Evaluation of optical propagation and radiation in optical waveguide using a numerical method

We introduce a mathematical model based on a concept of intrinsic mode in order to analyse and synthesise optical wave propagation and radiation occurring in a non-uniform optical waveguide used in integrated optics as optical coupler. The model is based on numerical evaluation of electromagnetic wave by applying an intrinsic field integral to evaluate the field behaviour inside the optical waveguide. To analyse the field distribution inside the non-uniform waveguide and predict the beam propagation of optical energy involved in the propagation process, it is necessary to track the motion of any observation point along the tapered waveguide itself. Physically, the rays of the spectrum undergo reflections on the waveguide boundaries until the cut-off occurs and the phenomena of radiation begin. The numerical results show good agreement with those obtained by classical methods of evaluation used bv other works.     

Direct Evidence for Intermolecular Oxidative Addition of σ(SiSi) Bonds to Gold

Oxidative addition plays a major role in transition‐metal catalysis, but this elementary step remains very elusive in gold chemistry. It is now revealed that in the presence of GaCl₃, phosphine gold chlorides promote the oxidative addition of disilanes at low temperature. The ensuing bis(silyl) gold(III) complexes were characterized by quantitative ³¹P and ²⁹Si NMR spectroscopy. Their structures (distorted Y shape) and the reaction profile of σ(Si? Si) bond activation were analyzed by DFT calculations. These results provide evidence for the intermolecular oxidative addition of σ(Si? Si) bonds to gold and open promising perspectives for the development of new gold‐catalyzed redox transformations.     

Enhanced π‐Backdonation from Gold(I): Isolation of Original Carbonyl and Carbene Complexes

The specific electronic properties of bent o‐carborane diphosphine gold(I) fragments were exploited to obtain the first classical carbonyl complex of gold [(DPCb)AuCO]⁺ (ν(CO)=2143 cm^?1) and the diphenylcarbene complex [(DPCb)Au(CPh₂)]⁺, which is stabilized by the gold fragment rather than the carbene substituents. These two complexes were characterized by spectroscopic and crystallographic means. The [(DPCb)Au]⁺ fragment plays a major role in their stability, as substantiated by DFT calculations. The bending induced by the diphosphine ligand substantially enhances π‐backdonation and thereby allows the isolation of carbonyl and carbene complexes featuring significant π‐bond character.     

Analytical model for thermal resistance due to multiple moving circular contacts on a coated bodyModèle analytique pour la résistance thermique due à des contacts circulaires mobiles multiples à la surface d'un solide revêtu

The heat transfer at the interface of two solids in sliding/rolling contact depends on the constriction phenomenon which occurs at the vicinity of asperities. In order to study this problem, the micro-contacts are represented by multiple moving circular heat sources on the surface of a body. The studied body is constituted of a substrate and a surface coating. The thermal constriction resistance due to those contacts is determined analytically in this paper. The solution is developed by using the integral Fourier transforms, and it is valid regardless of the velocity and the relative contact size values. To cite this article: A. Baïri, C. R. Mecanique 331 (2003).     

Dirichlet product for boolean functions

Boolean functions play an important role in many symmetric cryptosystems and are crucial for their security. It is important to design boolean functions with reliable cryptographic properties such as balancedness and nonlinearity. Most of these properties are based on specific structures such as Möbius transform and Algebraic Normal Form. In this paper, we introduce the notion of Dirichlet product and use it to study the arithmetical properties of boolean functions. We show that, with the Dirichlet product, the set of boolean functions is an Abelian monoid with interesting algebraic structure. In addition, we apply the Dirichlet product to the sub-family of coincident functions and exhibit many properties satisfied by such functions.     

Matched asymptotic expansions for the determination of the electromagnetic field near the edge of a patch antenna

We consider a simple but representative model incorporating the main behavior of the electromagnetic field near the edge of a patch antenna. Recall that this kind of antenna is obtained by a metal patch laying on a dielectric substrate covering a ground metallic plane. The functioning principle of such an electric device is based on the matching of an N-dimensional behavior of the field outside the antenna with an (N-1)-dimensional one inside the zone limited by the patch and the ground plane, N = 3 or 2 according to the considered model. In this study, we make use of the technique of matched asymptotic expansions and computation of singularities to describe this behavior for the two-dimensional case. Proved error estimates enable us to give a rigorous background to the underlying asymptotic analysis. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On a Conjecture of Erdos on 3-Powerful Numbers

A conjecture of P. Erdös says that the diophantine equationx+y = z has infinitely many solutions with (x,y) = 1 and suchthat if a prime p divides xyz, then p³ divides xyz. In thispaper, we give a proof of this conjecture.