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31.
Matthias Hoschneider 《Communications in Mathematical Physics》1994,160(3):457-473
In this paper we want to give a new definition of fractal dimensions as small scale behavior of theq-energy of wavelet transforms. This is a generalization of previous multi-fractal approaches. With this particular definition we will show that the 2-dimension (=correlation dimension) of the spectral measure determines the long time behavior of the time evolution generated by a bounded self-adjoint operator acting in some Hilbert space ?. It will be proved that for φ, ψ∈? we have $$\mathop {\lim \inf }\limits_{T \to \infty } \frac{{\log \int_0^T {d\omega \left| {\left\langle {\psi \left| {e^{ - iA\omega } } \right.\phi } \right\rangle } \right|^2 } }}{{\log T}} = - \kappa ^ + (2)$$ and that $$\mathop {\lim \sup }\limits_{T \to \infty } \frac{{\log \int_0^T {d\omega \left| {\left\langle {\psi \left| {e^{ - iA\omega } } \right.\phi } \right\rangle } \right|^2 } }}{{\log T}} = - \kappa ^ - (2),$$ wherek ±(2) are the upper and lower correlation dimensions of the spectral measure associated with ψ and ?. A quantitative version of the RAGE theorem shall also be given. 相似文献
32.
Matthias Gelbrich 《Mathematische Nachrichten》1990,147(1):185-203
For a separable metric space (X, d) Lp Wasserstein metrics between probability measures μ and v on X are defined by where the infimum is taken over all probability measures η on X × X with marginal distributions μ and v, respectively. After mentioning some basic properties of these metrics as well as explicit formulae for X = R a formula for the L2 Wasserstein metric with X = Rn will be cited from [5], [9], and [21] and proved for any two probability measures of a family of elliptically contoured distributions. Finally this result will be generalized for Gaussian measures to the case of a separable Hilbert space. 相似文献
33.
Matthias Luter 《PAMM》2003,3(1):48-51
The shallow‐water equations on the sphere are compressible Navier‐Stokes equations that describe hydrostatic atmospheric dynamics. An adaptive Lagrange‐Galerkin method is applied on the spherical domain to develop a simplified global atmospheric model. Computational results show the experimental convergence of this numerical method. 相似文献
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Double-quantum filtered MAS NMR spectra of an isolated homonuclear spin-1/2 pair are considered, at and away from rotational resonance conditions. The pulse sequence used is the solid-state NMR equivalent of double-quantum filtered COSY, known from solution-state NMR. The 119Sn spin pair in [(chex3Sn)2S] is characterized by a difference in isotropic chemical shielding smaller than the two chemical shielding anisotropies and by direct dipolar and isotropic J-coupling constants of similar magnitudes. At rotational resonance, one-dimensional double-quantum filtered 119Sn lineshapes yield the relative orientation of the two 119Sn chemical shielding tensors. Good double-quantum filtration efficiencies are found at and away from rotational resonance conditions, despite the presence of large chemical shielding anisotropies. Numerical simulations illustrate the interplay of the direct dipolar and J-coupling pathways and identify the latter as the main pathway even at rotational resonance conditions. 相似文献
36.
A lattice spin-fermion model for diluted magnetic semiconductors (DMS) is investigated numerically, improving on previously used mean-field approximations. Curie temperatures are obtained varying the Mn spin x and hole n densities, and the impurity-hole exchange J in units of the hop-ping t. Optimal values are found in the subtle intermediate regime between itinerant and localized carriers. At intermediate and large J/t, a "clustered" state is observed above the Curie temperature and ferromagnetism is suppressed. Formal analogies between DMS and manganites are discussed. 相似文献
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