Class I graphs of nonnegative characteristic without special cycles

In this paper, we prove that every graph with maximum degree six that can be embedded in a surface of nonnegative characteristic is of Class I if it does not contain a 5- or 6-cycle with a chord, which extends some known results.     

Multilinear Hausdorff operators and their best constants

In this paper, we study two different extensions of the Hausdorff operator to the multilinear case. Boundedness on Lebesgue spaces and Herz spaces is obtained. The bound on the Lebesgue space is optimal. Our results are substantial extensions of some known results on Multilinear high dimensional Hardy operator.     

Stability analysis in a nonlinear ecological model

A high dimension predator-prey model is considered in this paper. Some novel criteria are established for the existence and global asymptotic stability of a unique equilibrium of such model. The approaches are based on fixed point theory, matrix spectral theory and Lyapunov functional. The existence and stability conditions given in terms of spectral radius of explicit matrices are better than conditions obtained by using classic norms. Finally, an example and its simulations show the feasibility of our results.     

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.     

Planar graphs with maximum degree 7 and without 5-cycles are 8-totally-colorable

It is proved that planar graphs with maximum degree 7 and without 5-cycles are 8-totally-colorable.     

Aerobic oxidation of alcohols to aldehydes and ketones using ruthenium(III)/Et3N catalyst

A simple, efficient method for oxidation of primary and secondary alcohols to the corresponding aldehydes and ketones has been developed. Using RuCl₃/Et₃N as catalyst, the oxidation of benzyl alcohol with oxygen could be achieved with 332 h⁻¹ turnover frequency in the absence of solvent. The influence of versatile N‐containing additives on the catalytic efficiency has been discussed. The presence of minor water would substantially promote the catalytic efficiency, and its role in catalysis has been investigated in detail. The insensitive Hammett correlations of the substituted benzyl alcohols, the normal substrate isotope effect (k_H/k_D = 3.5 at 335 K), and the linear relationship between O₂ pressure and turnover frequency imply that the reoxidation of the Ru(III) hydride intermediate to the active species shares the rate‐determining step with the hydride transfer in the catalytic cycle. Copyright © 2011 John Wiley & Sons, Ltd.     

On the 9-total-colorability of planar graphs with maximum degree 8 and without intersecting triangles

Recently, Kowalik, Sereni, and ?krekovski proved that planar graphs with maximum degree 9 are 10-totally colorable. This work proves that planar graphs with maximum degree 8 and without intersecting triangles are 9-totally colorable.