A family of orthonormal wavelet bases with dilation factor 4

In this paper, we study a method for the construction of orthonormal wavelet bases with dilation factor 4. More precisely, for any integer M>0, we construct an orthonormal scaling filter mM(ξ) that generates a mother scaling function ?M, associated with the dilation factor 4. The computation of the different coefficients of ²|mM(ξ)| is done by the use of a simple iterative method. Also, this work shows how this construction method provides us with a whole family of compactly supported orthonormal wavelet bases with arbitrary high regularity. A first estimate of α(M), the asymptotic regularity of ?M is given by α(M)∼0.25M. Examples are provided to illustrate the results of this work.     

Approximations in Sobolev spaces by prolate spheroidal wave functions

Recently, there is a growing interest in the spectral approximation by the Prolate Spheroidal Wave Functions (PSWFs) ${\psi }_{n,c},c>0$. This is due to the promising new contributions of these functions in various classical as well as emerging applications from Signal Processing, Geophysics, Numerical Analysis, etc. The PSWFs form a basis with remarkable properties not only for the space of band-limited functions with bandwidth c, but also for the Sobolev space $H^s([?1,1])$. The quality of the spectral approximation and the choice of the parameter c when approximating a function in $H^s([?1,1])$ by its truncated PSWFs series expansion, are the main issues. By considering a function $f\in H^s([?1,1])$ as the restriction to $[?1,1]$ of an almost time-limited and band-limited function, we try to give satisfactory answers to these two issues. Also, we illustrate the different results of this work by some numerical examples.     

Finite element method for the stress analysis of isotropic cylindrical helical spring

This paper presents an efficient two nodes finite element with six degrees of freedom per node, capable to model the total behaviour of a helical spring. The formulation, which includes the shear deformation effects, is based on the assumed forces hybrid approach. The resultant forces approximation verifies exactly the resultant equilibrium equations. The developed model proves its accuracy compared with other elements. This element permits to get the distribution of different stresses along the spring and through the wire surface by only one element.     

Detection of rolling bearing defects using discrete wavelet analysis

In the detection of bearing faults the so much desired objective remains the extraction of the defect vibratory signature from the measured signal in which immerses the random noise and other components of the machine. In this article a denoising method of the measured signals is presented. Based on the optimization of wavelet multiresolution analysis, it uses the kurtosis as an optimization and evaluation criterion, several parameters were then selected. The experimental results show the validity of this method within the detection of several defects simulated on ball bearings. The various configurations, in which the signals were measured, allow leading to optimum conditions of its application. The application of WMRA on filtered signals allows better results than its application on wide bands signals or a simple band pass filtering.     

The interactions of thiophene with polycrystalline UO2

We have studied the adsorption and desorption of thiophene on polycrystalline UO₂ as function of coverage, over the temperature range 100-640 K, using X-ray photoelectron spectroscopy (XPS), temperature programmed desorption (TPD) and electron stimulated desorption (ESD). Thiophene is found to adsorb molecularly on stoichiometric UO₂. C 1s and S 2p XPS spectra are measured at different thiophene exposures and at different temperatures; they show no evidence for the presence of dissociation fragments, confirming that thiophene adsorbs and desorbs molecularly on a polycrystalline stoichiometric UO₂ surface. The variation of the S 2p and C 1s intensity as function of exposure, together with ESD measurements of O⁺ as function of exposure, can be connected to the growth mode of a thiophene film on UO₂; the thiophene film converts from a flat-lying configuration to an inclined structure as coverage increases. The effects of X-rays, UV, and electron irradiation on thiophene films have been studied in two different coverage regimes, monolayer and multilayer. Irradiation leads to a modification of thiophene films, and appreciable concentrations of species stable to 640 K are present on the surface for both regimes. The XPS results suggest that irradiation induces polymerization and oligomerization, as well as formation of thiolates and dissociation fragments of thiophene. The adsorption and reactivity of thiophene on defective UO₂ surfaces have also been studied. The O vacancies and defects in the oxide surface cause cleavage of C-H and C-S bonds leading to the dissociation of thiophene at temperatures as low as 100 K. These results illustrate the important role played by O vacancies in the chemistry of thiophene over an oxide surface.     

