The resonance spectrum of the cusp map in the space of analytic functions

We prove that the Frobenius-Perron operator $U$ of the cusp map $F:[-1,1]\to [-1,1]$, $F(x)=1-2 x^{1/2}$ (which is an approximation of the Poincare section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that for any $q\in (0,1)$ the spectrum of $U$ in the Hardy space in the disk $\{z\in C:|z-q|

Flatworm nerve-muscle: structural and functional analysis

Platyhelminthes occupy a unique position in nerve-muscle evolution, being the most primitive of metazoan phyla. Essentially, their nervous system consists of an archaic brain and associated pairs of longitudinal nerve cords cross-linked as an orthogon by transverse commissures. Confocal imaging reveals that these central nervous system elements are in continuity with an array of peripheral nerve plexuses which innervate a well-differentiated grid work of somatic muscle as well as a complexity of myofibres associated with organs of attachment, feeding, and reproduction. Electrophysiological studies of flatworm muscles have exposed a diversity of voltage-activated ion channels that influence muscle contractile events. Neuronal cell types are mainly multi- and bi-polar and highly secretory in nature, producing a heterogeneity of vesicular inclusions whose contents have been identified cytochemically to include all three major types of cholinergic, aminergic, and peptidergic messenger molecules. A landmark discovery in flatworm neurobiology was the biochemical isolation and amino acid sequencing of two groups of native neuropeptides: neuropeptide F and FMRFamide-related peptides (FaRPs). Both families of neuropeptide are abundant and broadly distributed in platyhelminths, occurring in neuronal vesicles in representatives of all major flatworm taxa. Dual localization studies have revealed that peptidergic and cholinergic substances occupy neuronal sets separate from those of serotoninergic components. The physiological actions of neuronal messengers in flatworms are beginning to be established, and where examined, FaRPs and 5-HT are myoexcitatory, while cholinomimetic substances are generally inhibitory. There is immunocytochemical evidence that FaRPs and 5-HT have a regulatory role in the mechanism of egg assembly. Use of muscle strips and (or) muscle fibres from free-living and parasitic flatworms has provided baseline information to indicate that muscle responses to FaRPs are mediated by a G-protein-coupled receptor, and that the signal transduction pathway for contraction involves the second messengers cAMP and protein kinase C.

Comparison of the functional responses of invasive and native amphipods

While we can usually understand the impacts of invasive species on recipient communities, invasion biology lacks methodologies that are potentially more predictive. Such tools should ideally be straightforward and widely applicable. Here, we explore an approach that compares the functional responses (FRs) of invader and native amphipod crustaceans. Dikerogammarus villosus is a Ponto-Caspian amphipod currently invading Europe and poised to invade North America. Compared with other amphipods that it actively replaces in fresh-waters, D. villosus exhibited significantly greater predation, consuming significantly more prey with a higher type II FR. This corroborates the known dramatic field impacts of D. villosus on invaded communities. In another species, FRs were nearly identical in invasive and native ranges. We thus propose that if FRs of other taxa and trophic groups follow such general patterns, this methodology has potential in predicting future invasive species impacts.

The functional role of Gammarus (Crustacea, Amphipoda): shredders, predators, or both?

Gammarus spp. are traditionally viewed under the functional feeding group (FFG) concept as herbivorous 'shredders'. Although recent studies suggest that Gammarus should also be viewed as predators, this latter role remains contentious. Here, in a laboratory experiment, we objectively examine the balance between shredder and predator roles in a common freshwater species. Gammarus pulex preyed significantly on mayfly nymph, Baetis rhodani, in both the presence and absence of excess leaf material. There was no significant difference in predation where the alternative food, that is, leaf material, was present as compared to absent. Also, G. pulex shredded leaf material in the presence and absence of B. rhodani. However, shredding was significantly reduced where alternative food, that is, B. rhodani prey, was present as compared to absent. Further, G. pulex had a clear leaf species preference. Our results suggest that Gammarus function as both predators and shredders, with the balance of the two roles perhaps depending on food availability and quality. We discuss implications for the use of the FFG concept in assessing freshwater processes, and the role that Gammarus predation may play in structuring macroinvertebrate communities.

Au on (111) and (110) surfaces of CeO2: A density-functional theory study

The atomic structures of gold supported on (111) and (110) surfaces of CeO2 have been studied using density-functional theory calculations. A single Au atom is placed on three adsorption sites on the surfaces; the stoichiometric surfaces, an oxygen vacancy and a Ce-vacancy. It is found that (i) the Au adsorption energies are in the following order: E-ad(Ce-vacancy) > E-ad(O-vacancy) > E-ad(stoichiometric surface); and (ii) the Au atom adsorption on the Ce-vacancy activates O atoms nearby. One 0 atom is less stable than that in O-2 in the gas phase and another O atom is much easier to remove compared to that of the stoichiometric surfaces. These results suggest that the Au adsorption on Ce-vacancies not only creates an O-vacancy but also activates an O atom nearby. This provides a piece of direct evidence that Au adsorption on a Ce-vacancy may be responsible for some unique catalytic properties of Au/CeO2. (C) 2008 Elsevier B.V. All rights reserved.

A quantitative determination of reaction mechanisms from density functional theory calculations: Fischer-Tropsch synthesis on flat and stepped cobalt surfaces

We systematically investigated the mechanism of the C-1 + C-1 coupling reactions using density functional theory. The activation energies of C-1 + C-1 coupling and carbon hydrogenation reactions on both flat and stepped surfaces were calculated and analyzed. Moreover, the coverages of adsorbed C-1 species were estimated, and the reaction rates of all possible C-1 + C-1 coupling pathways were quantitatively evaluated. The results suggest that the reactions of CH2 + CH2 and CH3 + C at steps are most likely to be the key C-1 + C-1 coupling steps in FT synthesis on Co catalysts. The reactions of C-2 + C-1 and C-3 + C-1 coupling also were studied; the results demonstrate that in addition to the pathways of RCH + CH2 and RCH2 + C, the coupling of RC + C and RC + CH also may contribute to the chain growth after C-1. (C) 2008 Elsevier Inc. All rights reserved.

Recent advances in understanding CO oxidation on gold nanoparticles using density functional theory

Since the discovery of a series of Au-based catalysts by Haruta et al. considerable progress has been made in understanding the active role of Au in CO oxidation catalysis. This review provides a summary of recent theoretical work performed in this field; in particular it addresses DFT studies of CO oxidation catalysis over free and supported gold nanoparticles. Several properties of the Au particles have been found to contribute to their unique catalytic activity. Of these properties, the low-coordination state of the Au atoms is arguably the most pertinent, although other properties of the Au cluster atoms, such as electronic charge, cannot be ignored. The current consensuses regarding the mechanism for CO oxidation over Au-based catalysts is also discussed. Finally, water-enhanced catalysis of CO oxidation on Au clusters is summarized.

Insight into the solvent effect: A density functional theory study of cisplatin hydrolysis

The solvent effect on reactions in solutions is crucial for many systems. In this study, the reaction barrier with respect to the number of solvent molecules included in the system is systematically studied using density function theory calculations. Our results show that the barriers rapidly converge with respect to the number of solvent molecules. The solvent effect is investigated by calculating cisplatin hydrolysis in several types of solvents. The results are analyzed and a linear relationship between the reaction barrier and the interaction strength of solvent-reactants is found. Insight into the general solvent effect is obtained. (c) 2006 American Institute of Physics.