The inverse problem for a class of nonlinear evolution equations of dispersive type type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equippi...The inverse problem for a class of nonlinear evolution equations of dispersive type type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution it,as given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhong-xin.展开更多
We show that all pure entangled states of two d-dimensional quantum systems （i.e., two qudits） can be generated from an initial separable state via a universal Yang-Baxter matrix if one is assisted by local unitary ...We show that all pure entangled states of two d-dimensional quantum systems （i.e., two qudits） can be generated from an initial separable state via a universal Yang-Baxter matrix if one is assisted by local unitary transformations.展开更多
We describe some recent developments of high-Reynolds-number asymptotic theory for the nonlinear stage of laminar-turbulent transition in nearly parallel flows.The classic weakly nonlinear theory of Landau and Stuart ...We describe some recent developments of high-Reynolds-number asymptotic theory for the nonlinear stage of laminar-turbulent transition in nearly parallel flows.The classic weakly nonlinear theory of Landau and Stuart is briefly revisited with the dual purposes of highlighting its fundamental ideas,which continue to underlie much of current theoretical thinking,as well as its difficulty in dealing with unbounded flows.We show that resolving such a difficulty requires an asymptotic approach based on the high-Reynolds-number assumption,which leads to a nonlinear critical-layer theory.Major recent results are reviewed with emphasis on the non-equilibrium effect.Future directions of investigation are indicated.展开更多
When the air temperature reaches 600 K or higher, vibration is excited. The specific heat is not a constant but a function of temperature. Under this condition, the transition position of hypersonic sharp wedge bounda...When the air temperature reaches 600 K or higher, vibration is excited. The specific heat is not a constant but a function of temperature. Under this condition, the transition position of hypersonic sharp wedge boundary layer is predicted by using the improved eN method considering variable specific heat. The transition positions with different Mach numbers of oncoming flow, half wedge angles, and wall conditions are computed condition, the nearer to the Mach number The results show that for the same oncoming flow condition and wall transition positions of hypersonic sharp wedge boundary layer move much leading edge than those of the flat plate. The greater the oncoming flow the closer the transition position to the leading edge.展开更多
We show that there is a quantum Sl_q(2) group symmetry in Hofstadter problem on square lattice.The cyclic representation of the quantum group is discussed and its application for computing the degeneracy density of th...We show that there is a quantum Sl_q(2) group symmetry in Hofstadter problem on square lattice.The cyclic representation of the quantum group is discussed and its application for computing the degeneracy density of the model is shown.展开更多
文摘The inverse problem for a class of nonlinear evolution equations of dispersive type type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution it,as given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhong-xin.
基金Supported in part by the National Natural Science Foundation of China under Grant No 10605013, the Program for New Century Excellent Talents in University, and the Project-sponsored by SRF for ROCS, SEM.
文摘We show that all pure entangled states of two d-dimensional quantum systems （i.e., two qudits） can be generated from an initial separable state via a universal Yang-Baxter matrix if one is assisted by local unitary transformations.
文摘We describe some recent developments of high-Reynolds-number asymptotic theory for the nonlinear stage of laminar-turbulent transition in nearly parallel flows.The classic weakly nonlinear theory of Landau and Stuart is briefly revisited with the dual purposes of highlighting its fundamental ideas,which continue to underlie much of current theoretical thinking,as well as its difficulty in dealing with unbounded flows.We show that resolving such a difficulty requires an asymptotic approach based on the high-Reynolds-number assumption,which leads to a nonlinear critical-layer theory.Major recent results are reviewed with emphasis on the non-equilibrium effect.Future directions of investigation are indicated.
基金supported by the National Natural Science Foundation of China(Nos.11172203 and91216111)the National Basic Research Program of China(No.2009CB724103)
文摘When the air temperature reaches 600 K or higher, vibration is excited. The specific heat is not a constant but a function of temperature. Under this condition, the transition position of hypersonic sharp wedge boundary layer is predicted by using the improved eN method considering variable specific heat. The transition positions with different Mach numbers of oncoming flow, half wedge angles, and wall conditions are computed condition, the nearer to the Mach number The results show that for the same oncoming flow condition and wall transition positions of hypersonic sharp wedge boundary layer move much leading edge than those of the flat plate. The greater the oncoming flow the closer the transition position to the leading edge.
文摘We show that there is a quantum Sl_q(2) group symmetry in Hofstadter problem on square lattice.The cyclic representation of the quantum group is discussed and its application for computing the degeneracy density of the model is shown.
