A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable...A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable Hausdorff topological gyrogroup has a suitable set;moreover,it is shown that each separable metrizable strongly topological gyrogroup has a suitable set.展开更多
The evolution of both the metric and topological properties of the microstructure for Ni pow- der compacts at the late stages of sintering(V_v^s>0.90)has been investigated by means of stereological method.The effec...The evolution of both the metric and topological properties of the microstructure for Ni pow- der compacts at the late stages of sintering(V_v^s>0.90)has been investigated by means of stereological method.The effects of precompaction pressure and loose sintering have been stu- died and discussed.展开更多
Let (X, ∑, μ) be a σ-finite measure space, P : LI → L1 be a Markov operator, and Qt = ∑n=0 ∞ qn(t)Pn, where {qn(t)} be a sequence satisfying:i) qn(t) ≥ 0 and ∑n=0 ∞ qn(t)=1 for all t >0;ii)lim (q0(t) + ∑n...Let (X, ∑, μ) be a σ-finite measure space, P : LI → L1 be a Markov operator, and Qt = ∑n=0 ∞ qn(t)Pn, where {qn(t)} be a sequence satisfying:i) qn(t) ≥ 0 and ∑n=0 ∞ qn(t)=1 for all t >0;ii)lim (q0(t) + ∑n=1 ∞ |qn(t) -qn-1(t)|) = 0.t→∞f ∈ L1, it is proved that Qt(f) convergent strongly to a fixed point of P as t → 0 if and only if {Qt(f)}t>0 is precompact. Qt(f) is convergent if and only if the ergodic mean operator An(f) is convergent, and they have the same limit. If P is a double stochastic operator then lim Qtf = E(f|∑0) for all f ∈ L1, where ∑0 is the invariant σ-algebra ofP. Some related results are also given.展开更多
This paper studies the global behavior to 3D focusing nonlinear Schrodinger equation (NLS), the scaling index here is (0<sc<1), which is the mass-supercritical and energy-subcritical, and we prove under some con...This paper studies the global behavior to 3D focusing nonlinear Schrodinger equation (NLS), the scaling index here is (0<sc<1), which is the mass-supercritical and energy-subcritical, and we prove under some condition the solution u(t) is globally well-posed and scattered. We also show that the solution “blows-up in finite time” if the solution is not globally defined, as t→T we can provide a depiction of the behavior of the solution, where T is the “blow-up time”.展开更多
基金supported by Fujian Provincial Natural Science Foundation of China(2024J02022)the NSFC(11571158)+1 种基金supported by the NSFC(12071199)supported by the Young and middle-aged project in Fujian Province(JAT190397)。
文摘A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable Hausdorff topological gyrogroup has a suitable set;moreover,it is shown that each separable metrizable strongly topological gyrogroup has a suitable set.
文摘The evolution of both the metric and topological properties of the microstructure for Ni pow- der compacts at the late stages of sintering(V_v^s>0.90)has been investigated by means of stereological method.The effects of precompaction pressure and loose sintering have been stu- died and discussed.
基金Research is partially supported by the NSFC (60174048)
文摘Let (X, ∑, μ) be a σ-finite measure space, P : LI → L1 be a Markov operator, and Qt = ∑n=0 ∞ qn(t)Pn, where {qn(t)} be a sequence satisfying:i) qn(t) ≥ 0 and ∑n=0 ∞ qn(t)=1 for all t >0;ii)lim (q0(t) + ∑n=1 ∞ |qn(t) -qn-1(t)|) = 0.t→∞f ∈ L1, it is proved that Qt(f) convergent strongly to a fixed point of P as t → 0 if and only if {Qt(f)}t>0 is precompact. Qt(f) is convergent if and only if the ergodic mean operator An(f) is convergent, and they have the same limit. If P is a double stochastic operator then lim Qtf = E(f|∑0) for all f ∈ L1, where ∑0 is the invariant σ-algebra ofP. Some related results are also given.
文摘This paper studies the global behavior to 3D focusing nonlinear Schrodinger equation (NLS), the scaling index here is (0<sc<1), which is the mass-supercritical and energy-subcritical, and we prove under some condition the solution u(t) is globally well-posed and scattered. We also show that the solution “blows-up in finite time” if the solution is not globally defined, as t→T we can provide a depiction of the behavior of the solution, where T is the “blow-up time”.
