Zero weights and non-zero slacks: Different solutions to the same problem

This paper re-assesses three independently developed approaches that are aimed at solving the problem of zero-weights or non-zero slacks in Data Envelopment Analysis (DEA). The methods are weights restricted, non-radial and extended facet DEA models. Weights restricted DEA models are dual to envelopment DEA models with restrictions on the dual variables (DEA weights) aimed at avoiding zero values for those weights; non-radial DEA models are envelopment models which avoid non-zero slacks in the input-output constraints. Finally, extended facet DEA models recognize that only projections on facets of full dimension correspond to well defined rates of substitution/transformation between all inputs/outputs which in turn correspond to non-zero weights in the multiplier version of the DEA model. We demonstrate how these methods are equivalent, not only in their aim but also in the solutions they yield. In addition, we show that the aforementioned methods modify the production frontier by extending existing facets or creating unobserved facets. Further we propose a new approach that uses weight restrictions to extend existing facets. This approach has some advantages in computational terms, because extended facet models normally make use of mixed integer programming models, which are computationally demanding.     

Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

Category with a natural cone

Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples are given. We point out that the main results of this paper were already stated in [3], and the purpose of this article is to give full details of the foregoing.     

The LPCTrap experiment: measurement of the β–ν angular correlation in 6He using a transparent Paul trap

We report on the status of the LPCTrap experiment, devoted to measure the β–ν angular correlation in the pure Gamow–Teller decay of ⁶He. This measurement is motivated by the search for the presence of tensor type contributions to the weak interaction. The ⁶He ions are confined in a novel transparent Paul trap. The β particles and the recoil ions are detected in coincidence to deduce the angular correlation parameter. The commissioning run performed in 2005 has given the proof of principle of this experiment. Up to 10⁵ coincidences were recorded during a second run in 2006.     

A polar macroporous sorbent for gas chromatography

Summary The gas chromatographic behaviour of crosslinked macroporous 2-hydroxyethyl methacrylate grafted with 2-methyloxazoline was investigated and the range of applicability of the copolymer was assessed. Retention index values were measured on this copolymer and compared with those obtained on the terpolymer 2-hydroxyethyl methacrylate-ethylene dimethacrylate-acrylonitrile. Rohrschneider constants and efficiency data for selected sorbates are given. The use of this type of polymer in the separation of various types of compounds is documented by various examples.     

Equilibrium States in the Quadruple–Kerr Solution

The extended quadruple–Kerr metric is used to consider equilibrium states of four collinear Kerr particles. We explain our previous failure to solve numerically the full set of the balance equations, and we derive a self–consistent system of the axis conditions leading to the equilibrium of all four constituents which can be black holes or hyperextreme objects. The equilibrium configurations obtained in this paper exhibit similar features with those occurring in the systems of two Kerr particles, for instance, the balance of four Kerr black holes with positive masses does not seem possible. Equilibrium states of two identical compound Kerr objects are also discussed.     

JET: Preparing the future in fusion

JET (Joint European Torus) is the largest tokamak in the world and the only fusion facility able to operate with Tritium, the fusion fuel, and Beryllium, the ITER first wall material. JET also features the most complete remote handling equipment for invessel maintenance. As a multinational research center, JET provides logistic experience in preparing for operation of the global facility, tokamak ITER.Experiments on JET are focused on ITER-relevant studies, in particular on detailing the operational scenarios (EL My H-modes and advanced regimes), on enhancing the heating systems, on developing diagnostics for burning plasmas etc. Pioneering real-time control techniques have been implemented that maximize performance and minimize internal disturbances of JET plasmas. In helium plasmas, ion cyclotron heating (ICRH) created fast α-particles, mimicking their populations in future burning plasmas. The recent successful Trace Tritium campaign provided important new data on fuel transport. Current enhancements on JET include a new ITER-like ELM-resilient high power ICRH antenna (7 MW) and over twenty new diagnostics that will further extend the JET scientific capabilities and push the facility even closer to the ITER parameters.A special mention is given to the involvement of the fusion experts from Association EURATOM-IPP.CR, who have been actively participating in the collective use of JET facility for more than three years.     

Heuristic Rejection in Interval Global Optimization

Based on the investigation carried out in Ref. 1, this paper incorporates new studies about the properties of inclusion functions on subintervals while a branch-and-bound algorithm is solving global optimization problems. It is found that the relative place of the global minimum value within the inclusion function value of the objective function at the current interval indicates mostly whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a considerable amount of computation. Illustrative examples are discussed and an extended numerical study shows the advantages of the new approach.     

Magnetic phases in Mn<Subscript>1</Subscript>_<Subscript>x</Subscript>Fe<Subscript>x</Subscript>WO<Subscript>4</Subscript> studied by neutron powder diffraction

The magnetic structures of Mn_1-xFe_xWO₄ with x = 0.0, 0.16, 0.21, 0.225, 0.232, 0.24, 0.27, 0.29, and 1.0 were refined from neutron powder diffraction data. The magnetic phase diagram could be completed in the coexistence range of different magnetic structures up to x = 0.29. For the magnetic state at 1.5 K a commensurate antiferromagnetic structure with a propagation vector = (±1/4, 1/2, 1/2) was found for x ⩽ 0.22 while the magnetic spins order with = (1/2, 0, 0) for x ≥ 0.22. In the latter phase, additionally, weak magnetic reflections indexed to an incommensurate ordering with = (- 0.214, 1/2, 0.457) occur in the diffraction pattern up to x = 0.29 indicating the occurence of a reentrant phase. For 0.12 ⩽ x ⩽ 0.29 the low temperature phases are separated from a magnetic high temperature phase showing only magnetic reflections indexed to a spin arrangement with = (1/2, 0, 0). The magnetic phase diagram is discussed qualitatively considering random superexchange between the statistically distributed Mn²⁺- and Fe²⁺-ions in the coexistence range 0.12 ⩽ x ⩽ 0.29 of different magnetic structures related to those of pure MnWO₄ and FeWO₄. Received 9 October 2002 Published online 14 March 2003     

Equivalence between mixed finite element and multi-point finite volume methods

We consider the lowest-order Raviart–Thomas mixed finite element method for elliptic problems on simplicial meshes in two or three space dimensions. This method produces saddle-point type problems for scalar and flux unknowns. We show how to easily eliminate the flux unknowns, which implies an equivalence between this method and a particular multi-point finite volume scheme, without any approximate numerical integration. We describe the stencil of the final matrix and give sufficient conditions for its symmetry and positive definiteness. We present a numerical example illustrating the performance of the proposed method. To cite this article: M. Vohralík, C. R. Acad. Sci. Paris, Ser. I 339 (2004).