The complexification and degree of a semi-algebraic set

The complexification of a semi-algebraic set is the smallest complex algebraic set containing S. Let S be defined by s polynomials of degrees less than d. We prove that the geometric degree of the complexification is less than . Received: 9 January 1997; in final form: 11 August 2000 / Published online: 17 May 2001     

Analysis of a Poisson system with boundary conditions

We consider a class of problems originating from a Raman laser amplification model, for which the equations can be written as a Poisson system with boundary conditions. Once reformulated, this system becomes an integro-differential equation that we study here in some detail. In particular, we show the existence of a smooth solution under general assumptions, and prove its uniqueness for boundary values that are not too far apart. Eventually, we completely solve the question of uniqueness for systems of dimensions one and two. To cite this article: F. Castella et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Parametric Centers for Trigonometric Abel Equations

This article is devoted to one-dimensional perturbative theory on R × S ¹. There is a recursive formula for the successive obstructions to parametric center at any order of the perturbation parameter. The first obstruction is studied by means of complex analysis techniques. This extends to the trigonometric case what was done previously for the polynomial case (Israel J. Math. 142, 273–283, 2004). This article is dedicated to Professor Zhang Zhi-Fen on the occasion of her 80th Birthday     

The calculation of neutron self-shielding factors of a group of isolated resonances

The resonance neutron self-shielding factor, G _res, is required in neutron metrology and activation data analysis. In a previous paper, the authors have shown that a dimensionless variable can be introduced which converts the dependence of G _res on the physical and nuclear properties of the material samples into an universal curve, valid for the isolated resonances of any nuclide. This work presents a methodology based on the universal curve, which enables to calculate G _res for a group of isolated resonances by weighting its individual contributions. A good agreement was reached with results calculated by the MCNP code and with experimental values for Mo foils and wires. This revised version was published online in July 2006 with corrections to the Cover Date.     

光学系统光阑应用的实例

介绍了一种光学组合系统，通过构造光学系统虚拟的视场光阑实现人眼屈光度测量，它是光学系统光阑应用的生动实例.     

Fixed mesh approximation of ordinary differential equations with impulses

When trains of impulse controls are present on the right-hand side of a system of ordinary differential equations, the solution is no longer smooth and contains jumps which can accumulate at several points in the time interval. In technological and physical systems the sum of the absolute value of all the impulses is finite and hence the total variation of the solution is finite. So the solution at best belongs to the space BV of vector functions with bounded variation. Unless variable node methods are used, the loss of smoothness of the solution would a priori make higher-order methods over a fixed mesh inactractive. Indeed in general the order of -convergence is and the nodal rate is . However in the linear case -convergence rate remains but the nodal rate can go up to by using one-step or multistep scheme with a nodal rate up to when the solution belongs to . Proofs are given of error estimates and several numerical experiments confirm the optimality of the estimates. Received March 15, 1996 / Revised version received January 3, 1997     

饲料中微量无机砷测定方法的研究

本文提出了用活性炭吸附分离饲料中有机砷化合物的新方法。，有机砷化合物经分离后用ＤＤＴＣ－Ａｇ比色测定１０＾－６级的无机砷。本法操作简便、快速、其测定误差小于平均值的１５％。     

Infrared and Raman spectroscopic investigation of Eu3+-doped mono and Di-urethanesil hybrid siliceous materials

The general features of two series of sol-gel derived materials, designatedurethanesils (Ut), have been investigated by infrared and Raman spectroscopies with the goal of elucidating the chemical environment of the Eu³⁺ cations. The host frameworks of the two families of ormolytes studied have been represented by m-Ut(350) and d-Ut(300), where m stands for mono, d stands for di, 350 and 300 are the average molecular weights of the organic precursors (poly(ethylene glycol) methyl ether, PEGME, and poly(ethylene glycol), PEG, respectively). The hybrid matrix of the mono-xerogels is composed by a siliceous backbone bonded by means of urethane linkages (-NHC (=O)O-) to pendant methyl end capped oligopolymer chains with approximately 7 oxyethylene units, whereas that of the di-xerogels is based on a siliceous network grafted through urethane groups to both ends of poly(oxyethylene) segments containing about 6 (OCH₂CH₂) repeat units. Both classes of materials have been doped with europium triflate (Eu(CF₃SO₃)₃). The doped samples have been identified by m-Ut(350)_nEu(CF₃SO₃)₃ and d-Ut(300)_nEu(CF₃SO₃), where n is the molar ratio of (OCH₂CH₂) repeat units per Eu³⁺ ion. Materials with n ranging from ∞ to 5 have been analyzed. The spectral data obtained provide evidence that the cations begin to coordinate to the ether oxygen atoms of the oligopolymer chains at n=40 in the mono-urethanesils and at n=10 in the di-urethanesils. In mono-urethanesils samples with n>40 and in di-urethanesils materials with n>10, the Eu³⁺ coordinate exclusively to the carbonyl oxygen atoms of the urethane linkages. Paper presented at the 8th EuroConference on Ionics, Carvoeiro, Algarve, Portugal, Sept. 16–22, 2001.