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Convergence rates of cascade algorithms 总被引:2,自引:0,他引:2
Rong-Qing Jia 《Proceedings of the American Mathematical Society》2003,131(6):1739-1749
We consider solutions of a refinement equation of the form
where is a finitely supported sequence called the refinement mask. Associated with the mask is a linear operator defined on by . This paper is concerned with the convergence of the cascade algorithm associated with , i.e., the convergence of the sequence in the -norm.
where and is a constant. In particular, we confirm a conjecture of A. Ron on convergence of cascade algorithms.
where is a finitely supported sequence called the refinement mask. Associated with the mask is a linear operator defined on by . This paper is concerned with the convergence of the cascade algorithm associated with , i.e., the convergence of the sequence in the -norm.
Our main result gives estimates for the convergence rate of the cascade algorithm. Let be the normalized solution of the above refinement equation with the dilation matrix being isotropic. Suppose lies in the Lipschitz space , where 0$"> and . Under appropriate conditions on , the following estimate will be established:
where and is a constant. In particular, we confirm a conjecture of A. Ron on convergence of cascade algorithms.
115.
Kimura S Yashiro H Okunishi K Hagiwara M He Z Kindo K Taniyama T Itoh M 《Physical review letters》2007,99(8):087602
High field magnetization and ESR measurements on the quasi-one-dimensional (1D) antiferromagnet BaCo(2)V(2)O(8) have been performed in magnetic fields up to 50 T along the chain. The experimental results are explained well in terms of a 1D S=1/2 antiferromagnetic XXZ model in longitudinal fields. We show that the quantum phase transition from the Néel ordered phase to the spin liquid one in the model is responsible for a peculiar order to disorder transition in BaCo(2)V(2)O(8). 相似文献
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117.
The relativistic problem of neutral fermions subject to PT-symmetric trigonometric potential (∼iαtanαx) in 1+1 dimensions is investigated. By using the basic concepts of the supersymmetric quantum mechanics formalism and the functional analysis method, we solve exactly the position-dependent effective mass Dirac equation with the vector coupling scheme and obtain the bound state solutions in closed form. The behavior of the energy spectra is discussed in detail. 相似文献
118.
Investigation on improving characteristics of two-cell SBS system with CCl4/C2H5OH liquid mixture 下载免费PDF全文
In order to improve the performance of the two-cell stimulated Brillouin scattering (SBS) system, this paper proposes the methods of using mixtures, which require amplifier media to have small absorption rate, and generator media to have high optical breakdown threshold and Brillouin frequency shift equal to that of the amplification media. The characteristics of the two-cell SBS system are studied experimentally by using CCl4 as amplifier medium and CCl4, C2H5OH and CCl4/C2H5OH liquid mixture as generator medium pumped by Nd:YAG Q-switched laser. The obtained results show that liquid mixture in generator cell improves the power load ability, phase conjugation fidelity, energy reflectivity (ER) and ER stability. 相似文献
119.
Hongtao Sun Liyan Zhang Shilong Zhao Junjie Zhang Dongbing He Zhongchao Duan Lili Hu 《Solid State Communications》2005,133(6):357-361
Structural and infrared-to-visible upconversion fluorescence properties of Er3+/Yb3+-codoped oxychloride lead-germanium-bismuth glass have been studied. The Raman spectrum investigation indicates that PbCl2 plays an important role in the formation of glass network, and has an important influence on the upconversion luminescence owing to lower phonon energy. Intense green and red emissions centered at 525, 546, and 657 nm, corresponding to the transitions 2H11/2→4I15/2, 4S3/2→4I15/2, and 4F9/2→4I15/2, respectively, were observed at room temperature. The quadratic dependence of the 525, 546, and 657 nm emissions on excitation power indicates that a two-photon absorption process occurs under 975 nm excitation. 相似文献
120.
The continuous-wave laser properties of an efficient diode-pumped Nd:GdVO4 crystal operating at formed with a simple plane-concave cavity have been studied. With the incident pump power of 21 W, an output power of 6.9 W was obtained, giving an optical conversion efficiency of 32.8% and a slope efficiency of 35.3%. The laser characterization of two different Nd3+-doped concentration of Nd:GdVO4 crystals were studied. 相似文献