This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigati...This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.展开更多
Let X denote a finite or infinite dimensional Lie algebra of Cartan type W, S, H or K over a field of characteristic p 〉 3. In this paper it is proved that certain filtrations of the underlying algebras are invariant...Let X denote a finite or infinite dimensional Lie algebra of Cartan type W, S, H or K over a field of characteristic p 〉 3. In this paper it is proved that certain filtrations of the underlying algebras are invariant under the admissible groups relative to Lie algebras of Cartan type X.展开更多
This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin h...This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.展开更多
Formal credit is critical in agricultural production,allowing more expenditure and productive input,thereby improving farmers'welfare.In pastoral China,formal financial institutions are gradually increasing.Howeve...Formal credit is critical in agricultural production,allowing more expenditure and productive input,thereby improving farmers'welfare.In pastoral China,formal financial institutions are gradually increasing.However,a limited understanding remains of how formal credit affects herders'household expenses.Based on a survey of 544 herders from the Qinghai-Xizang Plateau of China,this study adopted the propensity score matching approach to identify the effect of formal credit on herders'total household expenses,daily expenses,and productive expenses.The results found that average age,grassland mortgage,and other variables significantly affected herders'participation in formal credit.Formal credit could significantly improve household expenses,especially productive expenses.A heterogeneity analysis showed that formal credit had a greater impact on the household total expense for those at higher levels of wealth;however,it significantly affected the productive expense of herders at lower wealth levels.Moreover,the mediating effect indicated that formal credit could affect herders'household income,thus influencing their household expenses.Finally,this study suggests that policies should improve herders'accessibility to formal credit.展开更多
Fair exchange protocols play a critical role in enabling two distrustful entities to conduct electronic data exchanges in a fair and secure manner.These protocols are widely used in electronic payment systems and elec...Fair exchange protocols play a critical role in enabling two distrustful entities to conduct electronic data exchanges in a fair and secure manner.These protocols are widely used in electronic payment systems and electronic contract signing,ensuring the reliability and security of network transactions.In order to address the limitations of current research methods and enhance the analytical capabilities for fair exchange protocols,this paper proposes a formal model for analyzing such protocols.The proposed model begins with a thorough analysis of fair exchange protocols,followed by the formal definition of fairness.This definition accurately captures the inherent requirements of fair exchange protocols.Building upon event logic,the model incorporates the time factor into predicates and introduces knowledge set axioms.This enhancement empowers the improved logic to effectively describe the state and knowledge of protocol participants at different time points,facilitating reasoning about their acquired knowledge.To maximize the intruder’s capabilities,channel errors are translated into the behaviors of the intruder.The participants are further categorized into honest participants and malicious participants,enabling a comprehensive evaluation of the intruder’s potential impact.By employing a typical fair exchange protocol as an illustrative example,this paper demonstrates the detailed steps of utilizing the proposed model for protocol analysis.The entire process of protocol execution under attack scenarios is presented,shedding light on the underlying reasons for the attacks and proposing corresponding countermeasures.The developedmodel enhances the ability to reason about and evaluate the security properties of fair exchange protocols,thereby contributing to the advancement of secure network transactions.展开更多
Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Hel...Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Helgason-spherical function on G is then established on .展开更多
At a meeting on cultural inheritance and development held in Beijing,June 2,2023,President Xi Jinping put forward a holistic and systematic explanation of the distinctive features of Chinese civilisation-consistency,o...At a meeting on cultural inheritance and development held in Beijing,June 2,2023,President Xi Jinping put forward a holistic and systematic explanation of the distinctive features of Chinese civilisation-consistency,originality,unity,inclusiveness,and a peaceful nature.President Xi Jinping's profound exposition has granted us a deeper understanding of the laws underlying the development of Chinese civilisation by shedding light on its intrinsic characteristics.展开更多
Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent...Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent Lie group Gk, defined by the nilpotent Lie algebra g/ak, where g is the Lie algebra of G, and ak is an ideal of g. Then, J gives rise to an almost complex structure Jk on Gk. The main conclusion obtained is as follows: if the almost complex structure J of a nilpotent Lie group G is nilpotent, then J can give rise to a left-invariant integrable almost complex structure Jk on the nilpotent Lie group Gk, and Jk is also nilpotent.展开更多
Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent m...Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).展开更多
In this work,we report long-term trends in the abundance and breeding performance of Adélie penguins(Pygoscelis adeliae)nesting in three Antarctic colonies(i.e.,at Martin Point,South Orkneys Islands;Stranger Poin...In this work,we report long-term trends in the abundance and breeding performance of Adélie penguins(Pygoscelis adeliae)nesting in three Antarctic colonies(i.e.,at Martin Point,South Orkneys Islands;Stranger Point/Cabo Funes,South Shetland Islands;and Esperanza/Hope Bay in the Antarctic Peninsula)from 1995/96 to 2022/23.Using yearly count data of breeding groups selected,we observed a decline in the number of breeding pairs and chicks in crèche at all colonies studied.However,the magnitude of change was higher at Stranger Point than that in the remaining colonies.Moreover,the index of breeding success,which was calculated as the ratio of chicks in crèche to breeding pairs,exhibited no apparent trend throughout the study period.However,it displayed greater variability at Martin Point compared to the other two colonies under investigation.Although the number of chicks in crèche of Adélie penguins showed a declining pattern,the average breeding performance was similar to that reported in gentoo penguin colonies,specifically,those undergoing a population increase(even in sympatric colonies facing similar local conditions).Consequently,it is plausible to assume a reduction of the over-winter survival as a likely cause of the declining trend observed,at least in the Stranger Point and Esperanza colonies.However,we cannot rule out local effects during the breeding season affecting the Adélie population of Martin Point.展开更多
Last week, I read news about school bullying with my parents, and it made me feel very sad. School bullying is a serious problem nowadays. It can happen in the classroom or even after school.
基金Supported by National Natural Science Foundation of China under Grant No. 10972151the Natural Science Foundation of Higher Education Institution of Jiangsu Province under Grant No. 08KJB130002
文摘This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.
基金The NSF(11171055)of Chinathe NSF(JC201004 and A200903)of Heilongjiang Province of Chinathe NSF(12511349)of Heilongjiang Educational Committee of China
文摘Let X denote a finite or infinite dimensional Lie algebra of Cartan type W, S, H or K over a field of characteristic p 〉 3. In this paper it is proved that certain filtrations of the underlying algebras are invariant under the admissible groups relative to Lie algebras of Cartan type X.
文摘This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.
基金funding from the National Natural Science Foundation of China (72303086)the Leading Scientist Project of Qinghai Province, China (2023-NK-147)+1 种基金the Consulting Project of Chinese Academy of Engineering (2023-XY-28,2022-XY-139)the Fundamental Research Funds for the Central Universities, China (lzujbky-2022-sp13)
文摘Formal credit is critical in agricultural production,allowing more expenditure and productive input,thereby improving farmers'welfare.In pastoral China,formal financial institutions are gradually increasing.However,a limited understanding remains of how formal credit affects herders'household expenses.Based on a survey of 544 herders from the Qinghai-Xizang Plateau of China,this study adopted the propensity score matching approach to identify the effect of formal credit on herders'total household expenses,daily expenses,and productive expenses.The results found that average age,grassland mortgage,and other variables significantly affected herders'participation in formal credit.Formal credit could significantly improve household expenses,especially productive expenses.A heterogeneity analysis showed that formal credit had a greater impact on the household total expense for those at higher levels of wealth;however,it significantly affected the productive expense of herders at lower wealth levels.Moreover,the mediating effect indicated that formal credit could affect herders'household income,thus influencing their household expenses.Finally,this study suggests that policies should improve herders'accessibility to formal credit.
基金the National Natural Science Foundation of China(Nos.61562026,61962020)Academic and Technical Leaders of Major Disciplines in Jiangxi Province(No.20172BCB22015)+1 种基金Special Fund Project for Postgraduate Innovation in Jiangxi Province(No.YC2020-B1141)Jiangxi Provincial Natural Science Foundation(No.20224ACB202006).
