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.     

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.     

Application of the Wavelet Multi-resolution Analysis and Hilbert transform for the prediction of gear tooth defects

In machine defect detection, namely those of gears, the major problem is isolating the defect signature from the measured signal, especially where there is significant background noise or multiple machine components. This article presents a method of gear defect detection based on the combination of Wavelet Multi-resolution Analysis and the Hilbert transform. The pairing of these techniques allows simultaneous filtering and denoising, along with the possibility of detecting transitory phenomena, as well as a demodulation. This paper presents a numerical simulation of the requisite mathematical model followed by its experimental application of acceleration signals measured on defective gears on a laboratory test rig. Signals were collected under various gear operating conditions, including defect size, rotational speed, and frequency bandwidth. The proposed method compares favourably to commonly used analysis tools, with the advantage of enabling defect frequency isolation, thereby allowing detection of even small or combined defects.     

Effect of radial flow in the die entrance region on gross melt fracture of PDMS extrudate

The gross melt fracture defect is related to the flow instabilities developed in the contraction region. To mitigate these upstream instabilities, a convergent radial flow in the die entrance has been created. In fact, the ultimate objective of the present work is to examine the effect of the clearance width of radial flow on the appearance and development of gross melt fracture defect. So, capillary rheometer experiments were performed with linear polydimethylsiloxane (PDMS) oil.As for the influence of radial flow width on the morphology of gross melt fracture defect, extrudate photographs show that this imperfection can be mitigated since its frequency is higher and amplitude smaller when the gap of radial flow decreases. Such results may be related both to shear and elongational components of radial flow. Actually, when gap width is very small compared to the external diameter of radial flow, shear deformations become more enhanced with respect to the elongational deformations and thus the helical gross melt fracture becomes more like a surface defect than volume defect.