Gaussian extended cubature formulae for polyharmonic functions

The purpose of this paper is to show certain links between univariate interpolation by algebraic polynomials and the representation of polyharmonic functions. This allows us to construct cubature formulae for multivariate functions having highest order of precision with respect to the class of polyharmonic functions. We obtain a Gauss type cubature formula that uses values of linear functionals (integrals over hyperspheres) and is exact for all -harmonic functions, and consequently, for all algebraic polynomials of variables of degree .

     

Auger electron spectroscopy depth profiling of Fe-oxide layers on electromagnetic sheets prepared by low temperature oxidation

Auger electron spectroscopy depth profiling was applied to characterize the Fe-oxide layers prepared by low temperature oxidation of Fe electromagnetic sheets produced on an industrial line for applications in the field of electrical motors. In addition the surface morphology, layer composition and layer structure were analysed by electron microscopy, energy dispersive X-ray spectroscopy and X-ray diffraction techniques. We found that the oxide layers on Fe-sheets with good adhesion between the oxide layer and Fe-substrate, consist mainly of magnetite and to a smaller extent of haematite; the layers are typically thinner than 1 μm and the interface between the oxide layer and the Fe-substrate is relatively broad, i.e. up to 0.3 μm. On the contrary, a decrease of adhesion between the oxide layer and the Fe-substrate was found when the layer is thicker than 1 μm and the layer/substrate interface is narrow and contaminated by foreign elements.     

Development and Validation of an LC–ESI-MS Ion-Trap Method for Analysis of Impurities in Transkarbam 12, a Novel Transdermal Accelerant

A new, sensitive LC–MS method for evaluation of the purity of Transkarbam 12 (T12), a novel and highly effective accelerant of transdermal penetration, has been developed and validated. T12 and its impurities (6-aminohexanoic acid, AH, ε-caprolactam, CA, and dodecyl 6-(6-aminohexanamido)hexanoate, DAH) were characterized by MS and MS–MS analysis. Separation was achieved on a 150 mm × 3 mm, 5-μm particle, phenyl–hexyl column. The mobile phase was a gradient prepared from water, formic acid, and acetonitrile. The method was validated within the concentration range 50–250 ng mL^?1; correlation coefficients were >0.998. The accuracy of the method was from 98.6–105.0% for AH, 102.6–104.8% for CA, and 97.9–100.9% for DAH. Precision was in the range 3.19–4.42% for AH, 3.22–5.81% for CA, and 4.8–8.78% for DAH. The selectivity of the method and sample stability were also confirmed. The practical applicability of the method was proven by analysis of T12 bulk substance.     

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Book reviews

     

General variable neighborhood search for the continuous optimization

We suggest a new heuristic for solving unconstrained continuous optimization problems. It is based on a generalized version of the variable neighborhood search metaheuristic. Different neighborhoods and distributions, induced from different metrics are ranked and used to get random points in the shaking step. We also propose VNS for solving constrained optimization problems. The constraints are handled using exterior point penalty functions within an algorithm that combines sequential and exact penalty transformations. The extensive computer analysis that includes the comparison with genetic algorithm and some other approaches on standard test functions are given. With our approach we obtain encouraging results.     

Measurement of safety factor using Hall probes on CASTOR tokamak

Hall sensors offer an attractive true non-inductive method of magnetic field measurements for fusion devices. However, there is only limited experience in using of these sensors in such demanding environment (high heat loads, radiation, and electromagnetic noise). Recently, a combined magnetic probe was developed for CASTOR tokamak, which contains 3 Hall sensors and 3 coils arranged to measure all three components of magnetic field approximately in a single point of space. The probe is compatible with in-vessel use well in confinement region of CASTOR. It is fully controlled by multi-functional electronic system that drives the Hall probes, amplifies their output signals, performs the A/D conversion and stores the measured data on PC. The bandwidth of the system is up to 200 kHz. Design of the system and its implementation on CASTOR is reviewed. Results obtained using this diagnostic on CASTOR tokamak is presented. Radial profile of the poloidal magnetic field is used to deduce radial profile of safety factor.     

Search for hadronic decays of a light Higgs boson in the radiative decay Υ→γA0

We search for hadronic decays of a light Higgs boson (A(0)) produced in radiative decays of an Υ(2S) or Υ(3S) meson, Υ→γA(0). The data have been recorded by the BABAR experiment at the Υ(3S) and Υ(2S) center-of-mass energies and include (121.3±1.2)×10(6) Υ(3S) and (98.3±0.9)×10(6) Υ(2S) mesons. No significant signal is observed. We set 90% confidence level upper limits on the product branching fractions B(Υ(nS)→γA(0))B(A(0)→hadrons) (n=2 or 3) that range from 1×10(-6) for an A(0) mass of 0.3 GeV/c(2) to 8×10(-5) at 7 GeV/c(2).     

Resonant States in High-Temperature Superconductors with Impurities

A microscopic theory of resonant states for the Zn-doped CuO₂ plane in the superconducting phase is formulated in the effective t–J model. In the model derived from the original p–d model, Zn impurities are considered as vacancies for the d states at Cu sites. In the superconducting phase, in addition to the local static perturbation induced by the vacancy, a dynamical perturbation appears that results in a frequency-dependent perturbation matrix. Using the T-matrix formalism for the Green's functions in terms of the Hubbard operators, we calculate the local density of electronic states with d, p, and s symmetries.