XXZ Bethe states as highest weight vectors of the sl2sl_2 loop algebra at roots of unity

We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at roots of unity is a highest weight vector of the $sl_2$ loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator $S^Z$, and evaluate explicitly the highest weight in terms of the Bethe roots. We also discuss whether a given regular Bethe state in the sectors generates an irreducible representation or not. In fact, we present such a regular Bethe state in the inhomogeneous case that generates a reducible Weyl module. Here, we call a solution of the Bethe ansatz equations which is given by a set of distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio

Selecting medicinal plants for cultivation at Nqabara on the Eastern Cape Wild Coast, South Africa

[From introduction:] The intensive harvesting of medicinal plants for commercial trade in South Africa poses a threat to many species. Cultivation has therefore been considered as an alternative to collection in the wild. This paper aims to assess the feasibility of cultivating medicinal plants in the Nqabara Administrative Area on South Africa's Wild Coast. A combination of participatory and formal research methods was used to collect data on the importance of medicinal plants, collection localities, market prices, the time spent collecting plants and their ease of cultivation. The values attached to medicinal plants were mainly dependent on their market prices. Four of the five Nqabara traditional healers interviewed cultivated these plants in their home gardens, but many medicinal products were obtained in indigenous forests from the bark of large trees, which were unsuitable for cultivation. Collectors said that the proximity of forests to their homesteads and the richness of forests in medicinal plants influenced their selection of harvesting localities. There was no correlation between time spent collecting species and their market prices. These prices were, however, positively correlated with the species' perceived healing properties. Users acknowledged that harvesting had an adverse effect on large trees, are eager to cultivate them and are taking action to conserve indigenous forests. Community-based enterprises should focus on species that are easy to cultivate and have a high demand, such as Stangeria eriopus, Acalypha glabrata and Behnia reticulata but not Araujia sericifera, which is exotic and abundant. The main barriers to commercial cultivation are availability of suitable land, water, lack of start-up capital, and access to markets and to seeds. Cultivation of medicinal plants could contribute to the economic empowerment of women in rural areas

COMPLETE SOLUTION OF THE XXZ-MODEL ON FINITE RINGS. DYNAMICAL STRUCTURE FACTORS AT ZERO TEMPERATURE.

The finite size effects of the dynamical structure factors in the XXZ-model are studied in the euclidean time $(\tau)$-representation. Away from the critical momentum $p=\pi$ finite size effects turn out to be small except for the large $\tau$ limit. The large finite size effects at the critical momentum $p=\pi$ signal the emergence of infrared singularities in the spectral $(\omega)$-representation of the dynamical structure factors.Comment: PostScript file with 12 pages + 11 figures uuencoded compresse

Temperature dependent spatial oscillations in the correlations of the XXZ spin chain

We study the correlation $$ for the XXZ chain in the massless attractive (ferromagnetic) region at positive temperatures by means of a numerical study of the quantum transfer matrix. We find that there is a range of temperature where the behavior of the correlation for large separations is oscillatory with an incommensurate period which depends on temperature.Comment: 4 pages, REVTEX, 6 table

Seasonal habitat selection by eland in arid savanna in southern Africa

The small scale seasonal habitat selection of eland in a semi-arid savanna was investigated. Linear discriminant functions and suitability index curves were calculated to differentiate between 314 m2 plots where eland were present and absent. Biological explanations were sought for the results. In winter eland relied on woody evergreen plants, while in summer they selected patches with good grass cover. Eland were independent of shelter and cover in both seasons. The ability of the discriminant functions to predict the presence and absence of eland was validated by classifying independent habitat samples. The functions were found to be reliable

Gaia Data Release 1: Pre-processing and source list creation

Context. The first data release from the Gaia mission contains accurate positions and magnitudes for more than a billion sources, and proper motions and parallaxes for the majority of the 2.5 million HIPPARCOS and Tycho-2 stars. Aims. We describe three essential elements of the initial data treatment leading to this catalogue: the image analysis, the construction of a source list, and the near real-time monitoring of the payload health. We also discuss some weak points that set limitations for the attainable precision at the present stage of the mission. Methods. Image parameters for point sources are derived from one-dimensional scans, using a maximum likelihood method, under the assumption of a line spread function constant in time, and a complete modelling of bias and background. These conditions are, however, not completely fulfilled. The Gaia source list is built starting from a large ground-based catalogue, but even so a significant number of new entries have been added, and a large number have been removed. The autonomous onboard star image detection will pick up many spurious images, especially around bright sources, and such unwanted detections must be identified. Another key step of the source list creation consists in arranging the more than 10^(10) individual detections in spatially isolated groups that can be analysed individually. Results. Complete software systems have been built for the Gaia initial data treatment, that manage approximately 50 million focal plane transits daily, giving transit times and fluxes for 500 million individual CCD images to the astrometric and photometric processing chains. The software also carries out a successful and detailed daily monitoring of Gaia health

Single Top Quark Production and Decay at Next-to-leading Order in Hadron Collision

We present a calculation of the next-to-leading order QCD corrections, with one-scale phase space slicing method, to single top quark production and decay process $p\bar{p},pp\to t\bar{b}+X\to b\ell\nu\bar{b}+X$ at hadron colliders. Using the helicity amplitude method, the angular correlation of the final state partons and the spin correlation of the top quark are preserved. The effect of the top quark width is also examined.Comment: 47 pages, 9 figure

The Q-operator for Root-of-Unity Symmetry in Six Vertex Model

We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-operator, the six-vertex transfer matrix and fusion matrices are derived from the Bethe equation, parallel to the Onsager-algebra-symmetry discussion in the superintegrable $N$-state chiral Potts model. We show that the whole set of functional equations is valid for the $Q$-operator. Direct calculations in certain cases are also given here for clearer illustration about the nature of the $Q$-operator in the symmetry study of root-of-unity six-vertex model from the functional-relation aspect.Comment: Latex 26 Pages; Typos and small errors corrected, Some explanations added for clearer presentation, References updated-Journal version with modified labelling of sections and formula

Auxiliary matrices on both sides of the equator

The spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show remarkable differences. In particular, it is shown that for even roots of unity and an odd number of sites the eigenvalues contain two linear independent solutions to Baxter's TQ-equation corresponding to the Bethe ansatz equations above and below the equator. In contrast, one finds for even spin-chains only one linear independent solution and complete strings. The other main result is the proof of a previous conjecture on the degeneracies of the six-vertex model at roots of unity. The proof rests on the derivation of a functional equation for the auxiliary matrices which is closely related to a functional equation for the eight-vertex model conjectured by Fabricius and McCoy.Comment: 22 pages; 2nd version: one paragraph added in the conclusion and some typos correcte