Carleson measures on planar sets

In this paper, we investigate what are Carleson measures on open subsets in the complex plane. A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles. We call a domain G multi-nicely connected if there exists a circular domain W and a conformal map ψ from W onto G such that ψ is almost univalent with respect the arclength on δW. We characterize all Carleson measures for those open subsets so that each of their components is multinicely connected and harmonic measures of the components are mutually singular. Our results suggest the extension of Carleson measures probably is up to this class of open subsets     

The equivalence between the TE,TM model and the Darwin models

In this paper,we study the TE,TM model by using the decompositions of the vector fields in 2-D bounded multiply connected domains and 2-D unbounded domains,respectively.We find that the TE,TM model and the Darwin models are equivalent if we assume some regularity of the initial data.     

The Neumann problem and Helmholtz decomposition in convex domains

We show that the Neumann problem for Laplace's equation in a convex domain Ω with boundary data in Lp(∂Ω) is uniquely solvable for 1<p<∞. As a consequence, we obtain the Helmholtz decomposition of vector fields in Lp(Ω,Rd).     

Mechanical properties of amphiphilic urethane acrylate ionomer hydrogels having heterophasic gel structure

Amphiphilic urethane acryale hydrogels containing ionic groups (dimethylolpropionic acid) were prepared by varying the molecular weight of the soft segment (polyether type) and the type of diisocyanate, and their mechanical properties were examined. They showed heterophasic gel structure composed of ionic hard domains induced by aggregation of the ionic groups and polyether soft domains comprising the urethane acrylate network. This heterophasic structure could be confirmed by dynamic mechanical analysis (DMA) and by wide-angle X-ray scattering analysis (WAXS); the crystallinity detected by WAXS and the transition peak of the ionic hard domains detected by DMA strongly suggested that there were ionic aggregates. These ionic aggregates acted as reinforcing fillers in the network, which eventually enhanced the tensile strength of the hydrogels. Above all, the tensile properties of the hydrogels were of interest in that the trends of the stress-strain curves were consistent with the rubbery ones. It is believed that the higher purity of the polyether soft domains resulted from the heterophasic gel structure imparting further elastomeric properties on the network. Received: 31 July 1998 Accepted in revised form: 15 October 1998     

On solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives

We obtain estimates and blow-up conditions for solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives.     

The Lp - Lq Estimates for the Wave Equation with A nonnegative Potential

In this paper, some Fredholm properties of the Dirichlet problem for the Laplace operator in an exterior domain are given in weighted Hölder spaces. These results extend the corresponding approach in weighted L ^p -Sobolev spaces.     

Canonical Metrics on Generalized Cartan-Hartogs Domains

In this paper, the author considers a class of bounded pseudoconvex domains,i.e., the generalized Cartan-Hartogs domains Ω(μ, m). The first result is that the natural Khler metric g~(Ω(μ,m)) of Ω(μ, m) is extremal if and only if its scalar curvature is a constant. The second result is that the Bergman metric, the Ka¨hler-Einstein metric, the Carathéodary metric, and the Koboyashi metric are equivalent for Ω(μ, m).     

Large ‐ or ‐Minors in 3‐Connected Graphs

There are numerous results bounding the circumference of certain 3‐connected graphs. There is no good bound on the size of the largest bond (cocircuit) of a 3‐connected graph, however. Oporowski, Oxley, and Thomas (J Combin Theory Ser B 57 (1993), 2, 239–257) proved the following result in 1993. For every positive integer k, there is an integer such that every 3‐connected graph with at least n vertices contains a ‐ or ‐minor. This result implies that the size of the largest bond in a 3‐connected graph grows with the order of the graph. Oporowski et al. obtained a huge function iteratively. In this article, we first improve the above authors' result and provide a significantly smaller and simpler function . We then use the result to obtain a lower bound for the largest bond of a 3‐connected graph by showing that any 3‐connected graph on n vertices has a bond of size at least . In addition, we show the following: Let G be a 3‐connected planar or cubic graph on n vertices. Then for any , G has a ‐minor with , and thus a bond of size at least .     

Reinhardt域上一类推广的Roper-Suffridge算子

研究一类推广的Roper-Suffridge算子F(z)=(f(z_1)+f′(z_1)∑_(k=2)~nakz_k~pk,f′(z)1)(~1/p2)z_2,…,f′(z_1)~(1/pn)z_n)′,证明该算子在复欧氏空间中的Reinhardt域Ω_(n,p2,%…,pn)={z=(z_1,…,z_n)∈C~n:|z_|~2+∑_(k=2)~n|zk|~(pk)1,Pk∈N~+,k=2,…,n}上分别保持α次的殆β型螺形性,α次的β型螺形性及强β型螺形性.