only at the present days. Discovering whether the Volterra operator satisfies or not a given operator property leads to new methods and ideas that are useful in the setting of Concrete Operator Theory as well as the one of General Operator Theory. In particular, a wide variety of techniques like summability kernels, theory of entire functions, Gaussian cylindrical measures, approximation theory, Laguerre and Legendre polynomials are needed to analyze different properties of the Volterra operator. We also include a characterization of the commutator of the Volterra operator acting on L-P[0, 1], 1

Time operator for diffusion

Volume: 11 Issue: 4 Pages: 465-477 Published: MAR 2000 Times Cited: 9 References: 15 Citation MapCitation Map beta Abstract: We extend the concept of time operator for general semigroups and construct a non-self-adjoint time operator for the diffusion equation which is intertwined with the unilateral shift. We obtain the spectral resolution, the age eigenstates and a new shift representation of the solution of the diffusion equation. Based on previous work we obtain similarly a self-adjoint time operator for Relativistic Diffusion. (C) 2000 Elsevier Science Ltd. All rights reserved.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

Invasion by the amphipod Gammarus pulex alters community composition of native freshwater macroinvertebrates

Assessing the effects of invading species on native community structure is often confounded by environmental factors and weakened by lack of replicated, long-term pre- and post-invasion monitoring. Here, we uncouple the community effects of a freshwater amphipod invader from environmental differences. In Irish rivers, the introduced Gammarus pulex replaces the native Gammarus duebeni celticus. However, the River Lissan in Northern Ireland is dissected by a weir that has slowed the upstream invasion by G. pulex. This allowed us in 2000 to sample three contiguous 150-m reaches that were (1) G. pulex dominated; (2) mixed Gammarus spp.; and (3) G. duebeni celticus only. In 2003, we resampled these reaches and one additional of mixed Gammarus species and one with only G. duebeni celticus further upstream. In temperature, conductivity, and pH, there were statistically significant but no biologically relevant differences among the five reaches of 2003, and between the three reaches surveyed in both years. Although there was evidence of recovery in macroinvertebrate diversity and richness in invaded reaches between years, continued upstream invasion was associated with sustained reductions in these community metrics as compared to un-invaded sites. Community ordination indicated (1) different associations of community composition attributed to the distribution, abundance, and biomass of the invader; and (2) increasing similarity of invaded communities over time. The impact mechanisms of G. pulex on macroinvertebrate community composition may include predation and competition. The consequences of the observed community changes for ecosystem functioning require further investigation.

Differences in composition of macroinvertebrate communities with invasive and native Gammarus spp. (Crustacea : Amphipoda)

1. Assessing the effects on communities of invasive species is often confounded by environmental factors. In Irish rivers, the introduced amphipod Gammarus pulex replaces the native G. duebeni celticus in lowland stretches. The two amphipods are associated with different macroinvertebrate communities, which may in part be the result of natural longitudinal physicochemical change. However, this hinders assessment of any direct community impacts of the invasive as compared with the native species. Here, we report on a fortuitous circumstance that allowed us to uncouple the community effects of Gammarus species from environmental differences.

Strasheela: Design and usage of a music composition environment based on the Oz programming model

Strasheela provides a means for the composer to create a symbolic score by formally describing it in a rule-based way. The environment defines a rich music representation for complex polyphonic scores. Strasheela enables the user to define expressive compositional rules and then to apply them to the score. Compositional rules can restrict many aspects of the music - including the rhythmic structure, the melodic structure and the harmonic structure - by constraining the parameters (e.g. duration or pitch) of musical events according to some numerical or logical relation. Strasheela combines this expressivity with efficient search strategies.