Prediction problem in quantum mechanics is intractable (NP-Hard)

It is proved that both the prediction problem and the problem of reconstructing the state from the observations in quantum mechanics are NP-hard.     

Some new topological cardinal inequalities

In this paper we make use of the Pol-Šapirovski?'s technique to prove several cardinal inequalities, which generalize other well-known inequalities.     

An elementary proof of the uniqueness of invariant product measures for some infinite dimensional processesUne preuve élémentaire de l'unicité des mesures invariantes produits pour certains processus en dimension infinie

Consider an infinite dimensional diffusion process with state space , where T is the circle, and defined by an infinitesimal generator L which acts on local functions f as . Suppose that the coefficients a_i and b_i are smooth, bounded, of finite range, have uniformly bounded second order partial derivatives, that a_i are uniformly bounded from below by some strictly positive constant, and that a_i is a function only of η_i. Suppose that there is a product measure ν which is invariant. Then if ν is the Lebesgue measure or if d=1,2, it is the unique invariant measure. Furthermore, if ν is translation invariant, it is the unique invariant, translation invariant measure. The proofs are elementary. Similar results can be proved in the context of an interacting particle system with state space , with uniformly positive bounded flip rates which are finite range. To cite this article: A.F. Ram??rez, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 139–144     

Microperforated insertion units: An alternative strategy to design microperforated panels

Microperforated panels (MPPs) coupled to a rigid wall have been proposed recently as an alternative to porous absorbers in situations having concerns with bacterial contamination and small particles discharge, like food, pharmaceutical and microelectronic industries. There exists also an increasing interest for MPP absorbers in the transportation industry and civil engineering. In general, an optimally designed MPP with good broadband absorption requires many submillimetric holes distributed over a panel of also submillimetric thickness. Such thin plates or foils become so fragile that they need to be protected from mechanical damage. In this paper, an alternative strategy is investigated which allows the design of MPPs with panels of millimetric thickness while maintaining their acoustic performance. These absorbers, named microperforated insertion units (MIUs), avoid the structural problems of the classical MPPs. An assessment of the sound absorption properties of these structures is presented. Comparisons between calculations and measurements are also made under two experimental conditions: plane waves at normal incidence (impedance tube) and free field (anechoic room).     

Preparation and Characterization of Compositions Based on PbO-MgO-Nb2O5 Using the Sol-Gel Method

Lead Magnesium Niobate, Pb(Mg_1/3Nb_2/3)O₃ (PMN), is an important relaxor ferroelectric material. A significant problem exists, however, in the preparation of this material: it is very difficult to prepare pure phase, without the presence of a pyrochlore impurity phase which degrades the dielectric properties. Depending on the processing conditions, the amount of pyrochlore phase varies.Considering the ternary diagram PbO-MgO-Nb₂O₅, different compositions have been prepared by a simple sol-gel method at room temperature using Pb(CH₃COO)₂, Mg(CH₃COO)₂, Nb(OC₂H₅)₅ as precursors. After the heat treatment, the samples obtained were analyzed by XRD and EPMA with the purpose of studying the compositions formed.From the analysis of these results, it seems to be that the appearance of pyrochlore can be related to the reactivity of the MgO and/or the presence of other phases of the binary system PbO-Nb₂O₅. An excess of Pb and Mg is necessary for compositions to be formed near the PMN. The control of the amount of these two elements is very important because an excess of MgO would lead to rich compositions in Mg as a secondary phase.