The exchange rings without unity, first introduced by Ara, are further investigated. Some new characterizations and properties of exchange general rings are given. For example, a general ring I is exchange if and only...The exchange rings without unity, first introduced by Ara, are further investigated. Some new characterizations and properties of exchange general rings are given. For example, a general ring I is exchange if and only if for any left ideal L of I and a^-= a^-2 ∈I/L, there exists w ∈ r. ureg（I） such that w^- = a^-; E（R, I） （ the ideal extension of a ring R by its ideal I） is an exchange ring if and only if R and I are both exchange. Furthermore, it is presented that if I is a two-sided ideal of a unital ring R and I is an exchange general ring, then every central element of I is a clean element in 1.展开更多
In this paper,we give definition and moduler representation of Kothe root for additive cate gories.Using these results,get inner representation of J-root and fully homomorph class of Jscmisimple additive categories.
Piezoelectric ceramic is hard to be integrated with the normal spring structure.To address the above problem,this paper proposed a new geometry of a clip‑like spring which is very similar to binder clip in our daily l...Piezoelectric ceramic is hard to be integrated with the normal spring structure.To address the above problem,this paper proposed a new geometry of a clip‑like spring which is very similar to binder clip in our daily life.The equivalent stiffness of the designed piezoelectric clip‑like spring is thoroughly researched and discussed through the theoretical model,the finite element simulation and the experimental measurement.The results confirm the possibility of designing a compact piezoelectric clip‑like spring,and the equivalent stiffness can be tuned through the several key geometric parameters.Finally,theoretical predictions confirmed by experimental results show that the equivalent stiffness of the spring structure is as function of the instantaneous angle of the clip,this stiffness variation caused by the geometric nonlinearity can be ignored in some practical engineering applications,which means it is possible to linearize the clip‑like spring and simplify the following dynamic model of the corresponding piezoelectric oscillators.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11571024)the Natural Science Foundation of Beijing(Grant No.1132008)a program of Hebei Province(Grant No.QN2017116)
基金The National Natural Science Foundation of China(No10571026),the Natural Science Foundation of Jiangsu Province(NoBK2005207), the Teaching and Research Award Program for Out-standing Young Teachers in Higher Education Institutions of MOE,PRC
文摘The exchange rings without unity, first introduced by Ara, are further investigated. Some new characterizations and properties of exchange general rings are given. For example, a general ring I is exchange if and only if for any left ideal L of I and a^-= a^-2 ∈I/L, there exists w ∈ r. ureg（I） such that w^- = a^-; E（R, I） （ the ideal extension of a ring R by its ideal I） is an exchange ring if and only if R and I are both exchange. Furthermore, it is presented that if I is a two-sided ideal of a unital ring R and I is an exchange general ring, then every central element of I is a clean element in 1.
文摘In this paper,we give definition and moduler representation of Kothe root for additive cate gories.Using these results,get inner representation of J-root and fully homomorph class of Jscmisimple additive categories.
基金This work was supported by the National Natural Science Foundation of China(No.51705251)the Introduction of Talent Research Start-up Fund of Nanjing Institute of Technology(No.YKJ201960).
文摘Piezoelectric ceramic is hard to be integrated with the normal spring structure.To address the above problem,this paper proposed a new geometry of a clip‑like spring which is very similar to binder clip in our daily life.The equivalent stiffness of the designed piezoelectric clip‑like spring is thoroughly researched and discussed through the theoretical model,the finite element simulation and the experimental measurement.The results confirm the possibility of designing a compact piezoelectric clip‑like spring,and the equivalent stiffness can be tuned through the several key geometric parameters.Finally,theoretical predictions confirmed by experimental results show that the equivalent stiffness of the spring structure is as function of the instantaneous angle of the clip,this stiffness variation caused by the geometric nonlinearity can be ignored in some practical engineering applications,which means it is possible to linearize the clip‑like spring and simplify the following dynamic model of the corresponding piezoelectric oscillators.
