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).     

Topological Simplicity of a Certain LF-Algebra

We show that the LF-algebra considered by Akkar and Nacir in [1] is topologically simple.     

Families of Line-Graphs and Their Quantization

Any directed graph G with N vertices and J edges has an associated line-graph L(G) where the J edges form the vertices of L(G). We show that the non-zero eigenvalues of the adjacency matrices are the same for all graphs of such a family L ⁿ (G). We give necessary and sufficient conditions for a line-graph to be quantisable and demonstrate that the spectra of associated quantum propagators follow the predictions of random matrices under very general conditions. Line-graphs may therefore serve as models to study the semiclassical limit (of large matrix size) of a quantum dynamics on graphs with fixed classical behaviour.     

On Numerical Solution of Shape Inverse Problems

The new method is proposed for the numerical solution of a class of shape inverse problems. The size and the location of a small opening in the domain of integration of an elliptic equation is identified on the basis of an observation. The observation includes the finite number of shape functionals. The approximation of the shape functionals by using the so-called topological derivatives is used to perform the learning process of an artificial neural network. The results of computations for 2D examples show, that the method allows to determine an approximation of the global solution to the inverse problem, sufficiently closed to the exact solution. The proposed method can be extended to the problems with an opening of general shape and to the identification problems of small inclusions. However, the mathematical theory of the proposed approach still requires futher research. In particular, the proof of global convergence of the method is an open problem.     

Activity of TiO2 deposited by the CVD method on ammoxidized surface of a carbonaceous material in hydrogenation of styrene

Hydrogenation of styrene has been applied as a test reaction to study the catalytic activity of TiO₂ deposited by the CVD (chemical vapour deposition) method on the surface of a carbonaceous material enriched in nitrogen (C_N).     

The measure of a translated ball in uniformly convex spaces

Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r ^q , whereq depends on the properties of the norm. We specify it in the case ofL spaces, >1.     

Multiresidue determination of fluoroquinolones in shrimp by liquid chromatography-fluorescence-mass spectrometry

An efficient multiresidue method for analysis of fluoroquinolones in shrimp has been developed in which quantitation by fluorescence and confirmation by Multiple Stage Mass Spectrometry (MS) is achieved simultaneously. In this method, shrimp tissue is extracted with ammoniacal acetonitrile and the extract is defatted and then evaporated. After dissolution in basic phosphate buffer, fluoroquinolones in the extract are separated by liquid chromatography and quantitated, taking advantage of their intense fluorescence. Eluate from the fluorescence detector enters the MS, which allows for confirmation by monitoring ratios of 2 prominent product ions in the MS3 or MS2 spectrum. Using this method, 8 fluoroquinolones have been analyzed in shrimp samples fortified at 10, 25, 50, or 100 ppb levels. Recoveries for desethyleneciprofloxacin, norfloxacin, ciprofloxacin, danofloxacin, enrofloxacin, orbifloxacin, sarafloxacin, and difloxacin ranged from 75 to 92%, with relative standard deviation values of <6%. The limits of quantitation ranged from 0.1 to 1 ng/g. Enrofloxacin and ciprofloxacin were also successfully determined in enrofloxacin-incurred shrimp using this method.     

Retention of anions on silica-based metalloporphyrin stationary phases.

The silica-based Fe(III)-protoporphyrin and Zn-tetraphenylporphyrin stationary phases were examined for the HPLC separation of anions. The retention of nine common inorganic anions as well as benzoate anion (BA) and its hydroxy analogues (HBA) was examined using tartrate, acetate, and succinate eluents. The retention factors of inorganic anions on the FeProP stationary phase were in the order Cl- < NO3- < ClO4- < I- < SCN- and for organic anions benzoate < p-hydroxybenzoate < m-hydoxybenzoate < o-hydroxybenzoate. The retention factors of organic anions examined for a ZnTPP column were in the order p-HBA < m-HBA < BA < o-HBA.     

X-ray structure and multinuclear NMR studies of platinum(II) and palladium(II) complexes with 5,7-ditertbutyl-1,2,4-triazolo[1,5-a]pyrimidine

Pt(II) and Pd(II) dichloride complexes with 5,7-ditertbutyl-1,2,4-triazolo[1,5-a]pyrimidine (dbtp) have been synthesized and characterized by infrared and ¹H, ¹³C NMR, ¹³C CPMAS spectroscopy. The structures of the cis-PtCl₂(dbtp)₂ · EtOH (1) and cis-PdCl₂(dbtp)(dmso) (2) has been determined by signal-crystal X-ray diffraction. In both complexes the X-ray crystal structures shows that heterocycle ligand (dbtp) binds the central atom monodentate via nitrogen atom N(3). In addition, compound (2) is interesting for its structural features, because it is the first report of mixed dichloride Pd(II) complexes with N-donor (triazolopyrimidine) and S-donor (dimethylsulfoxide) ligands. In this structure the Pd–Cl distances are: 2.302(1) and 2.281(1) Å, Pd–N 2.041(3) Å and Pd–S 2.245(1) Å. The ¹H, ¹³C NMR studies show clearly that these structures are retained in solution.     

The influence of cosolvent polarity on the flow properties of hydroalcoholic gels: empirical models

The aim of this study was to investigate the influence of cosolvent polarity on the rheological flow properties of aqueous and hydroalcoholic gels obtained from the Carbopol Ultrez 10 base and used for topical applications. Specifically, we have examined the effect of pH (range 4.0--7.0) on the consistency and flow properties of dispersed systems in water and mixtures--15 : 85% v/v of methanol : water, ethanol : water, n-propanol : water and n-butanol : water--at a constant polymer concentration of 0.3% w/w. The gels, which had decreasing polarity values in the jellifying medium, showed qualitatively similar flow behavior, characteristic of pseudoplastic systems, and all of the flow curves were adjusted to the Ostwald model. Sigmoidal dose response functions were calculated to describe the flow and consistency indexes as a function of pH. As a result, the influence of alcohol polarity on the polymer network has been assessed meaningfully using the empirical parameters obtained: maximum consistency index value (k(max)), pH value required for 50% development of polymer network (pH(50)), and asymptotic flow index value (n(min)) for the fully structured gels.