非齐次马氏链二元泛函的若干极限性质

用分析方法研究非齐次马尔科夫链的极限性质,得到了关于有限非齐次马氏链二元函数的一类平均值的一组极限定理,其中包括对任意有限非齐次马氏链均成立的几个极限性质。     

对数似然比的一类极限性质

设Ｘｎ,ｎ≥１是在Ｓ＝１,２,…中取值的随机变量系列,其联合分布为ｐ（ｘ１,…,ｘｎ）,（ｐｎ（１））,ｐｎ（２）,…）是Ｓ上的一列分布,ｋ∈Ｓ,Ｓｎ（ｋ,ω）是ｋ在序列Ｘ１（ω）,…,Ｘｎ（ω）中出现的次数。令φｎ（ω）＝∑＾ｎｉ＝１ｌｏｇｐｉ（Ｘｉ）－ｌｏｇｐ（Ｘ１,…,Ｘｎ）,ψｎ（ｋ,ω）＝Ｓｎ（ｋ,ω）－∑＾ｎｉ＝１ｐｉ（ｋ）。本文研究φｎ（ω）与ψｎ（ｋ,ω）之间的某些极限关系     

Remarkable structure effects on thermoresponsive properties of dendritic macromolecules

Amphiphilic dendritic macromonomers and their corresponding dendronized polymers were synthesized, and their thermoresponsive properties investigated. These dendritic macromolecules are constructed with a second generation lysine-based dendron as the interior (hydrophobic part) and oligoethylene glycol (OEG) linear chains or dendrons (hydrophilic part) covered in their periphery. By changing from OEG linear chains to OEG dendrons, these dendritic macromolecules carry on their periphery different density of OEG moieties, to investigate the structural effects on their thermoresponsiveness. Topology of dendritic macromolecules changes through polymerization, and the fan-shaped dendritic macromonomers transfer into the corresponding cylindrically shaped dendronized polymers. Furthermore, the amphiphilic characteristic of these dendritic entities can be switched due to the thermally-induced dehydration of OEG moieties. It was found that topology, OEG density in the periphery and switchable amphiphilicity of these dendritic macromolecules show significantly effects on their thermoresponsiveness.