295 research outputs found

    A condition of Brauer-Cartan-Hua type-II

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    Constructions of free commutative integro-differential algebras

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    In this survey, we outline two recent constructions of free commutative integro-differential algebras. They are based on the construction of free commutative Rota-Baxter algebras by mixable shuffles. The first is by evaluations. The second is by the method of Gr\"obner-Shirshov bases.Comment: arXiv admin note: substantial text overlap with arXiv:1302.004

    Nurse sow strategies in the domestic pig: I. Consequences for selected measures of sow welfare

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    peer-reviewedManagement strategies are needed to optimise the number of piglets weaned from hyper-prolific sows. Nurse sow strategies involve transferring supernumerary new-born piglets onto a sow whose own piglets are either weaned or fostered onto another sow. Such ‘nurse sows’ have extended lactations spent in farrowing crates, which could have negative implications for their welfare. This study used 47 sows, 20 of which farrowed large litters and had their biggest piglets fostered onto nurse sows which were either 1 week (2STEP7, n=9) or 3 weeks into lactation (1STEP21, n=10). Sows from which piglets were removed (R) were either left with the remainder of the litter intact (I) (remain intact (RI) sows, n=10), or had their litters equalised (E) for birth weight using piglets of the same age from non-experimental sows (remain equalised (RE) sows, n=9). Piglets from 2STEP7 were fostered onto another nurse sow which was 3 weeks into lactation (2STEP21, n=9). Back-fat thickness was measured at entry to the farrowing house, at fostering (nurse sows only) and weaning. Sows were scored for ease of locomotion and skin and claw lesions at entry to the farrowing house and weaning. Salivary cortisol samples were collected and tear staining was scored at 0900 h weekly from entry until weaning. Saliva samples were also taken at fostering. Data were analysed using GLMs with appropriate random and repeated factors, or non-parametric tests were applied where appropriate. Back-fat thickness decreased between entry and weaning for all sows (F1,42=26.59, P0.05) and all nurse sows had a higher salivary cortisol concentration at fostering, compared with the other days (F10,426=3.47; P0.05). In conclusion, no difference was detected between nurse sows and non-nurse sows in body condition or severity of lesions. Although some nurse sows experienced stress at fostering, no long-term effect of the nurse sow strategies was detected on stress levels compared with sows that raised their own litter

    Nurse sow strategies in the domestic pig: II. Consequences for piglet growth, suckling behaviour and sow nursing behaviour

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    peer-reviewedNurse sow strategies are used to manage large litters on commercial pig farms. However, new-born piglets transferred to nurse sows in late lactation might be compromised in terms of growth and survival. We investigated the effects of two nurse sow strategies on piglet growth, suckling behaviour and sow nursing behaviour. At 1-day post-farrowing, the four heaviest piglets from large litters were transferred to a nurse sow either 21 (1STEP21, n=9 litters) or 7 (2STEP7, n=10 litters) days into lactation. The remainder of the litter remained with their mother and was either kept intact (remain intact (RI), n=10 litters) or had some piglets cross-fostered to equalise birth weights (remain equalised (RE), n=9 litters). The 7-day-old piglets from 2STEP7 were transferred onto a sow 21 days into lactation (2STEP21, n=10 litters). The growth of new-born piglets on 1STEP21 and 2STEP7 nurse sows was initially lower than in RI litters (F3,33.8=4.61; P0.5). After the 1st week of lactation, the weights and growth rates did not differ between treatments. Fighting behaviour during nursing bouts decreased over time. The frequency of fights was higher in 1STEP21 and 2STEP21 litters compared with RI litters (t122=3.06 and t123=3.00, respectively, P<0.05). The 2STEP21 litters had shorter nursing bouts than RI and 1STEP21 litters (t107=−2.81 and t81.7=2.8, respectively, P<0.05), which were more frequently terminated by 2STEP21 than RI sows (t595=2.93; P<0.05). Transferring heaviest piglets from RI and RE litters to nurse sows reduced the percentage of teat changes during nursing bouts (RI: F1,275=16.61; RE: F1,308=43.59; P<0.001). In conclusion, nurse sow strategies do not appear to compromise piglet growth. However, new-born piglets transferred onto sows in late lactation experienced more competition at the udder, suggesting that the sows’ stage of lactation is of importance to how achievable nurse sow strategies are. Thus, the two-step nurse sow strategy is likely the best option (in relation to growth and suckling behaviour), as it minimises the difference between piglet age and sow stage of lactation

