On the identification of degenerate indices in the nonlinear complementarity problem with the proximal point algorithm

In this paper we focus on the problem of identifying the index sets P(x):=i|x_i>0, N(x):={i|F_i(x)>0 and C(x):=i|x_i=F_i(x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution.This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan.Mathematics Subject Classification (2000): 90C33, 65K10     

Lang maps and Harris’s conjecture

We show that any variety in characteristic 0 possesses a universal dominant rational map, which we callthe Lang map, to a variety of general type. We discuss a conjecture of J. Harris regarding the relation between rational points and Lang maps. Partially supported by NSF grant DMS-9503276.     

Chemical synthesis and electric properties of the conducting copolymer of aniline and o‐aminophenol

A copolymer, poly(aniline‐co‐o‐aminophenol), was prepared chemically by using ammonium peroxydisulfate as an oxidant. The monomer concentration ratio of o‐aminophenol to aniline strongly influences the copolymerization rate and properties of the copolymer. The optimum composition of a mixture for the chemical copolymerization consisted of 0.3 M aniline, 0.021 M o‐aminophenol, 0.42 M ammonium peroxydisulfate, and 2 M H₂SO₄. The result of cyclic voltammograms in a potential region of ?0.20 to 0.80 V (vs.SCE) indicates that the electrochemical activity of the copolymer prepared under the optimum condition is similar to that of polyaniline in more acid solutions. However, the copolymer still holds the good electrochemical activity until pH 11.0. Therefore, the pH dependence of the electrochemical property of the copolymer is improved, compared with poly(aniline‐co‐o‐aminophenol) prepared electrochemically, and is much better than that of polyaniline. The spectra of IR and ¹H NMR confirm that o‐aminophenol units are included in the copolymer chain, which play a key role in extending the usable pH region of the copolymer. The visible spectra of the copolymers show that a high concentration ratio of o‐aminophenol to aniline in a mixture inhibits the chain growth. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5573–5582, 2007     

An improved synthesis of isonitrosoacetanilides

A novel two-step synthesis of isonitrosoacetanilides [2-(hydroxyimino)-N-phenylacetamides] has been developed, involving the initial acylation of aniline derivatives with 2,2-diacetoxyacetyl chloride, followed by reaction with hydroxylamine hydrochloride. The method works equally well with a variety of different aniline derivatives, including those with poor aqueous solubility and those containing electron rich ortho-substituents, neither of which react well under traditional conditions.     

具有消息恢复的数字签名方案的一个注记

对具有消息恢复的数字签名方案提出了两种攻击方法.此外,对原方案进行了改进,通过对改进方案的安全性分析得出结论:改进方案比原方案更安全,并且消息恢复过程只需要计算一次大数模幂乘和两次单向函数.     

The solvable radical of Sylow factorizable groups

Let G be a finite group. A complete Sylow product of G is a product of Sylow subgroups of G, one for each prime divisor of |G|. We shall call G a Sylow factorizable group if it is equal to at least one of its complete Sylow products. We prove that if G is a Sylow factorizable group then the intersection of all complete Sylow products of G is equal to the solvable radical of G. We generalize the concepts and the result to Sylow products which involve an arbitrary subset of the prime divisors of |G|. Received: 26 January 2005     

Estimation effective de la perte de positivité dans la régularisation des courants

Let (X,ω) be a compact complex Hermitian manifold, and let T?γ be a d-closed (1,1) almost positive current on X. A variant of Demailly's regularization-of-currents theorem states that T is the weak limit of a sequence of (1,1)-currents T_m with analytic singularities of coefficient 1/m, lying in the same cohomology class as T, whose Lelong numbers converge to those of T, and with a loss of positivity decaying to zero. We prove that if the (1,1)-form γ is assumed to be closed and C^∞, the regularizing currents T_m can be chosen such that $\text{T}{}_{\mathrm{m}}\text{?γ?}\text{C}\text{m}$ for a constant C>0 independent of m. To cite this article: D. Popovici, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Mathematical modeling of two-photon thermal fields in laser–solid interaction

In this paper, we have developed an analytical model to study the temperature distributions in IR optical materials heated by laser pulses. Our model takes into account the two-photon absorption (TPA). The calculations are based on a three-dimensional model of heat diffusion in solids using the integral transform method. We find out the rigorous analytical expression of the thermal field when one considers both one- and two-photon absorption. The model is valid for any laser–solid system whose interaction can be described by the generalized Beer–Lambert law. Specific results are presented for an application of the model to ZnSe sample. We find out that TPA can produce detectable temperature variation.