In this paper,the authors established a sharp version of the difference analogue of the celebrated Holder’s theorem concerning the differential independence of the Euler gamma functionГ.More precisely,if P is a poly...In this paper,the authors established a sharp version of the difference analogue of the celebrated Holder’s theorem concerning the differential independence of the Euler gamma functionГ.More precisely,if P is a polynomial of n+1 variables in C[X,Y0,…,Yn-1]such that P(s,Г(s+a0),…,Г(s+an-1))≡0 for some(a0,…,an-1)∈Cn and ai-aj■Z for any 0≤i<j≤n-1,then they have P≡0.Their result complements a classical result of algebraic differential independence of the Euler gamma function proved by H?lder in 1886,and also a result of algebraic difference independence of the Riemann zeta function proved by Chiang and Feng in 2006.展开更多
Ice accumulation is a safety and operational threat in power lines,wind turbines,and transportations.Surfaces having both passive anti-icing and active deicing functionalities are very rare.Here,we report a self-clean...Ice accumulation is a safety and operational threat in power lines,wind turbines,and transportations.Surfaces having both passive anti-icing and active deicing functionalities are very rare.Here,we report a self-cleaning slippery photothermal trap,which is icephobic passively and deice the surfaces actively by converting sun light to heat at the ice-substrate interface.The photothermal trap consists of three layers:a candle soot layer act as solar radiation absorber,a magnetic iron oxide Fe_(3)O_(4) nanoparticles layer act as heat spreader for lateral dispersal of sun light,and Room Temperature Vulcanized(RTV)insulation to reduce the transverse heat loss.Upon illumination under microsolar 300,the temperature of the surface increased by 40℃ within 200 s.The heat confinement at the magnetic Fe_(3)O_(4) na-noparticles layer leads to rapid increase of the surface temperature,ice start to melt and silicone lubricant facilitates the ice removal.The slippery photothermal trap removed the frozen droplet(10 fiL)within 40 s upon the illumination of sun light and the frozen droplet was completely converted into water after 7 min illumination of solar light at-20℃.The developed slippery photothermal trap also melted the fully frost covered layer within 100 s at-20℃ under sunlamp.The average defrosted length(25 mm)was also observed by irradiation of laser light for 45 s.The self-cleaning slippery photothermal coating showed outstanding deicing performance at subzero temperature for long term due to the infusion of silicone oil into the nanostructures and same chemical composition with binder.展开更多
基金supported by the National Natural Science Foundation of China(No.11901311)。
文摘In this paper,the authors established a sharp version of the difference analogue of the celebrated Holder’s theorem concerning the differential independence of the Euler gamma functionГ.More precisely,if P is a polynomial of n+1 variables in C[X,Y0,…,Yn-1]such that P(s,Г(s+a0),…,Г(s+an-1))≡0 for some(a0,…,an-1)∈Cn and ai-aj■Z for any 0≤i<j≤n-1,then they have P≡0.Their result complements a classical result of algebraic differential independence of the Euler gamma function proved by H?lder in 1886,and also a result of algebraic difference independence of the Riemann zeta function proved by Chiang and Feng in 2006.
基金The authors would like to gratefully acknowledge the National Natural Science Foundation of China(NSFC)for Award No.21878267 for supporting this research.
文摘Ice accumulation is a safety and operational threat in power lines,wind turbines,and transportations.Surfaces having both passive anti-icing and active deicing functionalities are very rare.Here,we report a self-cleaning slippery photothermal trap,which is icephobic passively and deice the surfaces actively by converting sun light to heat at the ice-substrate interface.The photothermal trap consists of three layers:a candle soot layer act as solar radiation absorber,a magnetic iron oxide Fe_(3)O_(4) nanoparticles layer act as heat spreader for lateral dispersal of sun light,and Room Temperature Vulcanized(RTV)insulation to reduce the transverse heat loss.Upon illumination under microsolar 300,the temperature of the surface increased by 40℃ within 200 s.The heat confinement at the magnetic Fe_(3)O_(4) na-noparticles layer leads to rapid increase of the surface temperature,ice start to melt and silicone lubricant facilitates the ice removal.The slippery photothermal trap removed the frozen droplet(10 fiL)within 40 s upon the illumination of sun light and the frozen droplet was completely converted into water after 7 min illumination of solar light at-20℃.The developed slippery photothermal trap also melted the fully frost covered layer within 100 s at-20℃ under sunlamp.The average defrosted length(25 mm)was also observed by irradiation of laser light for 45 s.The self-cleaning slippery photothermal coating showed outstanding deicing performance at subzero temperature for long term due to the infusion of silicone oil into the nanostructures and same chemical composition with binder.
