Identifications in modular group algebras

Let G be a group, S a subgroup of G, and F a field of characteristic p. We denote the augmentation ideal of the group algebra FG by ω(G). The Zassenhaus-Jennings-Lazard series of G is defined by D_n(G)=G∩(1+ωⁿ(G)). We give a constructive proof of a theorem of Quillen stating that the graded algebra associated with FG is isomorphic as an algebra to the enveloping algebra of the restricted Lie algebra associated with the D_n(G). We then extend a theorem of Jennings that provides a basis for the quotient ωⁿ(G)/ωⁿ⁺¹(G) in terms of a basis of the restricted Lie algebra associated with the D_n(G). We shall use these theorems to prove the main results of this paper. For G a finite p-group and n a positive integer, we prove that G∩(1+ω(G)ωⁿ(S))=D_n+1(S) and G∩(1+ω²(G)ωⁿ(S))=D_n+2(S)D_n+1(S∩D₂(G)). The analogous results for integral group rings of free groups have been previously obtained by Gruenberg, Hurley, and Sehgal.     

Response of periodic structures due to moving loadsRéponse de structures périodiques à des charges mobiles

A method is proposed to calculate the response of periodic structures subjected to moving loads. It is based on the Floquet decomposition which allows the restriction of the analysis for the overall system to a generic cell. The main contribution of the approach presented hereafter is that the response is directly deduced from transfer functions in the space-wavenumber domain calculated in an unbounded generic cell. Moreover, the equivalence of this new solution with the response of invariant structures obtained using Fourier transforms is established. To cite this article: H. Chebli et al., C. R. Mecanique 334 (2006).     

Effect of calcination temperature on the surface morphology and crystallinity of tungsten (VI) oxide nanorods prepared using colloidal gas aphrons method

The effect of calcination temperature on the surface morphology and crystallinity of tungsten (VI) oxide, WO₃ nanorods prepared using colloidal gas aphrons (CGAs) as template was studied. The synthesized WO₃ nanorods were calcined in a furnace for 4 h at four different temperatures, i.e., 400, 500, 600 and 700 °C. The morphology of the calcined WO₃ nanorods have been characterized by both transmission electron microscope (TEM) and variable pressure scanning electron microscope (SEM) equipped with energy dispersive X-ray analysis (EDAX). The results showed that the calcination temperature influenced the shape and size of the WO₃ nanorods produced. It is also found that the calcination at various temperature do not effect the composition and the purity of the WO₃ nanorods. In order to characterize the crystalinity of WO₃, X-ray diffraction (XRD) has been used. It shows that all the calcined WO₃ produced are in crystalline form compared to the as-prepared WO₃ nanorods, which is in amorphous form.     

On a Class of Quasilinear Elliptic Equations

We consider a class of quasilinear elliptic boundary problems, including the following Modified Nonlinear Schrödinger Equation as a special case: $$\begin{cases} ∆u+ \frac{1}{2} u∆(u^2)−V(x)u+|u|^{q−2}u=0 \ \ \ in \ Ω, \\u=0 \ \ \ \ \ \ \ ~ ~ ~ on \ ∂Ω, \end{cases}$$ where $Ω$ is the entire space $\mathbb{R}^N$ or $Ω ⊂ \mathbb{R}^N$ is a bounded domain with smooth boundary, $q∈(2,22^∗]$ with $2^∗=2N/(N−2)$ being the critical Sobolev exponent and $22^∗= 4N/(N−2).$ We review the general methods developed in the last twenty years or so for the studies of existence, multiplicity, nodal property of the solutions within this range of nonlinearity up to the new critical exponent $4N/(N−2),$ which is a unique feature for this class of problems. We also discuss some related and more general problems.     

Application of an Itô-based approximation method to random vibration of a pinching hysteretic system

In this paper, an extension of the Cumulant-Neglect closure scheme is utilized for the random vibration analysis of a single degree of freedom system with a general pinching hysteresis restoring force. The hysteresis element used in the system model can simulate commonly observed forms of stiffness, strength and pinching degradations. The second order statistics of the system response to a stationary Gaussian white noise input are derived using an Itô-based approximation technique. The validity of these response statistics are then verified by comparing them to Monte Carlo simulation results. The numerical studies performed for different combinations of degradation parameters and excitation levels show that the response estimates obtained by this solution method are in good agreement with Monte Carlo simulation. These studies also indicate the applicability of this technique for response analysis of complicated forms of non-linearities.     

