Radially symmetric solutions of the p‐Laplacian with critical Sobolev–Hardy exponent in perforated‐like domain

In this paper, we establish the existence of radially symmetric solutions of the p‐Laplacian with a concave term and critical Sobolev–Hardy exponent in a perforated‐like domain. Copyright © 2011 John Wiley & Sons, Ltd.     

Finiteness of conical algorithms with ω-subdivisions

In this paper the problem of finding the global optimum of a concave function over a polytope is considered. A well-known class of algorithms for this problem is the class of conical algorithms. In particular, the conical algorithm based on the so called ω-subdivision strategy is considered. It is proved that, for any given accuracy ε>0, this algorithm stops in a finite time by returning an ε-optimal solution for the problem, while it is convergent for ε=0. Received January 24, 1996 / Revised version received December 9, 1998 Published online June 11, 1999     

稳恒磁场下金属电沉积枝晶生长的模拟

采用Monte-Carlo模拟方法,给出用于描述稳恒磁场作用下电沉积枝晶生长的模型.该模型综合考虑了外加磁场B,电解溶液浓度和离子在阴极发生还原反应的几率P_s等因素对电沉积过程的影响,模拟得到与实验结果一致的枝晶生长图形.模拟结果表明:团簇的形状和它们的分形维数都与外加磁场B的强弱,即体现在模型中离子的旋转角速度ω的大小有关;随着磁场强度的增加,沉积团簇会从分形向非分形转变;在相对强的外加磁场作用下,较高离子浓度时的沉积物是非分形的;离子在阴极的反应概率P_s越小,随着磁场强度的增加枝晶生长越易趋向非分形.     

Dendritic Polymers in Biomedical Applications: From Potential to Clinical Use in Diagnostics and Therapy

Dendrimers are characterized by a combination of high end‐group functionality and a compact, precisely defined molecular structure. These characteristics can be used in biomedical applications, for example, for the amplification or multiplication of effects on a molecular level, or to create extremely high local concentrations of drugs, molecular labels, or probe moieties. A brief summary of the current state of the art in the field is given, and focuses on the application of dendrimers both in diagnostics as well as in therapy. In diagnostics, dendrimers that bear Gd^III complexes are used as contrast agents in magnetic resonance imaging. DNA dendrimers have potential for routine use in high‐throughput functional genomic analysis, as well as for DNA biosensors. Dendrimers are also being investigated for therapeutics, for example, as carriers for controlled drug delivery, in gene transfection, as well as in boron neutron‐capture therapy. Furthermore, the antimicrobial activity of dendrimers has been studied.     

Dendritic polymers: from efficient catalysis to drug delivery

Dendritic polymers constitute an intriguing class of macromolecules that offer tremendous potential in designing new materaisl for applications in areas such as catalysis and small molecule loading and delivery. Synthesis of a variety of dendritic polymers using a simple and highly versatile synthetic methodology has enabled us to carry out a detailed investigation of dendritic effects in transition metal catalyzed organic transformations. Small dye molecules such as p-nitroaninline and DR1 could be loaded into the intrinsic cavities of the backbone of 3,5-dihydroxybenzyl alcohol based dendrimers, leading to a change in physical properties of both the dye and the dendrimer. We are also exploring the use of dendrimers as templates to prepare network carriers containing cavities of predetermined size and disposition.     

Synthesis of hybrid dendritic‐linear block copolymers with dendritic initiators prepared by convergent living anionic polymerization

Hybrid dendritic‐linear block copolymers were made in one‐pot by convergent living anionic polymerization. Dendritic polystyrene macroinitiators were synthesized by slowly adding a mixture of either vinylbenzyl chloride (VBC) or 4‐(chlorodimethylsilyl)styrene (CDMSS) and styrene (1 : 10 molar ratio of coupling agent to styrene) to a solution of living polystyryllithium. The addition was ceased prior to the addition of a stoichiometric amount of coupling agent to retain a living chain end. To the living dendritically branched polystyrene was then added either styrene or isoprene to polymerize a linear block from the dendritic polystyrene. The resulting copolymers were characterized by gel permeation chromatography coupled with multiangle laser light scattering (GPC‐MALLS), which clearly demonstrated the formation of diblock copolymers. The diblock copolymers were further characterized by ¹H NMR, which showed the presence of the two blocks in the case of dendritic polystyrene‐block‐linear polyisoprene. The measurement of intrinsic viscosity showed that the dilute solution properties of the block copolymers are greatly influenced by the dendritic portion. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 152–161, 2001     

Hyperbranched polymers with maleic functional groups as radical crosslinkers

The crosslinking performance of the unsaturated hyperbranched polyester poly(allyloxy maleic acid‐co‐maleic anhydride) (MAHP) was investigated with copolymerizations of three different monomers: styrene, vinyl acetate, and methyl methacrylate. Both styrene and vinyl acetate afforded interpenetrating‐polymer‐network copolymer gels. The gels exhibited crosslink density gradients through the polymer matrices on a macroscopic level, and density maximums were concentrated around the MAHP moieties. The heterogeneity of the gels is briefly discussed in terms of a modified two‐phase model, where one phase consists of an elastic part of low crosslinking density and the other phase consists of an inelastic dendritic part with a highly condensed bond density. Unlike the two‐phase model developed by Choquet and Rietsch, the modified two‐phase model takes into account that both phases swell in good solvents. Unlike copolymerizations employing styrene or vinyl acetate, the copolymerization of MAHP with methyl methacrylate afforded noncrosslinked starbranched copolymers that consisted of a MAHP core from which long poly(methyl methacrylate) branches were protruding. The different behaviors of the copolymerizations of the three monomers used in this study can rationally be explained by their different reactivity ratios with maleic end groups of MAHP. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 964–972, 2001     

Poly(propylene imine) dendrimer complexes of Cu(II), Zn(II), and Co(III) as catalysts of hydrolysis of p-nitrophenyl diphenyl phosphate

Poly(propylene imine) dendrimers having 8, 32, and 64 primary amine end groups form diamino Cu(II), diamino Zn(II), and tetramino Co(III) complexes that are identified spectrophotometrically and titrimetrically. The dendrimer–metal ion complexes catalyze the hydrolysis of p-nitrophenyl diphenyl phosphate in zwitterionic buffer solutions at pH ≤ 8.1 with relative activities Cu(II) > Zn(II) > Co(III). The rates of hydrolysis are faster with sodium perchlorate than with sodium chloride to control ionic strength. In sodium perchlorate solutions with Cu(II) the rates increase with increasing size of the dendrimer. In sodium chloride solutions with Cu(II) the rates decrease with increasing size of the dendrimer. Rate constants in buffered sodium chloride solutions of dendrimers and 1.0mM Cu(II) are 1.3–6.3 times faster than in the absence of Cu(II). The fastest hydrolyses occurred at a dendrimer primary amine to Cu(II) ratio NH₂/Cu ≤ 2. At NH₂/Cu = 4 and with the 1,4,7,10-tetraazacyclodecane complex of Cu(II) hydrolysis rates were much slower. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 2727–2736, 1999