Determination of traces of As,Cd, Cr,Hg, Mn,Ni, Sb,Se, Sn and Pb in human hair by triple quadrupole ICP-MS

With the wide range of metallic contaminants discharged in the environment, studying the human health requires a growing number of elements to be monitored in biological samples. Hair analysis has been suggested as a suitable tool for biomonitoring environmental and occupational exposure to toxic elements. This study describes a method for the determination of 10 trace elements in hair samples using ICP-QQQ-MS. Combining the power of the MS/MS high-energy Helium mode with the MS/MS O₂ mass-shift mode, the method offers great analytical performances with detection limits reaching 0.0014 µg g^?1 for As, 0.0016 µg g^?1 for Cd, 0.012 µg g^?1 for Cr, 0.0035 µg g^?1 for Hg, 0.0055 µg g^?1 for Mn, 0.10 µg g^?1 for Ni, 0.0012 µg g^?1 for Sb, 0.0083 µg g^?1 for Sn, 0.011 µg g^?1 for Se and Pb. The accuracy of the method was tested on a human hair ERM® certified reference material. Percent recoveries varied from 91.3% and 106.9% being always in the acceptance range of 90–110%. For all analysed elements, RSD% of repeatability ranged between 0.6% and 9.0% and those of intermediate precision did not exceed the limit of 20% being always lower than 10% (except for As). The proposed method was applied for the determination of trace elements in hair samples from 20 unexposed subjects. The geometric mean levels were as follows: Cr 0.28 µg g^?1, Mn 0.30 µg g^?1, Sn 1.04µg g^?1, Sb 0.07 µg g^?1, Hg 0.42 µg g^?1, As 0.02 µg g^?1, Cd 0.03 µg g^?1, Ni 0.51 µg g^?1, Se 0.45 µg g^?1 and Pb 1.83 µg g^?1. Element concentrations were in the same range with the reported data. The reported results may be useful for environmental exposure assessment or comparisons studies when establishing reference values of trace elements in exposed population.     

Electron stimulated desorption of anionic fragments from films of pure and electron-irradiated thiophene

The electron stimulated desorption (ESD) of anions is used to explore the effects of electron irradiation on a thiophene film and we report measurements for electron impact on multilayer thiophene condensed on a polycrystalline platinum substrate. Below 22 eV and at low electron dose, desorbed anions include H- (the dominant signal) as well as S-, CH2-, SH- and SCH2-. Yield functions show that anions are desorbed both by dissociative electron attachment (DEA) with resonances observed at 9.5, 11, and 16 eV, and for energies >13 eV, by dipolar dissociation (DD). An increase in the S- signal from electron irradiated (beam-damaged) thiophene films and the appearance of a new DEA resonance in the S- yield function at 6 eV are linked to rupture of the thiophene ring and the formation of sulfur-terminated products within the film. The threshold energy for ring rupture is 5 eV. The desorption of new anions such as C4H3S- (Thiophene-H)- is also observed from electron irradiated films and these likely arise from the decomposition of large radiation product molecules synthesized in the film. The yield functions of H-, S-, SH-, (Thiophene-H)-, and (Thiophene+H)- anions from irradiated thiophene films that have been annealed to 300 K, each exhibit a single resonant feature centered around 5.1 eV, suggesting that all signals derive from DEA to the same molecular radiation product. In contrast, only H- and S- are observed to desorb from films of 2-2-bithiophene and no resonance is seen below approximately 10 eV in the anion yield functions. These data suggest that electron irradiation causes formation of ring-opened oligomers, and that closed-ring or 'classical" oligomers, (similar to bithiophene) if formed, contribute little to the ESD of anions.     

Towards gas chromatography-mass spectrometry coupling protocols for both identifying and quantification essential oils of Thymus capitatus Hoff et Link

Essential oil of Thymus capitatus Hoff et Link is analysed by using four techniques: GC/pyrolyse/MS, GC/FID, electronic impact GC/MS (quadripole), and GC/MS (ion trap). Both major and trace components are analysed. The GC/pyrolyse/MS coupling provides reference to the exact mass compositions without any need of the previously purified references, neither for major or trace components. The comparison between this reference analysis and GC/FID shows that the FID response coefficients may vary by a mean 7% from one component to another. As it was expected, quadripole or ion trap response coefficients vary to a much greater extent (a mean 25%), although the two MS techniques response coefficients are first order consistent. We conclude that GC/MS coupling could be used not only as it is usual for reliable identifications, but also for a complete quantitative routine analysis of essential oils. Expected precision could be very similar to GC/FID precision provided correcting species by species the MS analysis by a mean value of the response coefficient measured for the MS 70 eV electronic impact ionisation technologies. The GC/pyrolyse/MS coupling is proposed as a relevant tool for analysing reference samples containing trace natural species that could not be purified.