In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of ...In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.展开更多
By using the time-independent formal scattering theoretical approach,we develop a nonperturbative quantum electrodynamics theory to describe high-order harmonic generation(HHG).This theory recovers the semi-classical ...By using the time-independent formal scattering theoretical approach,we develop a nonperturbative quantum electrodynamics theory to describe high-order harmonic generation(HHG).This theory recovers the semi-classical interpretation of Corkum(Phys.Rev.Lett.71(1993)1994)and gives the same phenomenological cutoff law.The HHG emission rate is expressed as an analytic closed form.We also discuss the connection between HHG and the above threshold ionization from the scattering viewpoint.展开更多
In this paper, we investigate the space of <em>L<sup>p</sup> p</em>-harmonic 1-forms on a complete noncompact orientable <em>δ</em>-stable hypersurface <em>M<sup>m</...In this paper, we investigate the space of <em>L<sup>p</sup> p</em>-harmonic 1-forms on a complete noncompact orientable <em>δ</em>-stable hypersurface <em>M<sup>m</sup></em> that is immersed in space form <img src="Edit_6fbc11b9-ac23-40e2-b045-0fb25419337d.png" width="35" height="23" alt="" /> with nonnegative BiRic curvature. We prove the nonexistence of <em>L<sup>p</sup> p</em>-harmonic 1-forms on <em>M<sup>m</sup></em>. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.展开更多
Harmonic mappings from the hexagasket to the circle are described in terms of boundary values and topological data. Explicit formulas are also given for the energy of the mapping. We have generalized the results in [10].
基金Supported by the National Natural Science Foundation of China (10971224)the Hebei Natural ScienceFoundation (07M003)
文摘In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.
基金Supported by the Chinese Academy of Sciences,the National Natural Science Foundation of China under Grant Nos.69725010,69678008,and the Climbing Program from the Chinese Commission of Science and Technology.
文摘By using the time-independent formal scattering theoretical approach,we develop a nonperturbative quantum electrodynamics theory to describe high-order harmonic generation(HHG).This theory recovers the semi-classical interpretation of Corkum(Phys.Rev.Lett.71(1993)1994)and gives the same phenomenological cutoff law.The HHG emission rate is expressed as an analytic closed form.We also discuss the connection between HHG and the above threshold ionization from the scattering viewpoint.
文摘In this paper, we investigate the space of <em>L<sup>p</sup> p</em>-harmonic 1-forms on a complete noncompact orientable <em>δ</em>-stable hypersurface <em>M<sup>m</sup></em> that is immersed in space form <img src="Edit_6fbc11b9-ac23-40e2-b045-0fb25419337d.png" width="35" height="23" alt="" /> with nonnegative BiRic curvature. We prove the nonexistence of <em>L<sup>p</sup> p</em>-harmonic 1-forms on <em>M<sup>m</sup></em>. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.
基金Supported by the grant 08KJD110011,NSK2008/B11,NSK2009/B07,NSK2009/C042008 Jiangsu Government Scholarship for Overseas Studies
文摘Harmonic mappings from the hexagasket to the circle are described in terms of boundary values and topological data. Explicit formulas are also given for the energy of the mapping. We have generalized the results in [10].
基金Supported by the National Key R and D Program of China(2020YFA0713100)the Natural Science Foundation of Jiangsu Province(BK20230900)National Natural Science Foundation of China(12141104)。
