In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong （Glasgow Math. J., 48（1）（2006）） negatively. Moreover, some new...In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong （Glasgow Math. J., 48（1）（2006）） negatively. Moreover, some new results about VNL-rings and GVNL-ringsare also given.展开更多
Let R be a unitary ring and a,b∈R with ab=0.We find the 2/3 property of Drazin invertibility:if any two of a,b and a+b are Drazin invertible,then so is the third one.Then,we combine the 2/3 property of Drazin inverti...Let R be a unitary ring and a,b∈R with ab=0.We find the 2/3 property of Drazin invertibility:if any two of a,b and a+b are Drazin invertible,then so is the third one.Then,we combine the 2/3 property of Drazin invertibility to characterize the existence of generalized inverses by means of units.As applications,the need for two invertible morphisms used by You and Chen to characterize the group invertibility of a sum of morphisms is reduced to that for one invertible morphism,and the existence and expression of the inverse along a product of two regular elements are obtained,which generalizes the main result of Mary and Patricio(2016)about the group inverse of a product.展开更多
Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, letTF（X） = {f ∈ Tx ： arbieary （x, y） ∈ F, （f（x）,f（y）） ∈ F}.Then TF（X） is a subsemigroup of Tx. Let E be ano...Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, letTF（X） = {f ∈ Tx ： arbieary （x, y） ∈ F, （f（x）,f（y）） ∈ F}.Then TF（X） is a subsemigroup of Tx. Let E be another equivalence on X and TFE（X） = TF（X） ∩ TE（X）. In this paper, under the assumption that the two equivalences F and E are comparable and E lohtain in F, we describe the regular elements and characterize Green＇s relations for the semigroup TFE（X）.展开更多
The normal dynamic infinite element in elastic foundation cannot be used in time-domain due to it's inclusive frequency term.A novel 3D regular grid infinite element is constructed to deal with the time-domain pro...The normal dynamic infinite element in elastic foundation cannot be used in time-domain due to it's inclusive frequency term.A novel 3D regular grid infinite element is constructed to deal with the time-domain problem.This new infinite element method can easily transform the frequency terms of mass matrix and stiffness matrix to the terms in higher-order dynamic equation,thus a higher-order dynamic equilibrium equation is formed.Based on the second-order Wilson-θ dynamic equation,a new time-domain numeric formula of higher-order dynamic equation is deduced,and the time-domain calculation coupling with finite element and infinite element can be realized.The classic 3D fluctuation problem in elastic foundation is employed as an illustrative example to investigate the accuracy and validity of this new infinite element.The result indicates that the new dynamic infinite element has a high accuracy.展开更多
文摘In this note, a counterexample is given to show that a noncommutative VNL-ring need not be an SVNL-ring, answering an open question of Chen and Tong （Glasgow Math. J., 48（1）（2006）） negatively. Moreover, some new results about VNL-rings and GVNL-ringsare also given.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12171083,11871145,12071070)the Qing Lan Project of Jiangsu Provincethe Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX22-0231)。
文摘Let R be a unitary ring and a,b∈R with ab=0.We find the 2/3 property of Drazin invertibility:if any two of a,b and a+b are Drazin invertible,then so is the third one.Then,we combine the 2/3 property of Drazin invertibility to characterize the existence of generalized inverses by means of units.As applications,the need for two invertible morphisms used by You and Chen to characterize the group invertibility of a sum of morphisms is reduced to that for one invertible morphism,and the existence and expression of the inverse along a product of two regular elements are obtained,which generalizes the main result of Mary and Patricio(2016)about the group inverse of a product.
基金the Natural Science Found of Henan Province (No.0511010200)the Doctoral Fund of Henan Polytechnic University (No.2009A110007)the Natural Science Research Project for Education Department of Henan Province (No.2009A110007)
文摘Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, letTF（X） = {f ∈ Tx ： arbieary （x, y） ∈ F, （f（x）,f（y）） ∈ F}.Then TF（X） is a subsemigroup of Tx. Let E be another equivalence on X and TFE（X） = TF（X） ∩ TE（X）. In this paper, under the assumption that the two equivalences F and E are comparable and E lohtain in F, we describe the regular elements and characterize Green＇s relations for the semigroup TFE（X）.
文摘The normal dynamic infinite element in elastic foundation cannot be used in time-domain due to it's inclusive frequency term.A novel 3D regular grid infinite element is constructed to deal with the time-domain problem.This new infinite element method can easily transform the frequency terms of mass matrix and stiffness matrix to the terms in higher-order dynamic equation,thus a higher-order dynamic equilibrium equation is formed.Based on the second-order Wilson-θ dynamic equation,a new time-domain numeric formula of higher-order dynamic equation is deduced,and the time-domain calculation coupling with finite element and infinite element can be realized.The classic 3D fluctuation problem in elastic foundation is employed as an illustrative example to investigate the accuracy and validity of this new infinite element.The result indicates that the new dynamic infinite element has a high accuracy.
