A Generalization of Lappan’s Theorem to Higher Dimensional Complex Projective Space

In this paper, the authors discuss a generalization of Lappan’s theorem to higher dimensional complex projective space and get the following result: Let f be a holomorphic mapping of ? into Pⁿ(C), and let H₁, · · · , H_q be hyperplanes in general position in Pⁿ(C).Assume that sup {(1 ? |z|²)f^?(z) : z ∈ q[ j=1 f^?1(H_j )o < ∞,if q ≥ 2n² + 3, then f is normal.     

Ground States of K-component Coupled Nonlinear Schrödinger Equations with Inverse-square Potential

In this paper, the authors study ground states for a class of K-component coupled nonlinear Schr¨odinger equations with a sign-changing potential which is periodic or asymptotically periodic. The resulting problem engages three major difficulties: One is that the associated functional is strongly indefinite, the second is that, due to the asymptotically periodic assumption, the associated functional loses the Z^N -translation invariance,many effective methods for periodic problems cannot be applied to asymptotically periodic ones. The third difficulty is singular potential μ_i/|x|² , which does not belong to the Kato’s class. These enable them to develop a direct approach and new tricks to overcome the difficulties caused by singularity and the dropping of periodicity of potential.     

Boundedness and continuity of maximal singular integrals and maximal functions on Triebel-Lizorkin spaces

In this paper, we systematically study several classes of maximal singular integrals and maximal functions with rough kernels in F_β(S~(n-1)), a topic that relates to the Grafakos-Stefanov class. The boundedness and continuity of these operators on Triebel-Lizorkin spaces and Besov spaces are discussed.     

The Refined Schwarz-Pick Estimates for Positive Real Part Holomorphic Functions in Several Complex Variables

In this article,the refined Schwarz-Pick estimates for positive real part holomorphic functions■are given,where k is a positive integer,and G is a balanced domain in complex Banach spaces.In particular,the results of first order Fréchet derivative for the above functions and higher order Frechet derivatives for positive real part holomorphic functions■are sharp for G=B,where B is the unit ball of complex Banach spaces or the unit ball of complex Hilbert spaces.Their results reduce to the classic...     

Large m asymptotics for minimal partitions of the Dirichlet eigenvalue

In this paper,we study large m asymptotics of the l 1 minimal m-partition problem for the Dirichlet eigenvalue.For any smooth domainΩ?Rⁿsuch that|Ω|=1,we prove that the limit lim_m→∞l¹_m(Ω)=c 0 exists,and the constant c 0 is independent of the shape ofΩ.Here,l¹_m(Ω)denotes the minimal value of the normalized sum of the first Laplacian eigenvalues for any m-partition ofΩ.