Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.
In this paper, some examples, such as iterated functional systems, scaling equation of wavelet transform,and invariant measure system, are used to show that the homoclinic orbit solutions exist in the functional equat...In this paper, some examples, such as iterated functional systems, scaling equation of wavelet transform,and invariant measure system, are used to show that the homoclinic orbit solutions exist in the functional equations too.And the solitary wave exists in generalized dynamical systems and functional systems.展开更多
Among all CO2 electroreduction products,methane(CH4)and ethylene(C_(2)H_(4))are two typical and valuable hydrocarbon products which are formed in two different pathways:hydrogenation and dimerization reactions of the ...Among all CO2 electroreduction products,methane(CH4)and ethylene(C_(2)H_(4))are two typical and valuable hydrocarbon products which are formed in two different pathways:hydrogenation and dimerization reactions of the same CO intermediate.Theoretical studies show that the adsorption configurations of CO intermediate determine the reaction pathways towards CH4/C_(2)H_(4).However,it is challenging to experimentally control the CO adsorption configurations at the catalyst surface,and thus the hydrocarbon selectivity is still limited.Herein,we seek to synthesize two well-defined copper nanocatalysts with controllable surface structures.The two model catalysts exhibit a high hydrocarbon selectivity toward either CH4(83%)or C_(2)H_(4)(93%)under identical reduction conditions.Scanning transmission electron microscopy and X-ray absorption spectroscopy characterizations reveal the low-coordination Cu^(0)sites and local Cu^(0)/Cu^(+)sites of the two catalysts,respectively.CO-temperature programed desorption,in-situ attenuated total reflection Fourier transform infrared spectroscopy and density functional theory studies unveil that the bridge-adsorbed CO(CO_(B))on the low-coordination Cu^(0)sites is apt to be hydrogenated to CH4,whereas the bridge-adsorbed CO plus linear-adsorbed CO(CO_(B)+CO_(L))on the local Cu^(0)/Cu^(+)sites are apt to be coupled to C_(2)H_(4).Our findings pave a new way to design catalysts with controllable CO adsorption configurations for high hydrocarbon product selectivity.展开更多
This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations.By using the generalized Riccati transformation and the integral ave...This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations.By using the generalized Riccati transformation and the integral averaging technique,new oscillation criteria and asymptotic behavior are obtained for all solutions of the equation.Our results generalize and improve some known theorems.展开更多
文摘Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.
文摘In this paper, some examples, such as iterated functional systems, scaling equation of wavelet transform,and invariant measure system, are used to show that the homoclinic orbit solutions exist in the functional equations too.And the solitary wave exists in generalized dynamical systems and functional systems.
基金supported by the National Natural Science Foundation of China (21875042)Shanghai Science and Technology Committee (18QA1400800)+1 种基金the Program of Eastern Scholar at Shanghai Institutions and Yanchang Petroleum Groupsupported by the Frontier Research Center for Materials Structure, School of Materials Science and Engineering of Shanghai Jiao Tong University
文摘Among all CO2 electroreduction products,methane(CH4)and ethylene(C_(2)H_(4))are two typical and valuable hydrocarbon products which are formed in two different pathways:hydrogenation and dimerization reactions of the same CO intermediate.Theoretical studies show that the adsorption configurations of CO intermediate determine the reaction pathways towards CH4/C_(2)H_(4).However,it is challenging to experimentally control the CO adsorption configurations at the catalyst surface,and thus the hydrocarbon selectivity is still limited.Herein,we seek to synthesize two well-defined copper nanocatalysts with controllable surface structures.The two model catalysts exhibit a high hydrocarbon selectivity toward either CH4(83%)or C_(2)H_(4)(93%)under identical reduction conditions.Scanning transmission electron microscopy and X-ray absorption spectroscopy characterizations reveal the low-coordination Cu^(0)sites and local Cu^(0)/Cu^(+)sites of the two catalysts,respectively.CO-temperature programed desorption,in-situ attenuated total reflection Fourier transform infrared spectroscopy and density functional theory studies unveil that the bridge-adsorbed CO(CO_(B))on the low-coordination Cu^(0)sites is apt to be hydrogenated to CH4,whereas the bridge-adsorbed CO plus linear-adsorbed CO(CO_(B)+CO_(L))on the local Cu^(0)/Cu^(+)sites are apt to be coupled to C_(2)H_(4).Our findings pave a new way to design catalysts with controllable CO adsorption configurations for high hydrocarbon product selectivity.
基金Supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. ZR2010AM031 and ZR2011AL001the Development Program in Science and Technology of Shandong Province of China under Grant No. 2010GWZ20401
文摘This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of second order nonlinear functional differential equations.By using the generalized Riccati transformation and the integral averaging technique,new oscillation criteria and asymptotic behavior are obtained for all solutions of the equation.Our results generalize and improve some known theorems.
