Consider the following system of double coupled Schrodinger equations arising from Bose-Einstein condensates etc., where μ1, μ2 are positive and fixed; κ and β are linear and nonlinear coupling parameters respect...Consider the following system of double coupled Schrodinger equations arising from Bose-Einstein condensates etc., where μ1, μ2 are positive and fixed; κ and β are linear and nonlinear coupling parameters respectively. We first use critical point theory and Liouville type theorem to prove some existence and nonexistence results on the positive solutions of this system. Then using the positive and non-degenerate solution to the scalar equation -△ω ＋ ω = ω3, ω ∈ Hr1（RN）, we construct a synchronized solution branch to prove that for/3 in certain range and fixed, there exist a series of bifurcations in product space R×Hr1（RN）×Hr1（RN） with parameter κ,展开更多
Let g be an n-Lie superalgebra. We study the double derivation algebra 7）（g） and describe the relation between 7）（9） and the usual derivation Lie superalgebra Der（9）. We show that the set 7）（9） of all doubl...Let g be an n-Lie superalgebra. We study the double derivation algebra 7）（g） and describe the relation between 7）（9） and the usual derivation Lie superalgebra Der（9）. We show that the set 7）（9） of all double derivations is a subalgebra of the general linear Lie superalgebra gl（9） and the inner derivation algebra ad（9） is an ideal of 7）（9）. We also show that if 9 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad（9） in 7P（9） is trivial. Finally, we give that for every perfect n-Lie superalgebra 9, the triple derivations of the derivation algebra Der（9） are exactly the derivations of Der（9）.展开更多
We prove the so-called Unitary Hyperbolicity Theorem,a result on hyperbolicity of unitary involutions.The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the...We prove the so-called Unitary Hyperbolicity Theorem,a result on hyperbolicity of unitary involutions.The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the unitary one.While the original proofs in the orthogonal and symplectic cases were based on the incompressibility of generalized Severi-Brauer varieties,the proof in the unitary case is based on the incompressibility of their Weil transfers.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11325107,11271353 and 11331010)the China Postdoctoral Science Foundation
文摘Consider the following system of double coupled Schrodinger equations arising from Bose-Einstein condensates etc., where μ1, μ2 are positive and fixed; κ and β are linear and nonlinear coupling parameters respectively. We first use critical point theory and Liouville type theorem to prove some existence and nonexistence results on the positive solutions of this system. Then using the positive and non-degenerate solution to the scalar equation -△ω ＋ ω = ω3, ω ∈ Hr1（RN）, we construct a synchronized solution branch to prove that for/3 in certain range and fixed, there exist a series of bifurcations in product space R×Hr1（RN）×Hr1（RN） with parameter κ,
文摘Let g be an n-Lie superalgebra. We study the double derivation algebra 7）（g） and describe the relation between 7）（9） and the usual derivation Lie superalgebra Der（9）. We show that the set 7）（9） of all double derivations is a subalgebra of the general linear Lie superalgebra gl（9） and the inner derivation algebra ad（9） is an ideal of 7）（9）. We also show that if 9 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad（9） in 7P（9） is trivial. Finally, we give that for every perfect n-Lie superalgebra 9, the triple derivations of the derivation algebra Der（9） are exactly the derivations of Der（9）.
文摘We prove the so-called Unitary Hyperbolicity Theorem,a result on hyperbolicity of unitary involutions.The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the unitary one.While the original proofs in the orthogonal and symplectic cases were based on the incompressibility of generalized Severi-Brauer varieties,the proof in the unitary case is based on the incompressibility of their Weil transfers.