文摘Fair exchange protocols play a critical role in enabling two distrustful entities to conduct electronic data exchanges in a fair and secure manner.These protocols are widely used in electronic payment systems and electronic contract signing,ensuring the reliability and security of network transactions.In order to address the limitations of current research methods and enhance the analytical capabilities for fair exchange protocols,this paper proposes a formal model for analyzing such protocols.The proposed model begins with a thorough analysis of fair exchange protocols,followed by the formal definition of fairness.This definition accurately captures the inherent requirements of fair exchange protocols.Building upon event logic,the model incorporates the time factor into predicates and introduces knowledge set axioms.This enhancement empowers the improved logic to effectively describe the state and knowledge of protocol participants at different time points,facilitating reasoning about their acquired knowledge.To maximize the intruder’s capabilities,channel errors are translated into the behaviors of the intruder.The participants are further categorized into honest participants and malicious participants,enabling a comprehensive evaluation of the intruder’s potential impact.By employing a typical fair exchange protocol as an illustrative example,this paper demonstrates the detailed steps of utilizing the proposed model for protocol analysis.The entire process of protocol execution under attack scenarios is presented,shedding light on the underlying reasons for the attacks and proposing corresponding countermeasures.The developedmodel enhances the ability to reason about and evaluate the security properties of fair exchange protocols,thereby contributing to the advancement of secure network transactions.
文摘Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Helgason-spherical function on G is then established on .
文摘At a meeting on cultural inheritance and development held in Beijing,June 2,2023,President Xi Jinping put forward a holistic and systematic explanation of the distinctive features of Chinese civilisation-consistency,originality,unity,inclusiveness,and a peaceful nature.President Xi Jinping's profound exposition has granted us a deeper understanding of the laws underlying the development of Chinese civilisation by shedding light on its intrinsic characteristics.
文摘Consider the real, simply-connected, connected, s-step nilpotent Lie group G endowed with a left-invariant, integrable almost complex structure J, which is nilpotent. Consider the simply-connected, connected nilpotent Lie group Gk, defined by the nilpotent Lie algebra g/ak, where g is the Lie algebra of G, and ak is an ideal of g. Then, J gives rise to an almost complex structure Jk on Gk. The main conclusion obtained is as follows: if the almost complex structure J of a nilpotent Lie group G is nilpotent, then J can give rise to a left-invariant integrable almost complex structure Jk on the nilpotent Lie group Gk, and Jk is also nilpotent.
文摘Because homology on compact homogeneous nilpotent manifolds is closely related to homology on Lie algebras, studying homology on Lie algebras is helpful for further studying homology on compact homogeneous nilpotent manifolds. So we start with the differential sequence of Lie algebras. The Lie algebra g has the differential sequence E0,E1,⋯,Es⋯, which leads to the chain complex Es0→Δs0Ess→Δs1⋯→ΔsiEs(i+1)s→Δsi+1⋯of Esby discussing the chain complex E10→Δ10E11→Δ11⋯→Δ1r−1E1r→Δ1r⋯of E1and proves that Es+1i≅Hi(Es)=KerΔsi+1/ImΔsiand therefore Es+1≅H(Es)by the chain complex of Es(see Theorem 2).
基金Nacional de Promoción Científica y Tecnológica(Grant:PICTO 2010-0111)the Instituto Antártico Argentino-Dirección Nacional del Antártico(PINST-05)provided financial and logistical support.
文摘In this work,we report long-term trends in the abundance and breeding performance of Adélie penguins(Pygoscelis adeliae)nesting in three Antarctic colonies(i.e.,at Martin Point,South Orkneys Islands;Stranger Point/Cabo Funes,South Shetland Islands;and Esperanza/Hope Bay in the Antarctic Peninsula)from 1995/96 to 2022/23.Using yearly count data of breeding groups selected,we observed a decline in the number of breeding pairs and chicks in crèche at all colonies studied.However,the magnitude of change was higher at Stranger Point than that in the remaining colonies.Moreover,the index of breeding success,which was calculated as the ratio of chicks in crèche to breeding pairs,exhibited no apparent trend throughout the study period.However,it displayed greater variability at Martin Point compared to the other two colonies under investigation.Although the number of chicks in crèche of Adélie penguins showed a declining pattern,the average breeding performance was similar to that reported in gentoo penguin colonies,specifically,those undergoing a population increase(even in sympatric colonies facing similar local conditions).Consequently,it is plausible to assume a reduction of the over-winter survival as a likely cause of the declining trend observed,at least in the Stranger Point and Esperanza colonies.However,we cannot rule out local effects during the breeding season affecting the Adélie population of Martin Point.
文摘Last week, I read news about school bullying with my parents, and it made me feel very sad. School bullying is a serious problem nowadays. It can happen in the classroom or even after school.
