Towards a Eurasian Economic Union: the challenge of integration and unity. CEPS Special Report No. 75/December 2012

In the lead-up to the creation of a Eurasian Economic Union in 2015, the Customs Union and the Common Economic Space between Russia, Belarus and Kazakhstan represent two elements of the most ambitious regional integration project launched in the post-Soviet era since 1991. This CEPS Special Report examines both the potential and the limits of Eurasian economic integration. For the purpose of assessing the Eurasian integration process, CEPS applied a modified version of a framework first developed by Ernest B. Haas and Philippe C. Schmitter in 1964 to project whether economic integration of a group of countries automatically engenders political unity. Taking the data available for the early stages of the European integration process as a benchmark, the results for the Customs Union and the Common Economic Space point to a rather unfavourable outlook for Eurasian economic integration.

Unity as a unit

The arguments for regarding the number 1 as a unit of the SI are reviewed. Examples of dimensionless quantities are presented, and problems associated with representing the values of dimensionless quantities of very small magnitude are discussed. The logarithmic ratio units bel, decibel and neper are discussed.

Twofold adaptive partition of unity implicits

Partition of Unity Implicits (PUI) has been recently introduced for surface reconstruction from point clouds. In this work, we propose a PUI method that employs a set of well-observed solutions in order to produce geometrically pleasant results without requiring time consuming or mathematically overloaded computations. One feature of our technique is the use of multivariate orthogonal polynomials in the least-squares approximation, which allows the recursive refinement of the local fittings in terms of the degree of the polynomial. However, since the use of high-order approximations based only on the number of available points is not reliable, we introduce the concept of coverage domain. In addition, the method relies on the use of an algebraically defined triangulation to handle two important tasks in PUI: the spatial decomposition and an adaptive polygonization. As the spatial subdivision is based on tetrahedra, the generated mesh may present poorly-shaped triangles that are improved in this work by means a specific vertex displacement technique. Furthermore, we also address sharp features and raw data treatment. A further contribution is based on the PUI locality property that leads to an intuitive scheme for improving or repairing the surface by means of editing local functions.

The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.