Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of fun...Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of function of class A(D) are presented. Moreover in general the order of approximation is sharp.展开更多
Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges...Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.展开更多
This paper studies the asymptotic behavior of solutions to an evolutionary Ginzburg-Landau equation in 3 dimensions. It is shown that the motion of the Ginzburg-Landau vortex curves is the flow by its curvature. Away ...This paper studies the asymptotic behavior of solutions to an evolutionary Ginzburg-Landau equation in 3 dimensions. It is shown that the motion of the Ginzburg-Landau vortex curves is the flow by its curvature. Away from the vortices, the author uses some measure theoretic arguments used by F. H. Lin in [16] to show the strong convergence of solutions.展开更多
文摘Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of function of class A(D) are presented. Moreover in general the order of approximation is sharp.
基金supported by National Natural Science Foundation of China (Grant No.11071190)
文摘Abstract Let x = （xn）n≥1 be a martingale on a noncommutative probability space （М,τ） and （Wn）n≥1 a sequence of positive numbers such that Wn =∑^n_k=1 wk→∞ as n→∞. We prove that x = （Xn）n≥1 converges bilaterally almost uniformly （b.a.u.） if and only if the weighted average （σan（x））n≥1 of x converges b.a.u, to the same limit under some condition, where σn（x） is given by σn（x）=1/Wn ^n∑_k=1 wkxk,n=1,2,… Furthermore, we prove that x = （xn）n≥1 converges in Lp（М） if and only if （σ＇n（x））n≥1 converges in Lp（М）, where 1 ≤p 〈 ∞ .We also get a criterion of uniform integrability for a family in L1（М）.
基金the National Natural Science Foundation of China (No. 10071067).
文摘This paper studies the asymptotic behavior of solutions to an evolutionary Ginzburg-Landau equation in 3 dimensions. It is shown that the motion of the Ginzburg-Landau vortex curves is the flow by its curvature. Away from the vortices, the author uses some measure theoretic arguments used by F. H. Lin in [16] to show the strong convergence of solutions.
