Orthogonal and symplectic Yangians and Yang-Baxter R-operators

Yang-Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalised L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.Comment: 24 page

Estimates for capacity and discrepancy of convex surfaces in sieve-like domains with an application to homogenization

We consider the intersection of a convex surface Gamma with a periodic perforation of R-d, which looks like a sieve, given by T epsilon = boolean OR(d)(k is an element of Z) {epsilon k + a epsilon T} where T is a given compact set and a epsilon << epsilon is the size of the perforation in the epsilon-cell (0, epsilon)(d) subset of R-d. When epsilon tends to zero we establish uniform estimates for p- capacity, 1 < p < d, of the set Gamma n T-epsilon. Additionally, we prove that the intersections Gamma boolean AND {epsilon k + a(epsilon)T}(k) are uniformly distributed over Gamma and give estimates for the discrepancy of the distribution. As an application we show that the thin obstacle problem with the obstacle defined on the intersection of Gamma and the perforations, in a given bounded domain, is homogenizable when p < 1+ d/4. This result is new even for the classical Laplace operator

Integrable XYZ Model with Staggered Anisotropy Parameter

We apply to the XYZ model the technique of construction of integrable models with staggered parameters, presented recently for the XXZ case. The solution of modified Yang-Baxter equations is found and the corresponding integrable zig-zag ladder Hamiltonian is calculated. The result is coinciding with the XXZ case in the appropriate limit.Comment: 8 pages ; epic packag

The geometry of solutions to a segregation problem for nondivergence systems

The geometry of solutions to a segregation problem for non-divergence systems. Fixe

Structural results on convexity relative to cost functions

Mass transportation problems appear in various areas of mathematics, their solutions involving cost convex potentials. Fenchel duality also represents an important concept for a wide variety of optimization problems, both from the theoretical and the computational viewpoints. We drew a parallel to the classical theory of convex functions by investigating the cost convexity and its connections with the usual convexity. We give a generalization of Jensen's inequality for cost convex functions.Comment: 10 page

Mid Holocene vegetation reconstruction from Vanevan peat (south-eastern shore of Lake Sevan, Armenia)

International audienceA sediment core has been retrieved from Vanevan peat (south-eastern shore of Lake Sevan, Armenia), which is today disconnected from Lake Sevan thanks to an artificial shallowing of the lake. Based on 5 radiocarbon dates, Vanevan record covers the Mid Holocene (from ca. 7800 to ca. 5100 cal. BP). The Late Holocene is today absent in the peat stratigraphy due to modern peat exploitation by surface mining. This study focuses on a multi-proxy approach including pollen, charcoals, and pollen-inferred climate reconstruction. An open-land, steppic vegetation is recorded up to ca. 7700 cal. BP, followed by a more forested landscape during the Mid Holocene (up to ca. 5700 cal. BP), and ending again with an open-land vegetation (to the end of record, 5100 cal. BP). This vegetation dynamics responds to general climate changes documented in the Near East. Whether human activities are documented since ca. 7500 cal. BP (Late Neolithic) in Vanevan, they remain marginal and probably did not affect the area. Early Holocene dry climate, which caused the steppic environment to be widespread through the Near East, is strongly related to low late spring precipitation (PMay–Jun = 180 mm). Mid Holocene forested landscape and increasing lake-level seem related to late spring precipitation (+28%), which is the main change in estimated climate parameters. This has to be linked with reinforcement of the Westerlies and less active Siberian High, which are inversely involved in the following, dry phase starting at ca. 5700 cal. B

Factorization of R-matrix and Baxter's Q-operator

The general rational solution of the Yang-Baxter equation with the symmetry algebra sl(2) can be represented as the product of the simpler building blocks denoted as R-operators. The R-operators are constructed explicitly and have simple structure. Using the R-operators we construct the two-parametric Baxter's Q-operator for the generic inhomogeneous periodic XXX spin chain. In the case of homogeneous XXX spin chain it is possible to reduce the general Q-operator to the much simpler one-parametric operator.Comment: 17 page

Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions

The main result of this paper concerns the behavior of a free boundary arising from a minimization problem, close to the fixed boundary in two dimensions