The Single Crystal Structures of the Copper Usovites Ba2CaCuV2F14 and Ba2CaCuCr2F14

The results of single crystal X‐ray structure determinations are reported for Ba₂CaCuV₂F₁₄ (a = 1383.6(3), b = 540.89(8), c = 1493.1(3) pm, β = 91.65(3)°) and Ba₂CaCuCr₂F₁₄ (a = 1381.1(5), b = 535.5(1), c = 1481.4(6) pm, β = 91,50(4)°), both isotypic with usovite (space group C2/c, Z = 4). The resulting average distances are V‐F: 193.8 pm, Cr‐F: 190.7 pm, and Cu‐F: 209.2 resp. 207.1 pm for the Jahn‐Teller elongated [CuF₆] octahedra. Within the cross‐linked double chains of octahedra F‐bridged trimers M‐Cu‐M, magnetically studied earlier, are confirmed and discussed.     

On the Identifiability of Minimal VARMA Representations

By studying the geometry of relevant Hilbert spaces, we give a characterization of the identifiable standard representations of multivariate ARMA models in terms of the autocovariance function.     

SOS: A Quantile Estimation Procedure for Dynamic Lot-sizing Problems

This paper reviews some of the current approaches available for computing the demand quantiles required to plan the procurement of items with stochastic non-stationary demands. The paper first describes the stochastic single-item lot-sizing problem considered and then presents a practical solution approach based on a dynamic lot-sizing model. Three methods available to compute demand quantiles are then reviewed and a new procedure based on smoothed order statistics (SOS) is proposed. Finally, the behaviour of these estimation methods, when used to solve single-item lot-sizing problems with non-stationary stochastic demands, is studied by simulation.     

Fluctuations of empirical means at low temperature for finite Markov chains with rare transitions in the general case

Summary. The integrated autocovariance and autocorrelation time are essential tools to understand the dynamical behavior of a Markov chain. We study here these two objects for Markov chains with rare transitions with no reversibility assumption. We give upper bounds for the autocovariance and the integrated autocorrelation time, as well as exponential equivalents at low temperature. We also link their slowest modes with the underline energy landscape under mild assumptions. Our proofs will be based on large deviation estimates coming from the theory of Wentzell and Freidlin and others [4, 3, 12], and on coupling arguments (see [6] for a review on the coupling method). Received 5 August 1996 / In revised form: 6 August 1997     

Variable space search for graph coloring

Let G=(V,E) be a graph with vertex set V and edge set E. The k-coloring problem is to assign a color (a number chosen in {1,…,k}) to each vertex of G so that no edge has both endpoints with the same color. We propose a new local search methodology, called Variable Space Search, which we apply to the k-coloring problem. The main idea is to consider several search spaces, with various neighborhoods and objective functions, and to move from one to another when the search is blocked at a local optimum in a given search space. The k-coloring problem is thus solved by combining different formulations of the problem which are not equivalent, in the sense that some constraints are possibly relaxed in one search space and always satisfied in another. We show that the proposed algorithm improves on every local search used independently (i.e., with a unique search space), and is competitive with the currently best coloring methods, which are complex hybrid evolutionary algorithms.     

The Dynamics of Stretchable Rods in the Inertial Case

Nonlinear amplitude equations for the near-threshold behavior of twisted extensible elastic rods under tension with inertial and dissipative dynamics are derived. In the inertial case localized solutions to the amplitude equations are derived and a linear stability criterion for the pulse solutions is obtained using the Hamiltonian formulation of the problem.