In the present paper, we study the boundary concentration-breaking phenomena on two thermal insulation problems considered on Lipschitz domains, based on Serrin's overdetermined result, the perturbation argument, ...In the present paper, we study the boundary concentration-breaking phenomena on two thermal insulation problems considered on Lipschitz domains, based on Serrin's overdetermined result, the perturbation argument, and a comparison of Laplacian eigenvalues with different boundary conditions. Since neither of the functionals in the two problems is C^(1), another key ingredient is to obtain the global H?lder regularity of minimizers of both problems on Lipschitz domains. Also, the exact dependence on the domain of breaking thresholds is given in the first problem, and the breaking values are obtained in the second problem on ball domains, which are related to 2π in dimension 2.展开更多
This is a lecture note of my joint work with Chi-Kwong Li concerning various results on the norm structure of n 2 n matrices (as Hilbert-space operators). The main result says that the triangle inequality serves as th...This is a lecture note of my joint work with Chi-Kwong Li concerning various results on the norm structure of n 2 n matrices (as Hilbert-space operators). The main result says that the triangle inequality serves as the ultimate norm estimate for the upper bounds of summation of two matrices. In the case of summation of two normal matrices, the result turns out to be a norm estimate in terms of the spectral variation for normal matrices.展开更多
We improve the Monte-Carlo based QCD sum rules by introducing the rigorous Hoolder-inequalitydetermined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function.In this improv...We improve the Monte-Carlo based QCD sum rules by introducing the rigorous Hoolder-inequalitydetermined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function.In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters（the hadronic mass and width etc.）. We test the new approach in the ρ meson channel with re-examination and inclusion of αs corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11625103 and 12171144)Hunan Science and Technology Planning Project (Grant No. 2019RS3016)+3 种基金supported by the National Natural Science Fund for Youth Scholars (Grant No. 12101215)Scientific Research Start-Up Funds by Hunan Universitysupported by the National Natural Science Fund for Youth Scholars (Grant No. 12101216 )the Natural Science Fund of Hunan Province (Grant No. 2022JJ40030)。
文摘In the present paper, we study the boundary concentration-breaking phenomena on two thermal insulation problems considered on Lipschitz domains, based on Serrin's overdetermined result, the perturbation argument, and a comparison of Laplacian eigenvalues with different boundary conditions. Since neither of the functionals in the two problems is C^(1), another key ingredient is to obtain the global H?lder regularity of minimizers of both problems on Lipschitz domains. Also, the exact dependence on the domain of breaking thresholds is given in the first problem, and the breaking values are obtained in the second problem on ball domains, which are related to 2π in dimension 2.
文摘This is a lecture note of my joint work with Chi-Kwong Li concerning various results on the norm structure of n 2 n matrices (as Hilbert-space operators). The main result says that the triangle inequality serves as the ultimate norm estimate for the upper bounds of summation of two matrices. In the case of summation of two normal matrices, the result turns out to be a norm estimate in terms of the spectral variation for normal matrices.
基金Supported by NSFC(11175153,11205093,11347020)Open Foundation of the Most Important Subjects of Zhejiang Province+1 种基金K.C.Wong Magna Fund in Ningbo UniversitySupported by the Natural Sciences and Engineering Research Council of Canada(NSERC)
文摘We improve the Monte-Carlo based QCD sum rules by introducing the rigorous Hoolder-inequalitydetermined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function.In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters（the hadronic mass and width etc.）. We test the new approach in the ρ meson channel with re-examination and inclusion of αs corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.
