Superintegrability of rational Ruijsenaars-Schneider systems and their action-angle duals

We explain that the action-angle duality between the rational Ruijsenaars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the Darboux form of the reduced symplectic structure that arises in the `Ruijsenaars gauge' of the symplectic reduction underlying this case of action-angle duality. The same arguments apply to the BC(n) generalization of the pertinent dual pair, which was recently studied by Pusztai developing a method utilized in our direct calculation of the reduced symplectic structure.Comment: Extended version of talk at the conference "Geometry, Integrability and Quantization XIV" (Varna, June 2012), 15 page

Trigonometric Sutherland systems and their Ruijsenaars duals from symplectic reduction

Besides its usual interpretation as a system of $n$ indistinguishable particles moving on the circle, the trigonometric Sutherland system can be viewed alternatively as a system of distinguishable particles on the circle or on the line, and these 3 physically distinct systems are in duality with corresponding variants of the rational Ruijsenaars-Schneider system. We explain that the 3 duality relations, first obtained by Ruijsenaars in 1995, arise naturally from the Kazhdan-Kostant-Sternberg symplectic reductions of the cotangent bundles of the group U(n) and its covering groups $U(1) \times SU(n)$ and ${\mathbb R}\times SU(n)$, respectively. This geometric interpretation enhances our understanding of the duality relations and simplifies Ruijsenaars' original direct arguments that led to their discovery.Comment: 34 pages, minor additions and corrections of typos in v

On the superintegrability of the rational Ruijsenaars-Schneider model

The rational and hyperbolic Ruijsenaars-Schneider models and their non-relativistic limits are maximally superintegrable since they admit action variables with globally well-defined canonical conjugates. In the case of the rational Ruijsenaars-Schneider model we present an alternative proof of the superintegrability by explicitly exhibiting extra conserved quantities relying on a generalization of the construction of Wojciechowski for the rational Calogero model.Comment: added 2 references and some comments in v2, 10 page

An integrable BC(n) Sutherland model with two types of particles

A hyperbolic BC(n) Sutherland model involving three independent coupling constants that characterize the interactions of two types of particles moving on the half-line is derived by Hamiltonian reduction of the free geodesic motion on the group SU(n,n). The symmetry group underlying the reduction is provided by the direct product of the fixed point subgroups of two commuting involutions of SU(n,n). The derivation implies the integrability of the model and yields a simple algorithm for constructing its solutions.Comment: 14 pages, with minor modifications in v

Key drivers for copepod assemblages in a eutrophic coastal brackish lake

The copepod assemblages and abiotic parameters were investigated at 11 stations in a large coastal lake (Lake Manzalah, Nile Delta) from 2009-2010 in order to verify any impacts of eutrophication and salinity on the copepod species composition. The environmental conditions and the copepod assemblages appeared to have changed in comparison with previous studies, possibly because of increasing eutrophication and invasions of non-indigenous species (NIS). The aim of the present study was the identification of species which can be used as ecological indicators of high trophic status. Among the nine copepod species of Lake Manzalah, Acartia tonsa, Mesocyclops ogunnus, and Apocyclops panamensis were reported for the first time. Acartia tonsa, a well-known NIS for the Mediterranean, numerically dominated the copepod assemblages in some portions of the lake. The distribution of Acanthocyclops trajani and Thermocyclops consimilis was insensible to eutrophication because they can stand high levels of nutrients and hypoxia. Compared with previous reports, the copepod assemblage of Lake Manzalah was richer in species. The invasions of NIS, in addition to the heterogeneous progress of eutrophication in the lake, created an environmental mosaic with many species in total, but with single areas suitable for only a small number of them

Redetermination of AgPO3

Single crystals of silver(I) polyphosphate(V), AgPO3, were prepared via a phospho­ric acid melt method using a solution of Ag3PO4 in H3PO4. In comparison with the previous study based on single-crystal Weissenberg photographs [Jost (1961 ▶). Acta Cryst. 14, 779–784], the results were mainly confirmed, but with much higher precision and with all displacement parameters refined anisotropically. The structure is built up from two types of distorted edge- and corner-sharing [AgO5] polyhedra, giving rise to multidirectional ribbons, and from two types of PO4 tetra­hedra linked into meandering chains (PO3)n spreading parallel to the b axis with a repeat unit of four tetra­hedra. The calculated bond-valence sum value of one of the two AgI ions indicates a significant strain of the structure

Inhibition of Fungi and Gram-Negative Bacteria by Bacteriocin BacTN635 Produced by Lactobacillus plantarum sp. TN635

The aim of this study was to evaluate 54 lactic acid bacteria (LAB) strains isolated from meat, fermented vegetables and dairy products for their capacity to produce antimicrobial activities against several bacteria and fungi. The strain designed TN635 has been selected for advanced studies. The supernatant culture of this strain inhibits the growth of all tested pathogenic including the four Gram-negative bacteria (Salmonella enterica ATCC43972, Pseudomonas aeruginosa ATCC 49189, Hafnia sp. and Serratia sp.) and the pathogenic fungus Candida tropicalis R2 CIP203. Based on the nucleotide sequence of the 16S rRNA gene of the strain TN635 (1,540 pb accession no FN252881) and the phylogenetic analysis, we propose the assignment of our new isolate bacterium as Lactobacillus plantarum sp. TN635 strain. Its antimicrobial compound was determined as a proteinaceous substance, stable to heat and to treatment with surfactants and organic solvents. Highest antimicrobial activity was found between pH 3 and 11 with an optimum at pH = 7. The BacTN635 was purified to homogeneity by a four-step protocol involving ammonium sulfate precipitation, centrifugal microconcentrators with a 10-kDa membrane cutoff, gel filtration Sephadex G-25, and C18 reverse-phase HPLC. SDS-PAGE analysis of the purified BacTN635, revealed a single band with an estimated molecular mass of approximately 4 kDa. The maximum bacteriocin production (5,000 AU/ml) was recorded after a 16-h incubation in Man, Rogosa, and Sharpe (MRS) medium at 30 °C. The mode of action of the partial purified BacTN635 was identified as bactericidal against Listeria ivanovii BUG 496 and as fungistatic against C. tropicalis R2 CIP203

The forms of repetition in social and environmental reports: insights from Hume's notion of ?impressions?

This paper focuses on the use of repetition, both in narrative and visual forms, in social and environmental reports. It investigates the forms of repetition as a rhetorical device adopted by the preparer of a social and environmental report in helping the process of knowledge acquisition, as outlined by Hume (1739). Drawing from Hume?s (1739) philosophical idea of an ?impression?, and the work of Davison (2014a) we classify repetitions into ?identical?, ?similar? and ?accumulated? forms. It is argued that the rationale for distinguishing between the different forms of repetition can be linked to their different potential or intensity in acting on different stimuli with a view to enhance learning. The empirical element of this study is based on the stand-alone social and environmental reports of a sample of 86 cooperative banks in Northern Italy; the analysis of these reports indicates that repetition is widespread and that cooperative banks use all forms of repetition, albeit to a varying extent within the different reported themes. The paper contributes to the literature by offering an alternative interpretation of repetition using an interdisciplinary perspective and by providing new insights on social and environmental reporting practices in the cooperative banking sector