To find the predual spaces Pα（R^n） of Qα（R^n） is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent at...To find the predual spaces Pα（R^n） of Qα（R^n） is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent atomic characterization of Pα（Rn） is given, then its usual atomic characterization and Poisson extension characterization are given. Finally, the continuity on Pα of Calderon-Zygmund operators is studied, and the result can be also applied to give the Morrey characterization of Pα（Rn）.展开更多
Changes of the material fracture toughness with crack propagation can be described by a crack extension resistance curve,one of the fundamental fracture criteria in crack mechanics.Recently,experimental observation of...Changes of the material fracture toughness with crack propagation can be described by a crack extension resistance curve,one of the fundamental fracture criteria in crack mechanics.Recently,experimental observation of the fracture behavior in concrete was used to develop a new fracture criterion,the crack extension GR resistance curve,to analyze crack propagation during the entire concrete fracture process.The variation of the crack extension resistance is mainly associated with the energy consumption in the fracture process zone ahead of the stress-free crack tip.The crack extension resistance is then a function of the softening curve,which is a basic mechanical property in the fracture process zone.The relationship between the softening curve and the crack extension GR resistance curve is then analyzed based on results of three-point bending beams tests.The results indicate that the characteristic points of the crack extension resistance GR curve is closely related to the characteristic point on used tension softening curve.展开更多
基金supported by NNSF of China No.10001027, 90104004,10471002973 project of China G1999075105+1 种基金the innovation funds of Wuhan Universitythe subject construction funds of Mathematic and Statistic School, Wuhan University.
文摘To find the predual spaces Pα（R^n） of Qα（R^n） is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent atomic characterization of Pα（Rn） is given, then its usual atomic characterization and Poisson extension characterization are given. Finally, the continuity on Pα of Calderon-Zygmund operators is studied, and the result can be also applied to give the Morrey characterization of Pα（Rn）.
基金This paper was financially supported by the National Natural Science Foundation of China(Grant No.50438010).
文摘Changes of the material fracture toughness with crack propagation can be described by a crack extension resistance curve,one of the fundamental fracture criteria in crack mechanics.Recently,experimental observation of the fracture behavior in concrete was used to develop a new fracture criterion,the crack extension GR resistance curve,to analyze crack propagation during the entire concrete fracture process.The variation of the crack extension resistance is mainly associated with the energy consumption in the fracture process zone ahead of the stress-free crack tip.The crack extension resistance is then a function of the softening curve,which is a basic mechanical property in the fracture process zone.The relationship between the softening curve and the crack extension GR resistance curve is then analyzed based on results of three-point bending beams tests.The results indicate that the characteristic points of the crack extension resistance GR curve is closely related to the characteristic point on used tension softening curve.
