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).     

Proton-exchanged optical waveguides fabricated by glutaric acid

In this paper, we first report that a new proton source, glutaric acid, has been used to fabricate optical waveguides in Z-cut lithium niobate crystals. The relationship was experimentally established between proton-exchanged (PE) waveguide parameters and fabrication conditions. It is shown that this new organic acid can be used to obtain deep PE waveguides in fast diffusion speed (0.275 μm²/h at 221°C) and with low loss (0.2 dB/cm). It provides an alternative approach for fabricating PE waveguides in lithium niobate substrate.     

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.     

Transmission of a Gaussian beam after incidenting nonnormally on a Fabry–Perot etalon: a nonresonant case

Under the nonresonant case where the carrier frequency of a Gaussian beam deviates from the resonant frequency of a Fabry–Perot etalon, the transmission of a Gaussian beam after incidenting nonnormally on a Fabry–Perot etalon has been investigated. The results show that under the nonresonant case, variations of the peak intensity, the position of the peak intensity and the spot size of the transmitted beam with the input angle behave differently and even with a reversed tendency compared with those obtained under the resonant case.     

The Synthesis of Glycoglycerolipids

A convenient synthetic route was developed for the synthesis of the novel glycolipids: 1,2-di-O-acyl-3-O-(2‘-acylamide-2‘-denxy-ct-D-glucopyranosyl)-sn-glycerols. 10 new compounds of glycolipids with different acyl groups were obtained.     

Simple Entanglement Measure for Multipartite Pure States

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.     

一种新化合物K2Ti8O15纳米线

钛酸钾晶须通常是直径和长度在微米量级的无机晶须 ,可用Ｋ2 Ｏ·ｎＴｉＯ2 表示其组成 ,ｎ =1,2 ,4 ,6 ,8,[1] .六钛酸钾晶须具有耐高温、耐腐蚀、纤维拉伸强度高、导热系数小、红外反射率高 ,硬度低的特点 .在民用及工业方面有很多应用 .如催化剂载体、离子吸附交换材料、高温过滤器、绝热材料、耐摩擦材料等[2～ 5] .钛酸钾纳米线的合成尚未见报道 .我们在用电弧产生的Ｎ2 等离子体热解焦油时 ,生成了一种直径 9～ 2 0ｎｍ长约几百纳米线 .Ｘ射线能谱定量分析表明这种纳米线化学组成为Ｋ2 Ｔｉ8Ｏ15,是一种新的非化学计量化合物 .试验装…     

Optical characterization of bromo-alkoxyl-substituted copper phthalocyanine derivative thin films

A series of thin films of copper phthalocyanine derivatives with bromine and alkoxyl substituents [CuPc(OC₈H₁₇)₄Br_m, m=0,1,2,4] were prepared on single-crystal silicon substrates by spin coating. The ellipsometric spectra of the films have been studied on a rotating analyzer–polarizer type of scanning ellipsometer. The optical, dielectric constants and absorption coefficients of the films in 500–800 nm wavelength region were obtained. The results show that the complex refractive index, dielectric constants and absorption coefficient of these thin films are influenced regularly by bromine substituent on conjugated macrocycle. It was found that there are approximately linear relationships between the resonance absorption wavelengths of the films and the average number of bromine atoms substituted on the phthalocyanine ring.     

A New Pathway to Synthesize Cyclomercurated Ferrocenylimines Containing Heterocyclic Ring

The cyclomercurated ferrocenylimines containing heterocyclic ring were prepared by the condensation of cyclomercuration of acylferrocene with the appropriate heterocyclic amine.This procedure provides an efficient method for the synthesis of cyclomerucurated ferrocenylimines containing heterocyclic ring which are difficultly synthesized by the conventional method.The reaction mechanism is proposed.