Combinations of Right Half-Plane Mappings and Vertical Strip Mappings Convex in the Vertical Direction

In this paper, we explore the linear combinations of right half-plane mappings and vertical strip mappings. We demonstrate that the combinations of these harmonic mappings are convex in the vertical direction provided they are locally univalent and sense-preserving. Furthermore, we extend this analysis to a more general case by setting specific conditions. Additionally, we take some common parameters such as as the dilatation of these harmonic mappings, and prove the sufficient conditions that their combinations are locally univalent and convex in the vertical direction. Several examples are constructed by the Mathematica software to demonstrate our main results.

α_1-抗胰蛋白酶的分离纯化

为建立从Cohn′s组分IV沉淀中分离纯化α1-抗胰蛋白酶(α1-antitrypsin,α1-AT)的技术路线,以Cohn′s组分IV为原料,利用还原剂1,4-二硫苏糖醇(DTT)、气相二氧化硅等处理,再经压滤、离子交换层析和疏水层析提取α1-AT。用SDS-PAGE及合成基质法检测α1-AT的纯度以及生物活性。结果可见,Cohn组分IV沉淀中α1-AT占蛋白总量的11%～13%,经该工艺提取的α1-抗胰蛋白酶纯度为97.6%,疏水层析后α1-AT的收获率为21%,比活为每毫克总蛋白中含0.54mg功能活性α1-AT。可见用此方法从Cohn组分IV沉淀中可制备高纯度的α1-AT。