We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree. 相似文献
Based on the vector angular spectrum representation of optical beam and the method of stationary phase, the analytical TE and TM terms of vector Gaussian beam have been presented in the far field. By using the local polarization matrix, the polarization properties of the TE and TM terms in the far field are investigated, and it is found that the degree of their polarization is only determined by the spatial location. When the source is completely polarized, the TE and TM terms are both completely polarized in the far field. When the source is completely unpolarized, the TE and TM terms in the far field are partially polarized. The whole beam is also partially polarized except on the propagating axis. Moreover, the degrees of polarization of TE and TM terms are both larger than that of the whole beam.[第一段] 相似文献
A general simple algorithm is proposed to determine the average architecture of an acyclic branched polymer macromolecule from its number of branching points, whatever their functionality. The number of branching points can be derived from SEC measurements using a coupling of viscosimetric and refractometric detectors through the use of the Zimm‐Stockmayer equation. Since various isomers can be built for a given number of branching points, some basic rules are proposed in order to select the structures that are physically meaningful; the possibility of structural isomers has been also investigated and a probability of presence is assigned to each species starting from the compactness of the molecule. For each species corresponding to a given molecular weight in the sample, the average structure is then obtained from the number of branching points and the universal probability distribution of the isomers.