Column preconcentration and electrothermal atomic absorption spectrometric determination of rhodium in some food and standard samples

In the present work, an electrothermal atomic absorption spectrometric method has been developed for the determination of ultra‐trace amounts of rhodium after adsorption of its 2‐(5‐bromo‐2‐pyridylazo)‐5‐diethylaminophenol/tetraphenylborate ion associated complex at the surface of alumina. Several factors affecting the extraction efficiency such as the pH, type of eluent, sample and eluent flow rates, sorption capacity of alumina and sample volume were investigated and optimized. The relative standard deviation for eight measurements of 0.1 ng/mL of rhodium was ±6.3%. In this method, the detection limit was 0.003 ng/mL in the original solution. The sorption capacity of alumina and the linear range for Rh(III) were evaluated as 0.8 mg/g and 0.015–0.45 ng/mL in the original solution, respectively. The proposed method was successfully applied for the extraction and determination of rhodium content in some food and standard samples with high recovery values.     

Nanostructured polypyrrole for automated and electrochemically controlled in-tube solid-phase microextraction of cationic nitrogen compounds

The authors describe an efficient method for microextraction and preconcentration of trace quantities of cationic nitrogen compounds, specifically of anilines. It relies on a combination of electrochemically controlled solid-phase microextraction and on-line in-tube solid-phase microextraction (SPME) using polypyrrole-coated capillaries. Nanostructured polypyrrole was electrically deposited on the inner surface of a stainless steel tube and used as the extraction phase. It also acts as a polypyrrole electrode that was used as a cation exchanger, and a platinum electrode that was used as the anode. The solution to be extracted is passed over the inner surface of the polypyrrole electrode, upon which cations are extracted by applying a negative potential under flow conditions. This method represents an ideal technique for SPME of protonated anilines because it is fast, easily automated, solvent-free, and inexpensive. Under optimal conditions, the limits of detection are in the 0.10–0.30 μg L‾¹ range. The method works in the 0.10 to 300 μg L‾¹ concentration range. The inter- and intra-assay precisions (RSD%; for n = 3) range from 5.1 to 7.5 % and from 4.7 to 6.0 % at the concentration levels of 2, 10 and 20 μg L‾¹, respectively. The EC-in-tube SPME method was successfully applied to the analysis of methyl-, 4-chloro-, 3-chloro and 3,4-dichloroanilines in (spiked) water samples.

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Electrochemically controlled in-tube solid phase microextraction

We report a new in-tube solid phase microextraction approach named electrochemically controlled in-tube solid phase microextraction (EC in-tube SPME). This approach, which combined electrochemistry and in-tube SPME, led to decrease in total analysis time and increase in sensitivity. At first, pyrrole was elctropolymerized on the inner surface of a stainless steel tube. Then, the polypyrrole (PPy)-coated in-tube SPME was coupled on-line to liquid chromatography (HPLC) to achieve automated in-tube SPME–HPLC analysis. After the completion of EC-in-tube SPME–HPLC setup, the PPy-coated tube was used as working electrode for uptake of diclofenac as target analyte. Extraction ability of the tube in presence and in absence of applied electrical field was investigated. It was found that, under the same extraction conditions, the extraction efficiency could be greatly enhanced by using the constant potential. Important factors are also optimized. The detection limit (S/N = 3) and precision were 0.1 μg L⁻¹ and 4.4%, respectively.     

In-tube magnetic solid phase microextraction of some fluoroquinolones based on the use of sodium dodecyl sulfate coated Fe3O4 nanoparticles packed tube

In-tube magnetic solid phase microextraction (in-tube MSPME) of fluoroquinolones from water and urine samples based on the use of sodium dodecyl sulfate (SDS) coated Fe₃O₄ nanoparticles packed tube has been reported. After the preparation of Fe₃O₄ nanoparticles (NPs) by a batch synthesis, these NPs were introduced into a stainless steel tube by a syringe and then a strong magnet was placed around the tube, so that the Fe₃O₄ NPs were remained in the tube and the tube was used in the in-tube SPME-HPLC/UV for the analysis of fluoroquinolones in water and urine samples. Plackett–Burman design was employed for screening the variables significantly affecting the extraction efficiency. Then, the significant factors were more investigated by Box–Behnken design. Calibration curves were linear (R² > 0.990) in the range of 0.1–1000 μg L⁻¹ for ciprofloxacin (CIP) and 0.5–500 μg L⁻¹ for enrofloxacin (ENR) and ofloxacin (OFL), respectively. LODs for all studied fluoroquinolones ranged from 0.01 to 0.05 μg L⁻¹. The main advantages of this method were rapid and easy automation and analysis, short extraction time, high sensitivity, possibility of fully sorbent collection after analysis, wide linear range and no need to organic solvents in extraction.