Alien limit cycles near a Hamiltonian 2-saddle cycle

It is known that perturbations from a Hamiltonian 2-saddle cycle Γ can produce limit cycles that are not covered by the Abelian integral, even when it is generic. These limit cycles are called alien limit cycles. This phenomenon cannot appear in the case that Γ is a periodic orbit, a non-degenerate singularity, or a saddle loop. In this Note, we present a way to study this phenomenon in a particular unfolding of a Hamiltonian 2-saddle cycle, keeping one connection unbroken at the bifurcation. To cite this article: M. Caubergh et al., C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Fold‐2‐covering triangular embeddings

For a graph G and a positive integer m, G_(m) is the graph obtained from G by replacing every vertex by an independent set of size m and every edge by m² edges joining all possible new pairs of ends. If G triangulates a surface, then it is easy to see from Euler's formula that G_(m) can, in principle, triangulate a surface. For m prime and at least 7, it has previously been shown that in fact G_(m) does triangulate a surface, and in fact does so as a “covering with folds” of the original triangulation. For m = 5, this would be a consequence of Tutte's 5‐Flow Conjecture. In this work, we investigate the case m = 2 and describe simple classes of triangulations G for which G₍₂₎ does have a triangulation that covers G “with folds,” as well as providing a simple infinite class of triangulations G of the sphere for which G₍₂₎ does not triangulate any surface. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 79–92, 2003     

Evaluation of a purge-and-trap injection system for capillary gas chromatography-microwave induced plasma-atomic emission spectrometry for the determination of volatile selenium compounds in water

A method is presented for the selective determination of the volatile selenium species dimethylselenide and dimethyldiselenide, using a commercially available purge-and-trap injection system coupled to capillary gas chromatography-microwave induced plasma-atomic emission spectrometry. The efficiency of the purging step was evaluated and the parameters affecting the purge and trap processes were optimized. The method was applied to the determination of volatile selenium compounds in lake water. Relative detection limits of 2ng/l for dimethylselenide and dimethyldiselenide, corresponding to an absolute detection limit of 10 pg, were achieved.     

Transformation of highly ordered large pore silica mesophases (Fm3m, Im3m and p6mm) in a ternary triblock copolymer-butanol-water system

Exceptional control of the phase behavior of highly ordered large pore mesostructured silica (with the choice of Fm3m, Im3m or p6mm symmetry) is achieved using a triblock copolymer (EO(106)PO(70)EO(106)) and butanol at low acid concentrations.     

Synthesis of functionalized analogs of pyochelin, a siderophore of Pseudomonas aeruginosa and Burkholderia cepacia

Using an improved synthesis of pyochelin, a siderophore common to several pathogenic Pseudomonas species, three functionalized pyochelin analogs were efficiently synthesized starting from appropriate 2-hydroxybenzonitriles.     

Utilisation des mélanges H2O+H2SO4+SO3 en tant que solvants: I. Étude du ferrocène et de quelques hydrocarbures polynucléaires dans les mélanges H2O+H2SO4. Comparaison des domaines d'électroactivité

The variation of the electroactivity range with composition of water+ sulphuric acid mixtures has been studied. It is shown that ferrocene provides a reference potential independent of solvent at low H₂SO₄ contents while polynuclear hydrocarbons fulfill the same function at high H₂SO₄ contents. Water+H₂SO₄ mixtures become more oxidizing (reduction limit) and less reducing (oxidation limit) when the H₂SO₄ concentration increases.     

Methods of theoretical study of vibrational phenomena in liquids--comparative analysis

In this review, existing theoretical models of vibrational phenomena in liquids are analyzed and compared. Most attention is paid to sonoluminescence, sonolysis and related phenomena. The criteria of selection of the optimal theoretical model involve analyzing experimental results, its usefulness for evaluation of thermodynamic and other parameters of the liquid under vibration, simplicity of the mathematical solution and the time needed for computing. It is concluded that, according to these criteria, the optimal (between existing models) is the chemical model of vibration in liquid, while the best perspectives are for its combinations with other models.     

Controlled polymerization in mesoporous silica toward the design of organic-inorganic composite nanoporous materials

Free-radical polymerization inside mesoporous silica has been investigated in order to open a route to functional polymer-silica composite materials with well-defined mesoporosity. Various vinyl monomers, such as styrene, chloromethyl styrene, 2-hydroxyethyl methacrylate, and methacrylic acid, were polymerized after impregnation into mesoporous silicas with various structures, which were synthesized using polyalkylene oxide-type block copolymers. The location of the polymers was systematically controlled with detailed structures of the silica framework and the polymerization conditions. Particularly noteworthy is the polymer-silica composite structure obtained by in situ polymerization after the selective adsorption of monomers as a uniform film on silica walls. The analysis of XRD data and the N(2) adsorption isotherms indicates the formation of uniform polymer nanocoating. The resultant polymer-silica composite materials can easily be post-functionalized to incorporate diverse functional groups in high density, due to the open porous structure allowing facile access for the chemical reagent. The fundamental characteristics of the composite materials are substantiated by testing the biomolecule's adsorption capacity and catalytic reactivity. Depending on the structure and composition of polymers, the resultant polymer-silica composite materials exhibit notably distinct adsorption properties toward biomolecules, such as proteins. Furthermore, it is demonstrated that the nanocoatings of polymers deposited on the mesopore walls have remarkably enhanced catalytic activity and selectivity, as compared to that of bulk polymer resins. We believe that, due to facile functionalization and attractive textural properties, the mesoporous polymer-silica composite materials are very useful for applications, such as adsorption, separation, host-guest complexes, and catalysis.     

Modeling of interface phenomena in liquid under vibration, using the chemical model

An analysis of interface phenomena in a liquid under a vibration field is presented, based on the chemical model of vibration in a liquid. The objects studied are a bubble, a solid surface, and a linear macromolecule, in a vibrated liquid. It is concluded that many sonochemical phenomena can be realized in some different (two or more) mechanisms, and mutually stimulate. Inharmonic effects and the influence of distant neighbors are analyzed.