复环面情形的Suita猜想

对任意复环面的情形证明了推广的Suita猜想,即απK≥c~2(α∈R),其中c是修正后的对数容度,K是对角线上的Bergman核.还阐明了对任意亏格≥2的紧Riemann面情形的公开问题.文中结果的证明部分地依赖于椭圆函数理论.     

Lag projective synchronization of a class of complex network constituted nodes with chaotic behavior

In this paper, a method of the lag projective synchronization of a class of complex network constituted nodes with chaotic behavior is proposed. Discrete chaotic systems are taken as nodes to constitute a complex network and the topological structure of the network can be arbitrary. Considering that the lag effect between network node and chaos signal of target system, the control input of the network and the identification law of adjustment parameters are designed based on Lyapunov theorem. The synchronization criteria are easily verified.     

ON THE DIFFERENCE COUNTERPART OF BRUCK＇S CONJECTURE

In this article, for a transcendental entire function f（z） of finite order which has a finite Borel exceptional value a, we utilize properties of complex difference equations to prove the difference counterpart of Bruck＇s conjecture, that is, if △f（z） = f（z ＋ η） - f（z） and f（z） share one value a （≠α） CM, where η ∈ C is a constant such that f（z ＋η） ≠ f（z）,then
△f（z）-a/f（z）-a=a/a-α.     

Parameter space for families of parabolic-like mappings

In this paper we study families of degree 2 parabolic-like mappings _(fλ)λ∈Λ${(f_{\lambda })}_{\lambda \in \Lambda }$ (as defined in [4]). We prove that the hybrid conjugacies between a nice analytic family of degree 2 parabolic-like mappings and members of the family _Per1(1)${\mathit{Per}}_1(1)$ induce a continuous map χ:Λ→C$\chi :\Lambda \to \mathbb{C}$, which under suitable conditions restricts to a ramified covering from the connectedness locus of _(fλ)λ∈Λ${(f_{\lambda })}_{\lambda \in \Lambda }$ to the connectedness locus _M1?{1}$M_1?\{1\}$ of _Per1(1)${\mathit{Per}}_1(1)$. As an application, we prove that the connectedness locus of the family _Ca(z)=z+az²+z³$C_a(z)=z+a{z}^2+z^3$, a∈C$a\in \mathbb{C}$ presents baby _M1$M_1$.     

Relations between the Kähler cone and the balanced cone of a Kähler manifold

In this paper, we consider a natural map from the Kähler cone of a compact Kähler manifold to its balanced cone. We study its injectivity and surjectivity. We also give an analytic characterization theorem on a nef class being Kähler.     

Shatalov‐Sternin's construction of complex WKB solutions and the choice of integration paths

We re‐examine Shatalov‐Sternin's proof of existence of resurgent solutions of a linear ODE. In particular, we take a closer look at the “Riemann surface” (actually, a two‐dimensional complex manifold) whose existence, endless continuability and other properties are claimed by those authors. We present a detailed argument for a part of the “Riemann surface” relevant for the exact WKB method.