由公式C<sub>n</sub><sup>k</sup>+C<sub>n</sub><sup>k+1</sup>=C<sub>n+1</sub><sup>k+1</sup>,可得:C<sub>2</sub><sup>2</sup>+...由公式C<sub>n</sub><sup>k</sup>+C<sub>n</sub><sup>k+1</sup>=C<sub>n+1</sub><sup>k+1</sup>,可得:C<sub>2</sub><sup>2</sup>+C<sub>3</sub><sup>2</sup>+…+C<sub>n</sub><sup>2</sup>=C<sub>n+1</sub><sup>3</sup>,sum from k=2 to nC<sub>k</sub><sup>2</sup>=C<sub>n+1</sub><sup>3</sup>,展开更多
关于自然数组成的级数sum from k=1 to ∞ （k）和自然数平方组成的级数sum from k=1 to ∞ （k<sup>2</sup>）的前n项求和公式: S<sub>1</sub>（n）=sum from k=1 to n （k）=n（n+1）/2 S<sub>2</su...关于自然数组成的级数sum from k=1 to ∞ （k）和自然数平方组成的级数sum from k=1 to ∞ （k<sup>2</sup>）的前n项求和公式: S<sub>1</sub>（n）=sum from k=1 to n （k）=n（n+1）/2 S<sub>2</sub>（n）=sum from k=1 to n （k<sup>2</sup>）=1/6n（n+1）（2n+1） （2）我们大家非常熟悉,并且在一些文献中分别给出不同的证明。本文利用公式（1）,（2）介绍几种自然数立方组成的级数sum from k=1 to ∞ （k<sup>3</sup>）的前n项和公式:展开更多
The development of an efficient artificial H_(2)O_(2) photosynthesis system is a challenging work using H_(2)O and O_(2) as starting materials.Herein,3D In_(2.77)S_(4) nanoflower precursor was in-situ deposited on K^(...The development of an efficient artificial H_(2)O_(2) photosynthesis system is a challenging work using H_(2)O and O_(2) as starting materials.Herein,3D In_(2.77)S_(4) nanoflower precursor was in-situ deposited on K^(+)-doped g-C_(3)N_(4)(KCN)nanosheets using a solvothermal method,then In_(2.77)S_(4)/KCN(IS/KCN)het-erojunction with an intimate interface was obtained after a calcination process.The investigation shows that the photocatalytic H_(2)O_(2) production rate of 50IS/KCN can reach up to 1.36 mmol g^(-1)h^(-1)without any sacrificial reagents under visible light irradiation,which is 9.2 times and 4.1 times higher than that of KCN and In_(2.77)S_(4)/respectively.The enhanced activity of the above composite can be mainly attributed to the S-scheme charge transfer route between KCN and In_(2.77)S_(4) according to density functional theory calculations,electron paramagnetic resonance and free radical capture tests,leading to an expanded light response range and rapid charge separation at their interface,as well as preserving the active electrons and holes for H_(2)O_(2) production.Besides,the unique 3D nanostructure and surface hydrophobicity of IS/KCN facilitate the diffusion and transportation of O_(2) around the active centers,the energy barriers of O_(2) protonation and H_(2)O_(2) desorption steps are ef-fectively reduced over the composite.In addition,this system also exhibits excellent light harvesting ability and stability.This work provides a potential strategy to explore a sustainable H_(2)O_(2) photo-synthesis pathway through the design of heterojunctions with intimate interfaces and desired reac-tion thermodynamics and kinetics.展开更多
文摘由公式C<sub>n</sub><sup>k</sup>+C<sub>n</sub><sup>k+1</sup>=C<sub>n+1</sub><sup>k+1</sup>,可得:C<sub>2</sub><sup>2</sup>+C<sub>3</sub><sup>2</sup>+…+C<sub>n</sub><sup>2</sup>=C<sub>n+1</sub><sup>3</sup>,sum from k=2 to nC<sub>k</sub><sup>2</sup>=C<sub>n+1</sub><sup>3</sup>,
文摘关于自然数组成的级数sum from k=1 to ∞ （k）和自然数平方组成的级数sum from k=1 to ∞ （k<sup>2</sup>）的前n项求和公式: S<sub>1</sub>（n）=sum from k=1 to n （k）=n（n+1）/2 S<sub>2</sub>（n）=sum from k=1 to n （k<sup>2</sup>）=1/6n（n+1）（2n+1） （2）我们大家非常熟悉,并且在一些文献中分别给出不同的证明。本文利用公式（1）,（2）介绍几种自然数立方组成的级数sum from k=1 to ∞ （k<sup>3</sup>）的前n项和公式:
文摘The development of an efficient artificial H_(2)O_(2) photosynthesis system is a challenging work using H_(2)O and O_(2) as starting materials.Herein,3D In_(2.77)S_(4) nanoflower precursor was in-situ deposited on K^(+)-doped g-C_(3)N_(4)(KCN)nanosheets using a solvothermal method,then In_(2.77)S_(4)/KCN(IS/KCN)het-erojunction with an intimate interface was obtained after a calcination process.The investigation shows that the photocatalytic H_(2)O_(2) production rate of 50IS/KCN can reach up to 1.36 mmol g^(-1)h^(-1)without any sacrificial reagents under visible light irradiation,which is 9.2 times and 4.1 times higher than that of KCN and In_(2.77)S_(4)/respectively.The enhanced activity of the above composite can be mainly attributed to the S-scheme charge transfer route between KCN and In_(2.77)S_(4) according to density functional theory calculations,electron paramagnetic resonance and free radical capture tests,leading to an expanded light response range and rapid charge separation at their interface,as well as preserving the active electrons and holes for H_(2)O_(2) production.Besides,the unique 3D nanostructure and surface hydrophobicity of IS/KCN facilitate the diffusion and transportation of O_(2) around the active centers,the energy barriers of O_(2) protonation and H_(2)O_(2) desorption steps are ef-fectively reduced over the composite.In addition,this system also exhibits excellent light harvesting ability and stability.This work provides a potential strategy to explore a sustainable H_(2)O_(2) photo-synthesis pathway through the design of heterojunctions with intimate interfaces and desired reac-tion thermodynamics and kinetics.
