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
In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curv...In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory.展开更多
Within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type.The existence of infinitely many symmetr...Within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type.The existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace identity.When the involved two potential vectors are scalar,all the resulting integrable lattice equations are reduced to the standard Ablowitz-Ladik hierarchy.展开更多
The energy dependence of the spectral fluctuations in the interacting boson model(IBM)and its connections to the mean-field structures are analyzed by adopting two statistical measures:the nearest neighbor level spaci...The energy dependence of the spectral fluctuations in the interacting boson model(IBM)and its connections to the mean-field structures are analyzed by adopting two statistical measures:the nearest neighbor level spacing distribution P(S)measuring the chaoticity(regularity)in energy spectra and the Δ_(3)(L)statistics of Dyson and Metha measuring the spectral rigidity.Specifically,the statistical results as functions of the energy cutoff are determined for different dynamical scenarios,including the U(5)-SU(3)and SU(3)-O(6)transitions as well as those near the AW arc of regularity.We observe that most of the changes in spectral fluctuations are triggered near the stationary points of the classical potential,particularly for cases in the deformed region of the IBM phase diagram.Thus,the results justify the stationary point effects from the perspective of statistics.In addition,the approximate degeneracies in the 2^(+)spectrum on the AW arc is also revealed from the statistical calculations.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.
基金Supported by the National Science Foundation of China under Grant No.11371244the Applied Mathematical Subject of SSPU under Grant No.XXKPY1604
文摘In this paper, based on a discrete spectral problem and the corresponding zero curvature representation,the isospectral and nonisospectral lattice hierarchies are proposed. An algebraic structure of discrete zero curvature equations is then established for such integrable systems. the commutation relations of Lax operators corresponding to the isospectral and non-isospectral lattice flows are worked out, the master symmetries of each lattice equation in the isospectral hierarchyand are generated, thus a τ-symmetry algebra for the lattice integrable systems is engendered from this theory.
基金The work was supported in part by NSF(DMS-1664561)NSFC(11975145 and 11972291)+1 种基金the Natural Science Foundation for Colleges and Universities in Jiangsu Province(17KJB110020)Emphasis Foundation of Special Science Research on Subject Frontiers of CUMT(2017XKZD11).
文摘Within the zero curvature formulation,a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type.The existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace identity.When the involved two potential vectors are scalar,all the resulting integrable lattice equations are reduced to the standard Ablowitz-Ladik hierarchy.
基金Supported by National Natural Science Foundation of China(11875158,11875171)。
文摘The energy dependence of the spectral fluctuations in the interacting boson model(IBM)and its connections to the mean-field structures are analyzed by adopting two statistical measures:the nearest neighbor level spacing distribution P(S)measuring the chaoticity(regularity)in energy spectra and the Δ_(3)(L)statistics of Dyson and Metha measuring the spectral rigidity.Specifically,the statistical results as functions of the energy cutoff are determined for different dynamical scenarios,including the U(5)-SU(3)and SU(3)-O(6)transitions as well as those near the AW arc of regularity.We observe that most of the changes in spectral fluctuations are triggered near the stationary points of the classical potential,particularly for cases in the deformed region of the IBM phase diagram.Thus,the results justify the stationary point effects from the perspective of statistics.In addition,the approximate degeneracies in the 2^(+)spectrum on the AW arc is also revealed from the statistical calculations.
