共查询到20条相似文献,搜索用时 15 毫秒
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《Topology and its Applications》2009,156(2):420-432
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Yoshiyasu Ozeki 《Journal of Number Theory》2013,133(11):3810-3861
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We consider a real Gaussian process X with unknown smoothness where the mean-square derivative is supposed to be Hölder continuous in quadratic mean. First, from the discrete observations , we study reconstruction of , , with , a piecewise polynomial interpolation of degree . We show that the mean-square error of interpolation is a decreasing function of r but becomes stable as soon as . Next, from an interpolation-based empirical criterion, we derive an estimator of and prove its strong consistency by giving an exponential inequality for . Finally, we prove the strong convergence of toward with a similar rate as in the case ‘ known’. To cite this article: D. Blanke, C. Vial, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
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In this paper, by using Picard–Fuchs equations and Chebyshev criterion, we study the upper bounds of the number of limit cycles given by the first order Melnikov function for discontinuous differential systems, which can bifurcate from the periodic orbits of quadratic reversible centers of genus one (r19): , , and (r20): , , and the periodic orbits of the quadratic isochronous centers , , and , . The systems (r19) and (r20) are perturbed inside the class of polynomial differential systems of degree n and the system and are perturbed inside the class of quadratic polynomial differential systems. The discontinuity is the line . It is proved that the upper bounds of the number of limit cycles for systems (r19) and (r20) are respectively and counting the multiplicity, and the maximum numbers of limit cycles bifurcating from the period annuluses of the isochronous centers and are exactly 5 and 6 (counting the multiplicity) on each period annulus respectively. 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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《Journal de Mathématiques Pures et Appliquées》2006,85(1):2-16
Let ω be a domain in and let be a smooth immersion. The main purpose of this paper is to establish a “nonlinear Korn inequality on the surface ”, asserting that, under ad hoc assumptions, the -distance between the surface and a deformed surface is “controlled” by the -distance between their fundamental forms. Naturally, the -distance between the two surfaces is only measured up to proper isometries of .This inequality implies in particular the following interesting per se sequential continuity property for a sequence of surfaces. Let , , be mappings with the following properties: They belong to the space ; the vector fields normal to the surfaces , , are well defined a.e. in ω and they also belong to the space ; the principal radii of curvature of the surfaces , , stay uniformly away from zero; and finally, the fundamental forms of the surfaces converge in toward the fundamental forms of the surface as . Then, up to proper isometries of , the surfaces converge in toward the surface as .Such results have potential applications to nonlinear shell theory, the surface being then the middle surface of the reference configuration of a nonlinearly elastic shell. 相似文献
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Let be an isometric immersion from a Riemannian n-manifold into a Euclidean m-space. Denote by Δ and the Laplace operator and the position vector of M, respectively. Then M is called biharmonic if . The following Chen?s Biharmonic Conjecture made in 1991 is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper we prove that the biharmonic conjecture is true for -ideal and -ideal hypersurfaces of a Euclidean space of arbitrary dimension. 相似文献