Generalized T-Q relations and the open spin-s XXZ chain with nondiagonal boundary terms

We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we derive a generalized form of T-Q relation involving more than one independent Q(u), which we use to propose the Bethe-ansatz-type expressions for the eigenvalues of the transfer matrix. At most two of the boundary parameters are set to be arbitrary and the bulk anisotropy parameter has values \eta = i\pi/2, i\pi/4,... We also provide numerical evidence for the completeness of the Bethe-ansatz-type solutions derived, using s = 1 case as an example.Comment: 23 pages. arXiv admin note: substantial text overlap with arXiv:0901.3558; v2: published versio

The effect of data analysis strategies in density estimation of mountain ungulates using distance sampling

Distance sampling is being extensively used to estimate the abundance of animal populations. Nevertheless, the great variety of ways in which data can be analyzed may limit comparisons due to the lack of standardization of such protocols. In this study, the influence of analytical procedures for distance sampling data on density estimates and their precision was assessed. We have used data from 21 surveys of mountain ungulates in the Iberian Peninsula, France and the Italian Alps. Data from such surveys were analyzed with the program Distance 6.0. Our analyses show that estimated density can be higher for higher levels of data truncation. We also confirm that the estimates tend to be more precise when data are analyzed without binning and without truncating. We found no evidence of size biased sampling as group size and distances were uncorrelated in most of our surveys. Despite distance sampling being a fairly robust methodology, it can be sensitive to some data analysis strategies

Generalized Calogero-Moser systems from rational Cherednik algebras

We consider ideals of polynomials vanishing on the W-orbits of the intersections of mirrors of a finite reflection group W. We determine all such ideals which are invariant under the action of the corresponding rational Cherednik algebra hence form submodules in the polynomial module. We show that a quantum integrable system can be defined for every such ideal for a real reflection group W. This leads to known and new integrable systems of Calogero-Moser type which we explicitly specify. In the case of classical Coxeter groups we also obtain generalized Calogero-Moser systems with added quadratic potential.Comment: 36 pages; the main change is an improvement of section 7 so that it now deals with an arbitrary complex reflection group; Selecta Math, 201

Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models

We present the construction of the full set of eigenvectors of the open ASEP and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix Ansatz specific to the ASEP. This "matrix coordinate Bethe Ansatz" can be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative part being related to the algebra appearing inComment: 18 pages; Version to appear in J Phys

Uncertainty Relations in Deformation Quantization

Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson, Robertson-Schr\"odinger and trace uncertainty relations in deformation quantization are found. Some conditions under which the uncertainty relations are minimized are also given.Comment: 28+1 pages, harvmac file, no figures, typos correcte

Drinfeld twist and symmetric Bethe vectors of the open XYZ chain with non-diagonal boundary terms

With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex solid-on-solid (SOS) model, we find that in the F-basis provided by the twist the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form. This allows us to obtain the explicit and completely symmetric expressions of the two sets of Bethe states of the model.Comment: Latex file, 25 page

Toward an Identification of Resources Influencing Habitat Use in a Multi-Specific Context

Interactions between animal behaviour and the environment are both shaping observed habitat use. Despite the importance of inter-specific interactions on the habitat use performed by individuals, most previous analyses have focused on case studies of single species. By focusing on two sympatric populations of large herbivores with contrasting body size, we went one step beyond by studying variation in home range size and identifying the factors involved in such variation, to define how habitat features such as resource heterogeneity, resource quality, and openness created by hurricane or forest managers, and constraints may influence habitat use at the individual level. We found a large variability among individual's home range size in both species, particularly in summer. Season appeared as the most important factor accounting for observed variation in home range size. Regarding habitat features, we found that (i) the proportion of area damaged by the hurricane was the only habitat component that inversely influenced roe deer home range size, (ii) this habitat type also influenced both diurnal and nocturnal red deer home range sizes, (iii) home range size of red deer during the day was inversely influenced by the biomass of their preferred plants, as were both diurnal and nocturnal core areas of the red deer home range, and (iv) we do not find any effect of resource heterogeneity on home range size in any case. Our results suggest that a particular habitat type (i.e. areas damaged by hurricane) can be used by individuals of sympatric species because it brings both protected and dietary resources. Thus, it is necessary to maintain the openness of these areas and to keep animal density quite low as observed in these hunted populations to limit competition between these sympatric populations of herbivores