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.     

A mathematical model of the response of the semicircular canal and otolith to vestibular system rotation under gravity

A mathematical model of the system composed of two sensors, the semicircular canal and the sacculus, is suggested. The model is described by three lines of blocks, each line of which has the following structure: a biomechanical block, a mechanoelectrical transduction mechanism, and a block describing the hair cell ionic currents and membrane potential dynamics. The response of this system to various stimuli (head rotation under gravity and falling) is investigated. Identification of the model parameters was done with the experimental data obtained for the axolotl (Ambystoma tigrinum) at the Institute of Physiology, Autonomous University of Puebla, Mexico. Comparative analysis of the semicircular canal and sacculus membrane potentials is presented. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 7, pp. 207–220, 2005.     

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).     

The absolute configuration of peroxisomicines A1 and A2

Peroxisomicine A1 is a potentially antineoplastic compound isolated from the seeds of Karwinskia parvifolia. It is considered as a useful chemotype for the preparation of topoisomerase II targeted anticancer cells. Stereochemically, it is characterized by the presence of two stereocenters and a rotationally hindered and thus likewise stereogenic biaryl axis. In this contribution, the absolute configuration of peroxisomicine A1 and its epimer, peroxisomicine A2, was established by means of a five-step degradative procedure giving the respective R- and S-configured methyl 2-(2′-methyl-5′-oxotetrahydrofuryl)acetates. The configuration of the degradation product was obtained by means of optical rotation, ¹H NMR analysis using a chiral displacement reagent, and by experimental and quantum chemical circular dichroism (CD) investigations. Based on the results obtained here and considering our previous work on the relative configuration at centers versus axis of these compounds, peroxisomicine A1 resulted to be the P,3S,3′S-isomer and peroxisomicine A2 the P,3R,3′S-isomer.     

Direct and simultaneous spectrofluorometric determination of naproxen and salicylate in human serum assisted by chemometric analysis

A direct method for the simultaneous determination of naproxen and salicylate in human serum is reported, based on a combination of spectrofluorometric measurements with two multivariate calibration techniques: partial least-squares (PLS-1) and the novel net analyte preprocessing (NAP). The method is rapid, selective and sensitive, and is based on the measurement of the fluorescence spectra of NH₃ alkalinized whole human sera at the excitation wavelength of 315 nm. It can be applied within the ranges of concentrations 50-200 ng ml⁻¹ for naproxen and 100-300 ng ml⁻¹ for salicylate. The employed chemometric techniques have been compared on the basis of the statistical indicators for calibration and validation. Reproducibility and interference studies in abnormal sera have also been carried out.     

Determination of oxidized and reduced glutathione, by capillary zone electrophoresis, in Brassica juncea plants treated with copper and cadmium

A rapid method of capillary zone electrophoresis is described to determine the oxidized (GSSG) and reduced (GSH) form of glutathione in plant tissue. In order to separate both analytes in a fused-silica capillary, the pH and composition of the electrolyte solution were optimized. The electrolyte composition was 100 mmol/L, borate 25 mmol/L Tris, and 0.2% w/v metaphosphoric acid (MPA), pH 8.2. Some instrumental conditions used to run the samples were hydrostatic injection for 30 s, 30 kV applied voltage, and UV detection (185 nm) at 25 degrees C. Linearity and useful range obtained for the calibration curves were optimum, with correlation coefficients about 0.999 in the 0-120 micromol/L range. The migration time was highly reproducible, less than 5 min being afforded to run a sample. Electrolyte buffer and samples required a careful pH control for optimal separation of both analytes. This aspect constitutes a critical analytical step when acids are used in the procedure for sample preparation. Simultaneous analysis of GSH and GSSG may provide a useful tool for comparative studies of plants in order to select those species with a potential capacity for detoxification from toxic elements or those appearing promising from phytoremediation for these elements.