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.

3.0mm以下热轧薄规格宽带钢的开发

针对常规热连轧生产线开发薄规格带钢过程中通常遇到的加热温度、轧机设备精度、轧机负荷及各机架间的负荷分配、板形控制系统等制约因素,莱钢银山型钢有限公司板带厂通过采取钢坯前端低温加热、后端高温加热,均衡轧制节奏并建立适宜的轧辊热凸度,优化烫辊制度和轧制单位编排制度,优化精轧负荷分配方式和负荷分配参数,开发基于现场生产线的精轧模型仿真平台,调整辊型及辊温控制,降低卷取张力等措施,实现了厚3.0mm以下薄规格带钢的批量生产,且带钢厚度命中率达95.03%,通条凸度、楔形指标平均达标率达98.1%,平直度平均达标率为98.4%。