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...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.展开更多
After analysing the disadvantages of the traditional residue hydrotreating-catalytic cracking combination process, RIPP has proposed a bi-directional combination technology integrating residue hydrotreating with catal...After analysing the disadvantages of the traditional residue hydrotreating-catalytic cracking combination process, RIPP has proposed a bi-directional combination technology integrating residue hydrotreating with catalytic cracking called RICP which does not further recycles the FCC heavy cycle oil (HCO) inside the FCC unit and delivers HCO to the residue hydrotreating unit as a diluting oil for the residue that is concurrently subjected to hydrotreating prior to being used as the FCC feed oil. The RICP technology can stimulate residue hydrotreating reactions through utilization of HCO along with an in- creased yield of FCC light distillate, resulting in enhanced petroleum utilization and economic benefits of the refinery.展开更多
文摘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.
文摘After analysing the disadvantages of the traditional residue hydrotreating-catalytic cracking combination process, RIPP has proposed a bi-directional combination technology integrating residue hydrotreating with catalytic cracking called RICP which does not further recycles the FCC heavy cycle oil (HCO) inside the FCC unit and delivers HCO to the residue hydrotreating unit as a diluting oil for the residue that is concurrently subjected to hydrotreating prior to being used as the FCC feed oil. The RICP technology can stimulate residue hydrotreating reactions through utilization of HCO along with an in- creased yield of FCC light distillate, resulting in enhanced petroleum utilization and economic benefits of the refinery.
