Extended equivariant Picard complexes and homogeneous spaces

Let k be a field of characteristic 0 and let X be a smooth geometrically integral k-variety. In our previous paper we defined the extended Picard complex UPic(X) as a certain complex of Galois modules in degrees 0 and 1. We computed the isomorphism class of UPic(G) in the derived category of Galois modules for a connected linear k-group G. In this paper we assume that X is a homogeneous space of a connected linear k-group G with geometric stabilizer H. We compute the isomorphism class of UPic(X) in the derived category of Galois modules in terms of the character groups of G and H. The proof is based on the notion of the extended equivariant Picard complex UPic_G(X) of a G-variety X.Comment: 32 pages. Final version, to appear in Transformation Group

Fuzzy Weighted Average: Analytical Solution

An algorithm is presented for the computation of analytical expressions for the extremal values of the α-cuts of the fuzzy weighted average, for triangular or trapeizoidal weights and attributes. Also, an algorithm for the computation of the inverses of these expressions is given, providing exact membership functions of the fuzzy weighted average. Up to now, only algorithms exist for the computation of the extremal values of the α-cuts for a fixed value of α. To illustrate the power of our algorithms, they are applied to several examples from the literature, providing exact membership functions in each case

Interacting solitary waves in a damped driven Lennard-Jones chain

It is shown analytically that pulse solitary waves in a chain with Lennard-Jones type nearest neighbor interaction are strongly localized and marginally stable in the high energy limit.\ud \ud In a damped and periodically driven chain we obtain numerically families of states whose behavior is similar to that of equally many oscillators. We observe a period doubling sequence in a one-solitary wave family and bifurcation to (quasi-) periodic motion in a family of two solitary waves. We conclude that the damped and driven chain admits asymptotically stable states living on a low-dimensional manifold in phase space. These results depend sensitively on the shape of the driving term

Period-doubling density waves in a chain

The authors consider a one-dimensional chain of N+2 identical particles with nearest-neighbour Lennard-Jones interaction and uniform friction. The chain is driven by a prescribed periodic motion of one end particle, with frequency v and 'strength' parameter alpha . The other end particle is held fixed. They demonstrate numerically that there is a region in the alpha -v plane where the chain has a stable state in which a density wave runs to and fro between the two ends of the chain, similarly to a ball bouncing between two walls. More importantly, they observe a period-doubling transition to chaos, for fixed v and increasing alpha , while the localised (solitary wave) character of the motion is preserve

Integrated 3D Sound Intensity Sensor with Four-Wire Particle Velocity Sensors

A new symmetrical four-wire sensor configuration has resulted in a fully integrated sound intensity sensor with significant lower noise floor and smaller size than its predecessors. An integrated sound pressure sensor was further miniaturized by using a folded "back chamber" at both sides of the chip.Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/handle/2042/16838