共查询到20条相似文献,搜索用时 31 毫秒
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For a smooth geometrically integral algebraic variety X over a field k of characteristic 0, we define the extended Picard complex . It is a complex of length 2 which combines the Picard group and the group , where is a fixed algebraic closure of k and . For a connected linear k-group G we compute the complex (up to a quasi-isomorphism) in terms of the algebraic fundamental group . We obtain similar results for a homogeneous space X of a connected k-group G. To cite this article: M. Borovoi, J. van Hamel, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
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Risong Li 《Chaos, solitons, and fractals》2012,45(6):753-758
Let (X,d) be a compact metric space and (κ(X),dH) be the space of all non-empty compact subsets of X equipped with the Hausdorff metric dH. The dynamical system (X,f) induces another dynamical system , where f:X → X is a continuous map and is defined by for any A ∈ κ(X). In this paper, we introduce the notion of ergodic sensitivity which is a stronger form of sensitivity, and present some sufficient conditions for a dynamical system (X,f) to be ergodically sensitive. Also, it is shown that is syndetically sensitive (resp. multi-sensitive) if and only if f is syndetically sensitive (resp. multi-sensitive). As applications of our results, several examples are given. In particular, it is shown that if a continuous map of a compact metric space is chaotic in the sense of Devaney, then it is ergodically sensitive. Our results improve and extend some existing ones. 相似文献
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We investigate the effect of the interplay of positive and negative links, on the dynamical regularity of a random weighted network, with neuronal dynamics at the nodes. We investigate how the mean and the variance of the weights of links, influence the spatiotemporal regularity of this dynamical network. We find that when the connections are predominantly positive (i.e. the links are mostly excitatory, with ) the spatiotemporal fixed point is stable. A similar trend is observed when the connections are predominantly negative (i.e. the links are mostly inhibitory, with ). However, when the positive and negative feedback is quite balanced (namely, when the mean of the connection weights is close to zero) one observes spatiotemporal chaos. That is, the balance of excitatory and inhibitory connections preserves the chaotic nature of the uncoupled case. To be brought to an inactive state one needs one type of connection (either excitatory or inhibitory) to dominate. Further we observe that larger network size leads to greater spatiotemporal regularity. We rationalize our observations through mean field analysis of the network dynamics. 相似文献
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In this paper, we consider the Cauchy problem for a two-phase model with magnetic field in three dimensions. The global existence and uniqueness of strong solution as well as the time decay estimates in are obtained by introducing a new linearized system with respect to for constants and , and doing some new a priori estimates in Sobolev Spaces to get the uniform upper bound of in norm. 相似文献
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B. Narasimha Chary 《Journal of Pure and Applied Algebra》2018,222(9):2552-2561
Let G be a simple algebraic group over the field of complex numbers. Fix a maximal torus T and a Borel subgroup B of G containing T. Let w be an element of the Weyl group W of G, and let be the Bott–Samelson–Demazure–Hansen (BSDH) variety corresponding to a reduced expression of w with respect to the data .In this article we give complete characterization of the expressions such that the corresponding BSDH variety is Fano or weak Fano. As a consequence we prove vanishing theorems of the cohomology of tangent bundle of certain BSDH varieties and hence we get some local rigidity results. 相似文献