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
Selenium(Se)is an essential trace element involved in nearly all human physiological processes but suffers from a narrow margin between benefit and toxicity.The nanoform of selenium has been proven shown to be more bi...Selenium(Se)is an essential trace element involved in nearly all human physiological processes but suffers from a narrow margin between benefit and toxicity.The nanoform of selenium has been proven shown to be more bioavailable and less toxic,yet significant challenges remain regarding the efficient and feasible synthesis of biologically active nanoselenium.In addition,although nanoselenium has shown a variety of biological activities,more interesting nanoselenium features are expected.In this work,hydrosoluble nanoselenium termed Nano-Se in the zero oxidation state was synthesized between gray Se and PEG.A zebrafish screen was carried out in zebrafish larvae cocultured with Nano-Se.Excitingly,Nano-Se promoted the action of the FGFR,Wnt,and VEGF signaling pathways,which play crucial roles in tissue regeneration.As expected,Nano-Se not only achieved the regeneration of zebrafish tail fins and mouse skin but also promoted the repair of skin in diabetic mice while maintaining a profitable safe profile.In brief,the Nano-Se reported here provided an efficient and feasible method for bioactive nanoselenium synthesis and not only expanded the application of nanoselenium to regenerative medicine but also likely reinvigorated efforts for discovering more peculiarunique biofunctions of nanoselenium in a great variety of human diseases.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.
基金supported by grants from National Natural Science Foundation of China(No.81902801)National Natural Science Foundation of China(No.8217329)+3 种基金Operating Fund of Guangdong Provincial Key Laboratory of Bioengineering Medicine(No.2014B030301050)Guangdong grant“Key technologies for treatment of brain disorders”(No.2018B030332001)China Postdoctoral Foundation(No.2019M663375)Guangzhou Science and Technology Project(No.20212210007)。
文摘Selenium(Se)is an essential trace element involved in nearly all human physiological processes but suffers from a narrow margin between benefit and toxicity.The nanoform of selenium has been proven shown to be more bioavailable and less toxic,yet significant challenges remain regarding the efficient and feasible synthesis of biologically active nanoselenium.In addition,although nanoselenium has shown a variety of biological activities,more interesting nanoselenium features are expected.In this work,hydrosoluble nanoselenium termed Nano-Se in the zero oxidation state was synthesized between gray Se and PEG.A zebrafish screen was carried out in zebrafish larvae cocultured with Nano-Se.Excitingly,Nano-Se promoted the action of the FGFR,Wnt,and VEGF signaling pathways,which play crucial roles in tissue regeneration.As expected,Nano-Se not only achieved the regeneration of zebrafish tail fins and mouse skin but also promoted the repair of skin in diabetic mice while maintaining a profitable safe profile.In brief,the Nano-Se reported here provided an efficient and feasible method for bioactive nanoselenium synthesis and not only expanded the application of nanoselenium to regenerative medicine but also likely reinvigorated efforts for discovering more peculiarunique biofunctions of nanoselenium in a great variety of human diseases.
