In this paper we study the local or global(in time)existence of small data solutions to semi-linear fractionalσ-evolution equations with nonlinear memory.Our main goals is to explain on the one hand the influence of ...In this paper we study the local or global(in time)existence of small data solutions to semi-linear fractionalσ-evolution equations with nonlinear memory.Our main goals is to explain on the one hand the influence of the memory term and on the other hand the influence of higher regularity of the data on qualitative properties of solutions.展开更多
With the gradual depletion of conventional fossil fuels,serious energy shortage has become a major societal challenge.Among the numerous new energy generation technologies,photocatalytic water splitting for hydrogen p...With the gradual depletion of conventional fossil fuels,serious energy shortage has become a major societal challenge.Among the numerous new energy generation technologies,photocatalytic water splitting for hydrogen production only requires abundant solar energy as the driving force and the process conditions are mild,green,and pollution-free.Thus,this technology has been proposed as an effective strategy to solve the current energy shortage crisis.The core of the photocatalytic hydrogen production technology is the photocatalyst.Therefore,it is necessary to develop efficient and stable photocatalysts.However,single-component photocatalysts usually exhibit insufficient photocatalytic H_(2)evolution efficiencies owing to its rapid hole-electron recombination,limited redox ability and low solar energy utilization efficiency.Therefore,various modification approaches have been designed to improve the photocatalytic H_(2)evolution efficiency of singlecomponent photocatalysts,such as element doping,cocatalyst modification,heterojunction construction,etc.Generally,element doping and cocatalyst modification improve the photocatalytic hydrogen production activity but cannot effectively solve the drawbacks of single-component photocatalysts,which limits their ability to improve the photocatalytic performance.However,constructing heterojunctions between two or more semiconductors simultaneously resolves these drawbacks.Compared with currently used conventional type-II all-solid-state Z-scheme,and liquid-phase Z-scheme heterojunctions,S-scheme heterojunctions present a more reasonable charge transfer mechanism,which is of great concern to and extensively used by several researchers.Therefore,this review firstly introduces the research background on S-scheme heterojunction photocatalytic systems,including the photocatalytic charge transfer mechanism of conventional type-II,all-solid-state Z-scheme,and liquid-phase Z-scheme heterojunction systems.Subsequently,the photocatalytic mechanism of S-scheme heterojunctions is meticulously explained.Additionally,the corresponding characterization methods,including in situ irradiated X-ray photoelectron spectroscopy(ISIXPS),Kelvin probe force microscopy(KPFM),selective deposition,electron paramagnetic resonance(EPR),density functional theory(DFT)calculations,etc.,are briefly summarized.Moreover,currently reported photocatalytic water splitting S-scheme heterojunctions and the corresponding significant enhancement in the hydrogen evolution mechanism are systematically summarized,including g-C_(3)N_(4)-,metal sulfide-,TiO_(2)-,other oxide-,and other S-scheme heterojunction-based photocatalysts.Notably,S-scheme heterojunction photocatalysts typically exhibit highly improved photocatalytic H_(2)evolution performance owing to their effective carrier separation and enhanced photoredox capacities.Finally,the bottlenecks of developing S-scheme heterojunctions for photocatalytic H_(2)production are presented,which require further investigation to enhance the photocatalytic efficiency of S-scheme heterojunctions for achieving industrial application standards.展开更多
In this paper, nonstandard analysis is employed to present an existence theory of -valued stochastic differential equations involving evolution drift. And (C0, 1)-evolution systems are also defined and investigated on...In this paper, nonstandard analysis is employed to present an existence theory of -valued stochastic differential equations involving evolution drift. And (C0, 1)-evolution systems are also defined and investigated on dual multi-Hilbertian spaces.展开更多
基金The research of this article is supported by the DAAD,Erasmus+Project between the Hassiba Benbouali University of Chlef(Algeria)and TU Bergakademie Freiberg,2015-1-DE01-KA107-002026
文摘In this paper we study the local or global(in time)existence of small data solutions to semi-linear fractionalσ-evolution equations with nonlinear memory.Our main goals is to explain on the one hand the influence of the memory term and on the other hand the influence of higher regularity of the data on qualitative properties of solutions.
文摘With the gradual depletion of conventional fossil fuels,serious energy shortage has become a major societal challenge.Among the numerous new energy generation technologies,photocatalytic water splitting for hydrogen production only requires abundant solar energy as the driving force and the process conditions are mild,green,and pollution-free.Thus,this technology has been proposed as an effective strategy to solve the current energy shortage crisis.The core of the photocatalytic hydrogen production technology is the photocatalyst.Therefore,it is necessary to develop efficient and stable photocatalysts.However,single-component photocatalysts usually exhibit insufficient photocatalytic H_(2)evolution efficiencies owing to its rapid hole-electron recombination,limited redox ability and low solar energy utilization efficiency.Therefore,various modification approaches have been designed to improve the photocatalytic H_(2)evolution efficiency of singlecomponent photocatalysts,such as element doping,cocatalyst modification,heterojunction construction,etc.Generally,element doping and cocatalyst modification improve the photocatalytic hydrogen production activity but cannot effectively solve the drawbacks of single-component photocatalysts,which limits their ability to improve the photocatalytic performance.However,constructing heterojunctions between two or more semiconductors simultaneously resolves these drawbacks.Compared with currently used conventional type-II all-solid-state Z-scheme,and liquid-phase Z-scheme heterojunctions,S-scheme heterojunctions present a more reasonable charge transfer mechanism,which is of great concern to and extensively used by several researchers.Therefore,this review firstly introduces the research background on S-scheme heterojunction photocatalytic systems,including the photocatalytic charge transfer mechanism of conventional type-II,all-solid-state Z-scheme,and liquid-phase Z-scheme heterojunction systems.Subsequently,the photocatalytic mechanism of S-scheme heterojunctions is meticulously explained.Additionally,the corresponding characterization methods,including in situ irradiated X-ray photoelectron spectroscopy(ISIXPS),Kelvin probe force microscopy(KPFM),selective deposition,electron paramagnetic resonance(EPR),density functional theory(DFT)calculations,etc.,are briefly summarized.Moreover,currently reported photocatalytic water splitting S-scheme heterojunctions and the corresponding significant enhancement in the hydrogen evolution mechanism are systematically summarized,including g-C_(3)N_(4)-,metal sulfide-,TiO_(2)-,other oxide-,and other S-scheme heterojunction-based photocatalysts.Notably,S-scheme heterojunction photocatalysts typically exhibit highly improved photocatalytic H_(2)evolution performance owing to their effective carrier separation and enhanced photoredox capacities.Finally,the bottlenecks of developing S-scheme heterojunctions for photocatalytic H_(2)production are presented,which require further investigation to enhance the photocatalytic efficiency of S-scheme heterojunctions for achieving industrial application standards.
文摘In this paper, nonstandard analysis is employed to present an existence theory of -valued stochastic differential equations involving evolution drift. And (C0, 1)-evolution systems are also defined and investigated on dual multi-Hilbertian spaces.
