This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
设T是核满足Dini条件的多线性奇异积分算子,T∗是T的极大算子。T∗b,S是T∗与一类可测函数{bi}∞i=1生成的广义交换子。本文讨论了当{bi}∞i=1属于Lipschitz空间,T∗b,S在Lebesgue 空间的有界性。Let T be an m-linear Calder´on-Zygmu...设T是核满足Dini条件的多线性奇异积分算子,T∗是T的极大算子。T∗b,S是T∗与一类可测函数{bi}∞i=1生成的广义交换子。本文讨论了当{bi}∞i=1属于Lipschitz空间,T∗b,S在Lebesgue 空间的有界性。Let T be an m-linear Calder´on-Zygmund operator with kernel satisfying Dini-type condition, T∗be the maximal operator of T. T∗b,Sis the generalized commutator of T∗ with a class of measurable functions {bi}∞i=1.In this paper, we discuss the boundedness of T∗b,S on Lebesgue spaces when {bi}∞i=1 belongs to Lipschitz spaces.展开更多
本文讨论了p-进域上的奇异积分算子与Lipschitz函数生成的交换子的有界性, 证明了交换子是从Lebesgue空间IJCampanato空间有界的。In this paper, we discussed the boundedness of commutator generated by singular integral operator...本文讨论了p-进域上的奇异积分算子与Lipschitz函数生成的交换子的有界性, 证明了交换子是从Lebesgue空间IJCampanato空间有界的。In this paper, we discussed the boundedness of commutator generated by singular integral operator and Lipschitz function on the p-adic field. We proved that the commutator is bounded from Lebesgue space to certain Campanato space.展开更多
A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gr...A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
文摘设T是核满足Dini条件的多线性奇异积分算子,T∗是T的极大算子。T∗b,S是T∗与一类可测函数{bi}∞i=1生成的广义交换子。本文讨论了当{bi}∞i=1属于Lipschitz空间,T∗b,S在Lebesgue 空间的有界性。Let T be an m-linear Calder´on-Zygmund operator with kernel satisfying Dini-type condition, T∗be the maximal operator of T. T∗b,Sis the generalized commutator of T∗ with a class of measurable functions {bi}∞i=1.In this paper, we discuss the boundedness of T∗b,S on Lebesgue spaces when {bi}∞i=1 belongs to Lipschitz spaces.
文摘本文讨论了p-进域上的奇异积分算子与Lipschitz函数生成的交换子的有界性, 证明了交换子是从Lebesgue空间IJCampanato空间有界的。In this paper, we discussed the boundedness of commutator generated by singular integral operator and Lipschitz function on the p-adic field. We proved that the commutator is bounded from Lebesgue space to certain Campanato space.
基金supported by the Guangxi Science and Technology base and Talent Project(AD22080047)the National Natural Science Foundation of Guangxi Province(2023GXNFSBA 026063)+1 种基金the Innovation Funds of Chinese University(2021BCF03001)the special foundation for Guangxi Ba Gui Scholars.
文摘A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.