    A system of difference equations with elliptic coefficients and Bethe vectors

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    An elliptic analogue of the qq deformed Knizhnik-Zamolodchikov equations is introduced. A solution is given in the form of a Jackson-type integral of Bethe vectors of the XYZ-type spin chains.Comment: 20 pages, AMS-LaTeX ver.1.1 (amssymb), 15 figures in LaTeX picture environment

    Noncompact SL(2,R) spin chain

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    We consider the integrable spin chain model - the noncompact SL(2,R) spin magnet. The spin operators are realized as the generators of the unitary principal series representation of the SL(2,R) group. In an explicit form, we construct R-matrix, the Baxter Q-operator and the transition kernel to the representation of the Separated Variables (SoV). The expressions for the energy and quasimomentum of the eigenstates in terms of the Baxter Q-operator are derived. The analytic properties of the eigenvalues of the Baxter operator as a function of the spectral parameter are established. Applying the diagrammatic approach, we calculate Sklyanin's integration measure in the separated variables and obtain the solution to the spectral problem for the model in terms of the eigenvalues of the Q-operator. We show that the transition kernel to the SoV representation is factorized into a product of certain operators each depending on a single separated variable.Comment: 29 pages, 12 figure

    New Formula for the Eigenvectors of the Gaudin Model in the sl(3) Case

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    We propose new formulas for eigenvectors of the Gaudin model in the \sl(3) case. The central point of the construction is the explicit form of some operator P, which is used for derivation of eigenvalues given by the formula ∣w1,w2)=∑n=0∞Pn/n!∣w1,w2,0>| w_1, w_2) = \sum_{n=0}^\infty P^n/n! | w_1, w_2,0>, where w1w_1, w2w_2 fulfil the standard well-know Bethe Ansatz equations

    Interaction of Reggeized Gluons in the Baxter-Sklyanin Representation

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    We investigate the Baxter equation for the Heisenberg spin model corresponding to a generalized BFKL equation describing composite states of n Reggeized gluons in the multi-color limit of QCD. The Sklyanin approach is used to find an unitary transformation from the impact parameter representation to the representation in which the wave function factorizes as a product of Baxter functions and a pseudo-vacuum state. We show that the solution of the Baxter equation is a meromorphic function with poles (lambda - i r)^{-(n-1)} (r= 0, 1,...) and that the intercept for the composite Reggeon states is expressed through the behavior of the Baxter function around the pole at lambda = i . The absence of pole singularities in the two complex dimensional lambda-plane for the bilinear combination of holomorphic and anti-holomorphic Baxter functions leads to the quantization of the integrals of motion because the holomorphic energy should be the same for all independent Baxter functions.Comment: LaTex, 48 pages, 1 .ps figure, to appear in Phys. Rev.

    Separation of variables for the quantum SL(2,R) spin chain

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    We construct representation of the Separated Variables (SoV) for the quantum SL(2,R) Heisenberg closed spin chain and obtain the integral representation for the eigenfunctions of the model. We calculate explicitly the Sklyanin measure defining the scalar product in the SoV representation and demonstrate that the language of Feynman diagrams is extremely useful in establishing various properties of the model. The kernel of the unitary transformation to the SoV representation is described by the same "pyramid diagram" as appeared before in the SoV representation for the SL(2,C) spin magnet. We argue that this kernel is given by the product of the Baxter Q-operators projected onto a special reference state.Comment: 26 pages, Latex style, 9 figures. References corrected, minor stylistic changes, version to be publishe

    From finite geometry exact quantities to (elliptic) scattering amplitudes for spin chains: the 1/2-XYZ

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    Initially, we derive a nonlinear integral equation for the vacuum counting function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus paralleling similar results by Kl\"umper \cite{KLU}, achieved through a different technique in the {\it antiferroelectric regime}. In terms of the counting function we obtain the usual physical quantities, like the energy and the transfer matrix (eigenvalues). Then, we introduce a double scaling limit which appears to describe the sine-Gordon theory on cylindrical geometry, so generalising famous results in the plane by Luther \cite{LUT} and Johnson et al. \cite{JKM}. Furthermore, after extending the nonlinear integral equation to excitations, we derive scattering amplitudes involving solitons/antisolitons first, and bound states later. The latter case comes out as manifestly related to the Deformed Virasoro Algebra of Shiraishi et al. \cite{SKAO}. Although this nonlinear integral equations framework was contrived to deal with finite geometries, we prove it to be effective for discovering or rediscovering S-matrices. As a particular example, we prove that this unique model furnishes explicitly two S-matrices, proposed respectively by Zamolodchikov \cite{ZAMe} and Lukyanov-Mussardo-Penati \cite{LUK, MP} as plausible scattering description of unknown integrable field theories.Comment: Article, 41 pages, Late
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