Classes polaires associées aux distributions holomorphes de sous-espaces tangents*

Résumé. Nous définissons des classes polaires associées à une distribution holomorphe singulière de sous-espaces tangents d’une variété projective lisse. Nous prouvons que ces classes polaires peuvent être calculées en fonction des classes de Chern-Mather du faisceau tangent de la distribution et réciproquement. Nous utilisons leurs degrés pour borner les degrés de certaines classes polaires associés à une variété invariante. *Ce travail a été soutenu par l’Accord de Coopération France-Brésil (CNRS/CNPq) et par la Fondation CAPES-Brésil.     

A model of fads,fashions, and group formation

I develop a model of consumer behavior where agents purchase goods in order to signify personal characteristics. Agents purchase goods in order to imitate agents similar to them and agents they want to emulate. Depending on parameter values of consumer preferences the model generates stable groups, fads, and fashion cycles, or a mixture of both. The model is unique to the economic literature on fads in that the extinction of fads occurs endogenously in the model. © 2004 Wiley Periodicals, Inc. Complexity 9: 51–61, 2004     

On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z_2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H(5)≥25=5~2, where H(5)is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.     

A Ramsey‐type result for the hypercube

We prove that for every fixed k and ? ≥ 5 and for sufficiently large n, every edge coloring of the hypercube Q_n with k colors contains a monochromatic cycle of length 2 ?. This answers an open question of Chung. Our techniques provide also a characterization of all subgraphs H of the hypercube which are Ramsey, that is, have the property that for every k, any k‐edge coloring of a sufficiently large Q_n contains a monochromatic copy of H. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 196–208, 2006     

On the topological representation of catalytic cycles with nonlinear steps

Reaction route analysis is applied to visualize reaction networks in several heterogeneous catalytic reactions. Combination of the theory of complex reactions with the notion of catalytic cycles results in a topological representation of complex mechanisms with the nodes comprising all possible surface species including free sites and branches indicating interconnections between reactions.     

Bifurcation and Isochronicity at Infinity in a Class of Cubic Polynomial Vector Fields

In this paper, we study the appearance of limit cycles from the equator and isochronicity of infinity in polynomial vector fields with no singular points at infinity. We give a recursive formula to compute the singular point quantities of a class of cubic polynomial systems, which is used to calculate the first seven singular point quantities. Further, we prove that such a cubic vector field can have maximal seven limit cycles in the neighborhood of infinity. We actually and construct a system that has seven limit cycles. The positions of these limit cycles can be given exactly without constructing the Poincare cycle fields. The technique employed in this work is essentially different from the previously widely used ones. Finally, the isochronous center conditions at infinity are given.     

Algebraic cycles and topology of real Enriques surfaces

For a real Enriques surface Y we prove that every homology class in H₁(Y (R), Z/2) can be represented by a real algebraic curve if and only if all connected components of Y(R) are orientable. Furthermore, we give a characterization of real Enriques surfaces which are Galois-Maximal and/or Z-Galois-Maximal and we determine the Brauer group of any real Enriques surface Y.     

Effects of electrolytes used in roughening gold substrates by oxidation–reduction cycles on surface-enhanced Raman scattering

In this work, the effects of electrolytes used in roughening gold substrates by electrochemical methods on surface-enhanced Raman scattering (SERS) were first investigated. First, gold substrates were roughened by triangular-wave oxidation–reduction cycles (ORC) in aqueous solutions containing different kinds of 0.1 M electrolytes. Then Rhodamine 6G (R6G) was used as Raman probe to examine this effect of electrolytes used on the SERS observed. The result indicates that the highest intensity of SERS of R6G was obtained on the roughened Au substrate prepared in 0.1 M NaCl, which was less used in the literature. Meanwhile, it was also found that the rougher surface morphology observed, which is contributive to the higher SERS obtained, is corresponding to the smaller cathodic peak area shown in the cyclic voltammograms for roughening the Au substrate.