In this paper, a new viewpoint of the division by zero z/0 = 0 in matrices is introduced and the results will show that the division by zero is our elementary and fundamental mathematics. New and practical meanings fo...In this paper, a new viewpoint of the division by zero z/0 = 0 in matrices is introduced and the results will show that the division by zero is our elementary and fundamental mathematics. New and practical meanings for many mathematical and physical formulas for the denominator zero cases may be given. Furthermore, a new space idea for the point at infinity for the Eucleadian plane is also introduced.展开更多
Given their unique structure-dependent properties,strategically designing semiconductor-based photocatalysts,which expose highly reactive crystalline facets,is widely used to tune their performance.Herein,AgBr/Ag/TiO_...Given their unique structure-dependent properties,strategically designing semiconductor-based photocatalysts,which expose highly reactive crystalline facets,is widely used to tune their performance.Herein,AgBr/Ag/TiO_(2){100}nanorods Z-scheme heterojunction composites were prepared via hydrothermal and in situ facet-induced reduction.Transmission electron microscopy,X-ray diffraction,X-ray photoelectron spectroscopy,electron paramagnetic resonance spectroscopy,and density functional theory calculations reveal that the selective exposure of TiO_(2){100}facets with abundant oxygen vacancies(OV)promotes the formation of metallic silver on the interfaces between AgBr and TiO_(2){100}.Metallic silver can mediate interfacial charge transfer by facilitating the photogenerated carrier recombination of the conduction band of TiO_(2){100}and the valence band of AgBr.As a result,a Z-scheme heterojunction is formed in AgBr/Ag/TiO_(2){100}.The AgBr/Ag/TiO_(2){100}exhibits faster degradation of tetracycline in aqueous solution compared to pristine AgBr,TiO_(2){101},TiO_(2){100}and AgBr/TiO_(2){101}p-n heterojunctions.This is attributed to the effect of the Z-scheme heterojunction on prolonging the lifetime of photogenerated carriers,which is confirmed by femtosecond transient absorption spectroscopy.The photocatalytic mechanism and degradation pathways are discussed along with a toxicity assessment of the intermediates.Overall,this work develops a new approach for designing Z-scheme heterojunction photocatalysts via selective facet control of anatase TiO_(2).展开更多
We investigate the possibilities of finding the effects of the littlest Higgs (LH) model on the process e + e - →μ + μ - at the leadingorder at a possible Z 0-factory.We study the impacts of the LH model on the obs...We investigate the possibilities of finding the effects of the littlest Higgs (LH) model on the process e + e - →μ + μ - at the leadingorder at a possible Z 0-factory.We study the impacts of the LH model on the observables,such as,the total cross section,the distribution of the transverse momentum of μ-,and the forward-backward charge asymmetry of μin polarized and unpolarized electron-positron collision modes.Besides,we analyze the relations between the observables and the LH model parameters,and discuss the observables of process e + e→μ + μ-in different incoming electron-positron polarization modes.We conclude that one could observe the effects contributed by the LH model on the process e + e-→μ + μin a reasonable parameter space,or might put more stringent constraints on the LH parameters in the future experiments at the possible Z 0-factory.展开更多
The potential for probing the impacts of the left-right symmetric model (LRM) on the process e + e-→μ + μ-at a proposed Z 0-factory is investigated.Under different electron-positron polarization collision modes,we ...The potential for probing the impacts of the left-right symmetric model (LRM) on the process e + e-→μ + μ-at a proposed Z 0-factory is investigated.Under different electron-positron polarization collision modes,we calculate and compare the deviations of various observables in the framework of the LRM from the standard model (SM) predictions,such as the total cross section,the distribution of the transverse momentum of μ-,and the forward-backward charge asymmetry of μ-.In addition,we present the relations between the observables and the LRM parameters.We conclude that it is possible to observe the effects of the LRM on the process e + e-→μ + μ-by using optimal observables and favorable parameters at a Z 0-factory.展开更多
文摘In this paper, a new viewpoint of the division by zero z/0 = 0 in matrices is introduced and the results will show that the division by zero is our elementary and fundamental mathematics. New and practical meanings for many mathematical and physical formulas for the denominator zero cases may be given. Furthermore, a new space idea for the point at infinity for the Eucleadian plane is also introduced.
文摘Given their unique structure-dependent properties,strategically designing semiconductor-based photocatalysts,which expose highly reactive crystalline facets,is widely used to tune their performance.Herein,AgBr/Ag/TiO_(2){100}nanorods Z-scheme heterojunction composites were prepared via hydrothermal and in situ facet-induced reduction.Transmission electron microscopy,X-ray diffraction,X-ray photoelectron spectroscopy,electron paramagnetic resonance spectroscopy,and density functional theory calculations reveal that the selective exposure of TiO_(2){100}facets with abundant oxygen vacancies(OV)promotes the formation of metallic silver on the interfaces between AgBr and TiO_(2){100}.Metallic silver can mediate interfacial charge transfer by facilitating the photogenerated carrier recombination of the conduction band of TiO_(2){100}and the valence band of AgBr.As a result,a Z-scheme heterojunction is formed in AgBr/Ag/TiO_(2){100}.The AgBr/Ag/TiO_(2){100}exhibits faster degradation of tetracycline in aqueous solution compared to pristine AgBr,TiO_(2){101},TiO_(2){100}and AgBr/TiO_(2){101}p-n heterojunctions.This is attributed to the effect of the Z-scheme heterojunction on prolonging the lifetime of photogenerated carriers,which is confirmed by femtosecond transient absorption spectroscopy.The photocatalytic mechanism and degradation pathways are discussed along with a toxicity assessment of the intermediates.Overall,this work develops a new approach for designing Z-scheme heterojunction photocatalysts via selective facet control of anatase TiO_(2).
基金supported in part by the National Natural Science Foundation of China (Grant Nos.10875112 and 10675110)
文摘We investigate the possibilities of finding the effects of the littlest Higgs (LH) model on the process e + e - →μ + μ - at the leadingorder at a possible Z 0-factory.We study the impacts of the LH model on the observables,such as,the total cross section,the distribution of the transverse momentum of μ-,and the forward-backward charge asymmetry of μin polarized and unpolarized electron-positron collision modes.Besides,we analyze the relations between the observables and the LH model parameters,and discuss the observables of process e + e→μ + μ-in different incoming electron-positron polarization modes.We conclude that one could observe the effects contributed by the LH model on the process e + e-→μ + μin a reasonable parameter space,or might put more stringent constraints on the LH parameters in the future experiments at the possible Z 0-factory.
基金supported in part by the National Natural Science Foundation of China (Grant Nos.10875112 and 10675110)
文摘The potential for probing the impacts of the left-right symmetric model (LRM) on the process e + e-→μ + μ-at a proposed Z 0-factory is investigated.Under different electron-positron polarization collision modes,we calculate and compare the deviations of various observables in the framework of the LRM from the standard model (SM) predictions,such as the total cross section,the distribution of the transverse momentum of μ-,and the forward-backward charge asymmetry of μ-.In addition,we present the relations between the observables and the LRM parameters.We conclude that it is possible to observe the effects of the LRM on the process e + e-→μ + μ-by using optimal observables and favorable parameters at a Z 0-factory.
