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911.
A new promising organic chromophore for two-photon laser absorption at 1064 nm with 1,4-diethoxy-2,5-bis[2-(5-methylthien-2-yl)ethenyl]benzene (A-C) was synthesized. We have performed evaluations of the two-photon absorption for these chromophores incorporated into the polymer matrices. Following the obtained quantum chemical data, we have performed quantum chemical simulations of the third-order susceptibilities for the investigated chrompophore incorporated into the PMMA matrices. The calculations were done within the three-level model. We have established that the experimentally calculated data are a bit less than theoretically calculated; however, the general tendency of their changes shows a good coincidence. The maximally achieved value of the TPA is equal to about 59.2 cm/GW at wavelength 1064 nm, which, together with their high photothermal stabilities, make them good candidates for optical-limiting processes.  相似文献   
912.
The exterior Stokes problem between two parallel planes that are separated by a prismatic cylinder is extended to the interior of the prism by requiring the continuity of the velocity across the lateral faces. The well‐posedness of the exterior–interior problem is proved in suitable weighted Sobolev spaces. The solution is represented by Fourier series in the z‐variable. The Fourier coefficients, solutions of auxiliary two‐dimensional exterior–interior problems, are analyzed by viewing them as boundary integral equations of potential theory and global regularity of the densities, is established in weighted Sobolev spaces of traces. A boundary element method, with suitably refined mesh size, is implemented for the numerical treatment of the Fourier coefficients. This provides optimal convergent semi‐ and fully‐discrete spectral methods of Fourier–Galerkin type. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008  相似文献   
913.
We consider the Markov chainX n+1=T(X n )+ n , where { n ;n1} is a d -valued random sequence of independent identically distributed random variables, and the functionT: d d is measurable and satisfies a suitable growth condition. Under certain conditions involvingT and the probability distribution of n , we show that this Markov chain is ergodic. Moreover, we obtain sharp upper bounds for the tail of the corresponding stationary probability density function. In our proofs, we make use of the Leray-Schauder fixed-point theorem.  相似文献   
914.
This Note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux, and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities including in the limit case corresponding to the logarithmic Sobolev inequalities. To cite this article: J.-P. Bartier, J. Dolbeault, C. R. Acad. Sci. Paris, Ser. I 342 (2006).  相似文献   
915.
The function spaces Dk(Rn) are introduced and studied. The definition of these spaces is based on a regularity property for the critical Sobolev spaces Ws,p(Rn), where sp=n, obtained by J. Bourgain, H. Brezis, New estimates for the Laplacian, the div-curl, and related Hodge systems, C. R. Math. Acad. Sci. Paris 338 (7) (2004) 539-543 (see also J. Van Schaftingen, Estimates for L1-vector fields, C. R. Math. Acad. Sci. Paris 339 (3) (2004) 181-186). The spaces Dk(Rn) contain all the critical Sobolev spaces. They are embedded in BMO(Rn), but not in VMO(Rn). Moreover, they have some extension and trace properties that BMO(Rn) does not have.  相似文献   
916.
The aim of this note is to announce some recent results showing that an isotropic variant of the BMO-type norm introduced in [3] can be related via a precise formula to the perimeter of sets.  相似文献   
917.
In this paper, we introduce and study some low computational cost numerical methods for finding a solution of a variational inequality problem over the solution set of an equilibrium problem in a real Hilbert space. The strong convergence of the iterative sequences generated by the proposed algorithms is obtained by combining viscosity-type approximations with projected subgradient techniques. First a general scheme is proposed, and afterwards two practical realizations of it are studied depending on the characteristics of the feasible set. When this set is described by convex inequalities, the projections onto the feasible set are replaced by projections onto half-spaces with the consequence that most iterates are outside the feasible domain. On the other hand, when the projections onto the feasible set can be easily computed, the method generates feasible points and can be considered as a generalization of Maingé’s method to equilibrium problem constraints. In both cases, the strong convergence of the sequences generated by the proposed algorithms is proven.  相似文献   
918.
We consider the asymptotic behavior of semi-stable Markov processes valued in ]0,[ when the starting point tends to 0. The entrance distribution is expressed in terms of the exponential functional of the underlying Lévy process which appears in Lamperti's representation of a semi-stable Markov process.  相似文献   
919.
We consider a system of particles with arms that are activated randomly to grab other particles as a toy model for polymerization. We assume that the following two rules are fulfilled: once a particle has been grabbed then it cannot be grabbed again, and an arm cannot grab a particle that belongs to its own cluster. We are interested in the shape of a typical polymer in the situation when the initial number of monomers is large and the numbers of arms of monomers are given by i.i.d. random variables. Our main result is a limit theorem for the empirical distribution of polymers, where limit is expressed in terms of a Galton‐Watson tree. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010  相似文献   
920.
There are two main classes of iterative methods in nondifferentiable optimization (NDO). In thebasic NDO, the information is limited to the objective function and at least one element of its subdifferential, while in thecomposite NDO, the objective function is split into a sum of a smooth and a nonsmooth function. Our work unifies these two approaches for benefiting of their respective advantages.  相似文献   
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