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.     

Impact of photodepletion to amplified spontaneous emission of proton-transfer dyes in polymeric matrices

A six level rate equation system was used to investigate the impact of photodepletion to amplified spontaneous emission (ASE) of intramolecular proton-transfer (IPT) dyes incorporated into polymeric hosts. The model includes the most important transitions for the normal and tautomer form of the molecule as well as intersystem crossing and triplet–triplet transitions. The experimentally observed pulse shape as well as photodepletion phenomena, i.e. a first order exponential decay of the ASE intensity and a shortening in ASE pulse width, have been simulated successfully. Additionally, the model was used to propose an explanation of the unexpected high photodepletion of proton-transfer dyes in solids. The results show that the emission cross section and reabsorption cross section of the tautomer form of the molecule are the most important parameter not only for efficiency but also for photodepletion. The model was tested by comparison with experimental results of 2-(2’-hydroxyphenyl)benzimidazole in polymethylmethacrylate (PMMA), polystyrene (PS) and a 1:1 alternating copolymer matrix PS-co-PMMA. PACS 78.45.th; 42.55.Mv; 42.70.Jk     

Maximizing revenue in the airline industry under one-way pricing

The paper describes a methodology that has been implemented in a major British airline to find the optimal price to charge for airline tickets under one-way pricing. An analytical model has been developed to describe the buying behaviour of customers for flights over the selling period. Using this model and a standard analytical method for constrained optimization, we can find an expression for the optimal price structure for a flight. The expected number of bookings made on each day of the selling period and in each fare class given these prices can then be easily calculated. A simulation model is used to find the confidence ranges on the numbers of bookings and these ranges can be used to regulate the sale of tickets. A procedure to update the price structure based on the remaining capacity has also been developed.     

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).