Generalized differential spaces with dN=0d^N=0 and the qq-differential calculus

We present some results concerning the generalized homologies associated with nilpotent endomorphisms $d$ such that $d^N=0$ for some integer $N\geq 2$. We then introduce the notion of graded $q$-differential algebra and describe some examples. In particular we construct the $q$-analog of the simplicial differential on forms, the $q$-analog of the Hochschild differential and the $q$-analog of the universal differential envelope of an associative unital algebra.Comment: 8 pages, Latex2e, uses pb-diagram, available at http://qcd.th.u-psud.fr, to be published in the Proceedings of the 5th Colloquium ``Quantum Groups and Integrable Systems", Prague, June 199

Solving multi-criteria decision problems under possibilistic uncertainty using optimistic and pessimistic utilities

International audienceThis paper proposes a qualitative approach to solve multi-criteria decision making problems under possibilistic uncertainty. De-pending on the decision maker attitude with respect to uncertainty (i.e. optimistic or pessimistic) and on her attitude with respect to criteria (i.e. conjunctive or disjunctive), four ex-ante and four ex-post decision rules are dened and investigated. In particular, their coherence w.r.t. the principle of monotonicity, that allows Dynamic Programming is studied

Natural Orbitals and BEC in traps, a diffusion Monte Carlo analysis

We investigate the properties of hard core Bosons in harmonic traps over a wide range of densities. Bose-Einstein condensation is formulated using the one-body Density Matrix (OBDM) which is equally valid at low and high densities. The OBDM is calculated using diffusion Monte Carlo methods and it is diagonalized to obtain the "natural" single particle orbitals and their occupation, including the condensate fraction. At low Boson density, $na^3 < 10^{-5}$, where $n = N/V$ and $a$ is the hard core diameter, the condensate is localized at the center of the trap. As $na^3$ increases, the condensate moves to the edges of the trap. At high density it is localized at the edges of the trap. At $na^3 \leq 10^{-4}$ the Gross-Pitaevskii theory of the condensate describes the whole system within 1%. At $na^3 \approx 10^{-3}$ corrections are 3% to the GP energy but 30% to the Bogoliubov prediction of the condensate depletion. At $na^3 \gtrsim 10^{-2}$, mean field theory fails. At $na^3 \gtrsim 0.1$, the Bosons behave more like a liquid $^4$He droplet than a trapped Boson gas.Comment: 13 pages, 14 figures, submitted Phys. Rev.

Applying spatial reasoning to topographical data with a grounded geographical ontology

Grounding an ontology upon geographical data has been pro- posed as a method of handling the vagueness in the domain more effectively. In order to do this, we require methods of reasoning about the spatial relations between the regions within the data. This stage can be computationally expensive, as we require information on the location of points in relation to each other. This paper illustrates how using knowledge about regions allows us to reduce the computation required in an efficient and easy to understand manner. Further, we show how this system can be implemented in co-ordination with segmented data to reason abou

Quantum corrections to the ground state energy of a trapped Bose-Einstein condensate: A diffusion Monte Carlo calculation

The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, $n(0)a^3 \le 2 \cdot 10^{-3}$ [n(0): peak density, a: s-wave scattering length], our calculations confirm that the exact ground state energy for a sum of two-body interactions depends on only the atomic physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for N=2-50 particles in the trap with positive s-wave scattering length a=100-10000 a.u.. Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see e.g. E. Braaten and A. Nieto, Phys. Rev. B 56}, 14745 (1997)], leads to a greatly improved description of trapped Bose gases.Comment: 7 pages, 4 figure

MONOBOB II : Latest results of monocharged ions source for SPIRAL2 project

Original publication available at http://www.jacow.orgInternational audienceAmong the sources which can be installed in the radioactive ion production module of SPIRAL II, a singly-charged ECRIS has been chosen to produce ions from gaseous elements. Its characterization is under way on a test bench at GANIL. Extraction, transport and response time results are presented