Holomorphic Lefschetz Fixed Point Formula for Non-compact K¨ahler Manifolds

The authors obtain a holomorphic Lefschetz fixed point formula for certain non-compact “hyperbolic” Kǎihler manifolds （e.g. Kǎihler hyperbolic manifolds, bounded domains of holomorphy） by using the Bergman kernel. This result generalizes the early work of Donnelly and Fefferman.     

Bloch constant of holomorphic mappings on the unit polydisk of ℂ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In this paper, we give a definition of Bloch mappings defined in the unit polydisk D ⁿ , which generalizes the concept of Bloch functions defined in the unit disk D. It is known that Bloch theorem fails unless we have some restrictive assumption on holomorphic mappings in several complex variables. We shall establish the corresponding distortion theorems for subfamilies β(K) and β _loc(K) of Bloch mappings defined in the polydisk D ⁿ , which extend the distortion theorems of Liu and Minda to higher dimensions. As an application, we obtain lower and upper bounds of Bloch constants for various subfamilies of Bloch mappings defined in D ⁿ . In particular, our results reduce to the classical results of Ahlfors and Landau when n = 1. This work was supported by the National Natural Science Foundation of China (Grant No. 10571164) and Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) (Grant No. 20050358052)     

一些图的生成树数

图 G 的生成树是它的连通子图(子树).本文精确地计算出了一些图的生成树的数目, 例如双心轮图、双柄扇图等等.     

Organocatalytic and direct asymmetric vinylogous Michael addition of 3-cyano-4-methylcoumarins to α,β-unsaturated ketones

The first highly regio-, chemo-, and enantio-selective direct vinylogous Michael addition of 3-cyano-4-methylcoumarin derivatives to α,β-unsaturated ketones is described, employing readily available 9-amino-9-deoxy-epiquinine as the iminium organocatalyst.     

A Potassium-Lithium Double Salt of Decavanadate Showing Unprecedented(6, 8)-Connected Topology

A new potassium lithium double salt of decavanadate, K₄Li₂[V₁₀O₂₈]·10H₂O ( 1 ) has been synthesized and characterized. 1 crystallizes in the triclinic system, and features an unusual (6,8)‐connected network with the K₄O₃₂ clusters, Li₂O₁₀ clusters and V₁₀O₂₈ clusters. The K₄O₃₂ clusters and Li₂O₁₀ clusters share an edge and a triangle plane to form an infinite rod‐shaped chain. The chains are further interlinked by V₁₀O₂₈ clusters to generate the final 3D framework. UV‐Vis spectrum, fluorescent spectrum and cyclic voltammetry curves have been studied.     

Crystal Structure of catena-[（Tetrakis-μ2-acetato-μ2-4,4＇-bipyridine） dicopper（Ⅱ）] Acetonitrile Solvate

1 INTRODUCTION Much attention has been paid to 1D, 2D and 3D coordination polymers because they can meet the need of functional materials with desired structures and properties[1～5]. One strategy in the design and synthesis of coordination architectures is the buil- ding-block approach. Commonly, bi- or multidentate organic ligands containing N[6, 7] or O[8, 9] atoms have ever been used in the construction. In our cur- rent work, we have selected melamine ligand as the main building bl…     

Upper bounds on the linear chromatic number of a graph

A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is a union of vertex-disjoint paths. The linear chromatic number of G is the smallest number of colors in a linear coloring of G.Let G be a graph with maximum degree Δ(G). In this paper we prove the following results: (1) ; (2) if Δ(G)≤4; (3) if Δ(G)≤5; (4) if G is planar and Δ(G)≥52.     

Voltammetric sensor for caffeine based on a glassy carbon electrode modified with Nafion and graphene oxide

A facile, one-step and template-free method has been developed for the electrodeposition of well-dispersed platinum nanoparticles (Pt-NPs) on a glassy carbon electrode. The effects of various inorganic anions and overpotential on the morphologies and dimensions of the final products were investigated. The resulting Pt-NPs show high electrocatalytic activity towards methanol oxidation and are less easily poisoned by carbon monoxide.