An Uq(sl(n)) invariant transfer matrix with periodic boundary conditions is analysed by means of the algebraic nested Bethe ansatz for the case of q being a root of unity. The transfer matrix corresponds to a 2-dimensional vertex model on a torus with topological interaction w.r.t. the 3-dimensional interior of the torus. By means of finite size analysis we find the central charge of the corres...

In this paper we prove that two global semianalytic subsets of a real analytic manifold of dimension two are separable if and only if there is no analytic component of the Zariski closure of the boundary which intersects the interior of one of the two sets and they are separable in a neighbourhood of each singular point of the boundary. We show also that, unlike in the algebraic case, the obstr...

In this paper we consider two types of dimension that can be defined for products of one-dimensional topologically totally transcendental (t.t.t) structures. The first is topological and considers the interior of projections of the set onto lower dimensional products. The second one is based on algebraic dependence. We show that these definitions are equivalent for ω-saturated one-dimensional t...

Kuratowski’s 14-set theorem says that in a topological space, 14 is the maximum possible number of distinct sets which can be generated from a fixed set by taking closures and complements. In this article we consider the analogous questions for any possible subcollection of the operations {closure, complement, interior, intersection, union}, and any number of initially given sets. We use the al...

In his 1986 article [Th2], W. Thurston proposed that one might approachMarden’s conjecture from a dynamical point of view via a study of limits in the natural deformation space: its interior consists of geometrically finite manifolds, and promoting their tameness to algebraic limits on the boundary has proven to be a successful strategy to address Marden’s conjecture in special cases. In this p...

We consider the solution of large-scale nonlinear algebraic Hermitian eigenproblems of the form T (λ)v = 0 that admit a variational characterization of eigenvalues. These problems arise in a variety of applications and are generalizations of linear Hermitian eigenproblems Av=λBv. In this paper, we propose a Preconditioned Locally Minimal Residual (PLMR) method for efficiently computing interior...

In this paper, a high order compact difference scheme and a multigrid method are proposed for solving two-dimensional (2D) elliptic problems with variable coefficients and interior/boundary layers on nonuniform grids. Firstly, the original equation is transformed from the physical domain (with a nonuniform mesh) to the computational domain (with a uniform mesh) by using a coordinate transformat...

An n-simplex is said to be n-well-centered if its circumcenter lies in its interior. We introduce several other geometric conditions and an algebraic condition that can be used to determine whether a simplex is n-well-centered. These conditions, together with some other observations, are used to describe restrictions on the local combinatorial structure of simplicial meshes in which every simpl...

We describe an affine transformation on the (CIE) color matching functions and map the spectral locus as a circle. We then homogenize the right circular cylinder erected by the circle, with respect to a normalizing plane and develop an analytical equation to the chromaticity cone, for the spectral colors. In the interior of the (CIE) chromaticity diagram, by homogenizing elliptic cylinders with...