UtilisatIon D’un Processus de Renormalisation Pour L’étude Électromagnétique des Structures Fractales Bidimensionnelles

In this article, we apply the renormalization technique, used possibly in theorical physics, for electromagnetic studying of bi dimensional fractal structures. A recurrence relation based on the auto-similar nature of structures and on the model of the surface impedance, has permitted, thanks to the convergence to a fixed point, to determine the input impedance of these structures at any scale. Though, the suggested method has been validated by calculus of one-dimensional structures (Iris de Cantor) it may be applied easily to the analysis of planar circuits as the Sierpensky antenna.     

Determination of Chromium (VI) in Airborne Particulate Matter by Electrothermal Atomic Absorption Spectrometry

Hexavalent chromium Cr(VI) is a well-established carcinogen associated with lung, nasal, and sinus cancer. Cr(VI) threshold limit values in workroom air have been recently lowered. Consequently, the currently available analytical methods are insufficiently sensitive or high cost. In this paper, a simple, cost-effective, sensitive, and reproducible method using solid-phase extraction with electrothermal atomic absorption spectrometry for determination of hexavalent chromium in airborne samples is reported. The method validation included selectivity, linearity, accuracy, and precision. Interferences from other ions likely to be present in airborne samples, including trivalent chromium, were tested and selectivity was demonstrated. The detection and quantification limits were, respectively, as low as 0.1 and 0.4?µg?L^?1. The linearity ranged from 0.5 to 50.0?µg?L^?1, with a regression coefficients exceeding 0.998. The extraction recovery exceeded 98%. The developed method was successfully compared with a reference spectrophotometric method. The performances achieved were similar to ion chromatography and high-performance liquid chromatography approaches. The novel method was tested on airborne samples collected from the workplace. The method’s performance suggests that it may be an alternative to high-cost techniques for monitoring occupational exposure to hexavalent chromium.     

Syntheses of new benzoxazole derivatives

2‐(Arylidene)cyanomethylbenzoxazoles have been prepared in water from benzoxazole‐2‐ylacetonitriles. Using multi‐component reactions, a variety of heterocycles containing benzoxazole and nitrile functionality has been prepared. J. Heterocyclic Chem., (2011).     

On the theory of periodic solution for some nondensely nonautonomous delayed partial differential equations

We first study the Massera problem for the existence of a τ?periodic solution for some nondensely defined partial differential equation, where the autonomous linear part satisfies the Hille‐Yosida condition and the delayed nonlinear part satisfies a locally Lipschitz condition. Second, inspired by an existing study, we prove in the dichotomic case, for τ=1, the existence‐uniqueness and conditional stability of the periodic solution. Moreover, we show the existence of a local stable manifold around such solution. Our theoretical results are finally illustrated by an application.     

A design for testability approach for nano-CMOS analogue integrated circuits

Dependability requirements must be considered from the beginning when designing safety-critical systems. Therefore, testing should even be considered earlier, intertwined with the design process. The process of designing for better testability is called design for testability (DfT). This article presents two designs for testability and fault diagnosis techniques using a new design analogue checker circuit in order to improve the testability and the diagnosability of nano-CMOS (complementary metal oxide semiconductor) analogue circuits used in safety-critical applications based on the system-on-chip (SoC) approach design. The testing techniques presented in this work can be done during and after the system fabrication. The checker is implemented in full-custom 65 nm Complementary metal–oxide–semiconductor (CMOS) technology with low supply voltage and small-size capabilities. SPICE simulations of the post-layout extracted CMOS checker, which include all parasitic, are used to validate the technique and demonstrate the acceptable electrical behaviour of the checker.     

Study of electromagnetic waves diffraction by bi-dimensional fractal structures using the renormalization method

The analysis of fractal structures by conventional methods gets harder and harder when the number of length scales rises. In this study, we try to combine the renormalization method and the surface impedance model to help rigorous studying of electromagnetic diffraction of fractal structures at their final (infinitum) iteration. As an application, we applied the method to a couple of fractal structures: Cantor Iris 1D and 2D.     

Positive Harris recurrence and exponential ergodicity of the basic affine jump-diffusion

In this article, we find the transition densities of the basic affine jump-diffusion (BAJD), which has been introduced by Duffie and Gârleanu as an extension of the CIR model with jumps. We prove the positive Harris recurrence and exponential ergodicity of the BAJD. Furthermore, we prove that the unique invariant probability measure π of the BAJD is absolutely continuous with respect to the Lebesgue measure and we also derive a closed-form formula for the density function of π.