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This paper is devoted to the proof of almost global existence results for Klein‐Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds. © 2007 Wiley Periodicals, Inc. 相似文献
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Gerhard Lessner 《General Relativity and Gravitation》2004,36(5):1241-1242
14.
We solve numerically the Monge–Ampère equation with periodic boundary condition using a Newton's algorithm. We prove convergence of the algorithm, and present some numerical examples, for which a good approximation is obtained in 10 iterations. To cite this article: G. Loeper, F. Rapetti, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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Gerhard Starke 《Numerische Mathematik》1997,78(1):103-117
Summary. The convergence rate of Krylov subspace methods for the solution of nonsymmetric systems of linear equations, such as GMRES
or FOM, is studied. Bounds on the convergence rate are presented which are based on the smallest real part of the field of
values of the coefficient matrix and of its inverse. Estimates for these quantities are available during the iteration from
the underlying Arnoldi process. It is shown how these bounds can be used to study the convergence properties, in particular,
the dependence on the mesh-size and on the size of the skew-symmetric part, for preconditioners for finite element discretizations
of nonsymmetric elliptic boundary value problems. This is illustrated for the hierarchical basis and multilevel preconditioners
which constitute popular preconditioning strategies for such problems.
Received May 3, 1996 相似文献
20.
The change of the superstructure of different polyethylenes during uniaxial deformation is investigated. The method used is small-angle scattering with synchrotron radiation. For branched polyethylene (Lupolen 1840D) the whole deformation range is analyzed. Beginning with superstructure of the lamellar cluster type, the superstructure partly disappears on a time scale of a few minutes and the fibrillar structure is built up. The degree of destruction and rebuilding depends on the drawing temperature. For very high molecular weight polyethylene (GUR) a reversible change of the superstructure at higher deformation ratios and at different temperatures is observed. The superstructure of (ethylene—hexene) copolymers (TIPELIN) at high draw ratios depends on the drawing temperature and is almost independent of the side group content. Interfibrillar microcracks parallel to the draw direction are produced in samples with a low side group content for draw ratios λ ≥ 1.5. 相似文献