In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities...In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.展开更多
In this paper we study the average σ-K width and the average σ-linear width of the unit ball of l;（R） inl;（R）. The exact values of these widths are calculated and an optimal subspace with the optimal linear oper...In this paper we study the average σ-K width and the average σ-linear width of the unit ball of l;（R） inl;（R）. The exact values of these widths are calculated and an optimal subspace with the optimal linear opera-tor （for the σ- linear width） are identified.展开更多
In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are defined.We exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto...In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are defined.We exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto A(ф).Using these projections,we show that A(ф)~*≌A~1(ф)and A~1(ф)~*≌A(ф).展开更多
We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner...We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.展开更多
基金supported by the NNSF of China(11001074,11061015,11101124)the Foundation for University Young Key Teacher of Henan Province
文摘In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.
文摘In this paper we study the average σ-K width and the average σ-linear width of the unit ball of l;（R） inl;（R）. The exact values of these widths are calculated and an optimal subspace with the optimal linear opera-tor （for the σ- linear width） are identified.
基金Supported in part by the National Natural Science Foundation of China.
文摘In this paper three Banach spaces A(ф),A(ф)and A~1(ф)of functions holomor- phic in the unit ball B of ■~n are defined.We exhibit bounded projections from C(B)onto A(ф),from L~1(B)onto A~1(ф),and from L~∞(B)onto A(ф).Using these projections,we show that A(ф)~*≌A~1(ф)and A~1(ф)~*≌A(ф).
文摘We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.
