A new generalized modular design (GMD) method is proposed based on designpractice of frame structure of hydraulic press machines. By building a series of flexible modules(FMs), design knowledge and structure features ...A new generalized modular design (GMD) method is proposed based on designpractice of frame structure of hydraulic press machines. By building a series of flexible modules(FMs), design knowledge and structure features are integrated into parametric models. Then,parametric design and variational analysis methods for GMD are presented according to user defineddesign objectives and customized product characteristics. A FM-centered GMD system is developed andsuccessfully used in the rapid design of relevant products.展开更多
Let g be a classical complex simple Lie algebra and q be a parabolic subalgebra.Let M be a generalized Verma module induced from a one dimensional representation of q.Such M is called a scalar generalized Verma module...Let g be a classical complex simple Lie algebra and q be a parabolic subalgebra.Let M be a generalized Verma module induced from a one dimensional representation of q.Such M is called a scalar generalized Verma module.In this paper,we will determine the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras by computing explicitly the Gelfand-Kirillov dimension of the corresponding highest weight modules.展开更多
Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach mod...Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach modules over a unital Banach algebra.展开更多
Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the ...Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups:Tori[[ RS,≤]]([[MS,≤]],[NS,≤])≌ s∈S ToriR (M,N).展开更多
In this paper, we study the ring #(D,B) and obtain two very interesting results. First we prove in Theorem 3 that the category of rational left BU-modules is equivalent to both the category of #-rational left modules ...In this paper, we study the ring #(D,B) and obtain two very interesting results. First we prove in Theorem 3 that the category of rational left BU-modules is equivalent to both the category of #-rational left modules and the category of all (B,D)-Hopf modules D . Cai and Chen have proved this result in the case B = D = A. Secondly they have proved that if A has a nonzero left integral then A#A *rat is a dense subring of End k (A). We prove that #(A,A) is a dense subring of End k (Q), where Q is a certain subspace of #(A,A) under the condition that the antipode is bijective (see Theorem 18). This condition is weaker than the condition that A has a nonzero integral. It is well known the antipode is bijective in case A has a nonzero integral. Furthermore if A has nonzero left integral, Q can be chosen to be A (see Corollary 19) and #(A,A) is both left and right primitive. Thus A#A *rat ? #(A,A) ? End k (A). Moreover we prove that the left singular ideal of the ring #(A,A) is zero. A corollary of this is a criterion for A with nonzero left integral to be finite-dimensional, namely the ring #(A,A) has a finite uniform dimension.展开更多
Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD（H） is considered, where YD （H） means the disjoint union of the c...Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD（H） is considered, where YD （H） means the disjoint union of the category of generalized Yetter-Drinfeld modules nYD^H（ α, β） for any α, β E Aut Hopf（H）. First, the fact that YD（H） is closed under Mor is proved. Secondly, based on the properties of finitely generated projective modules and semisimplicity of H, YD（H） satisfies the exact condition. Thus each object in YD（H） can be decomposed into simple ones since H is noetherian and cosemisimple. Finally, it is proved that YD （H） is a sernisimple category.展开更多
The distributed parameterized intelligent product platform(DPIPP)contains many agents of a product minimum approximate autonomous subsystem(generalized module).These distributed agents communicate,coordinate,and coope...The distributed parameterized intelligent product platform(DPIPP)contains many agents of a product minimum approximate autonomous subsystem(generalized module).These distributed agents communicate,coordinate,and cooperate using their knowledge and skills and eventually accomplish the design for mass customization in a loosely coupled environment.In this study,a new method of isomorphism analysis on generalized modules oriented to DPIPP is proposed.First,on the basis of the bill of material partition and generalized module mining,the parameters of the main characteristics are extracted to construct the main characteristic parameter matrix.Second,similarity calculation of generalized modules is realized by improving the clustering using representatives algorithm,and isomorphism model sets are obtained.Generalized modules with a similar structure are combined to complete the isomorphism analysis.The effectiveness of the proposed method is verified by taking high-and medium-pressure valve data as an example.展开更多
The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left...The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.展开更多
文摘A new generalized modular design (GMD) method is proposed based on designpractice of frame structure of hydraulic press machines. By building a series of flexible modules(FMs), design knowledge and structure features are integrated into parametric models. Then,parametric design and variational analysis methods for GMD are presented according to user defineddesign objectives and customized product characteristics. A FM-centered GMD system is developed andsuccessfully used in the rapid design of relevant products.
基金Supported by the National Science Foundation of China(Grant No.12171344)the National Key R&D Program of China(Grant Nos.2018YFA0701700 and 2018YFA0701701)。
文摘Let g be a classical complex simple Lie algebra and q be a parabolic subalgebra.Let M be a generalized Verma module induced from a one dimensional representation of q.Such M is called a scalar generalized Verma module.In this paper,we will determine the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras by computing explicitly the Gelfand-Kirillov dimension of the corresponding highest weight modules.
基金supported by the National Natural Science Foundation of China (10671013,60972089,11171022)
文摘Using a fixed-point method, we establish the generalized Hyers-Ulam stability of a general mixed additive-cubic equation： f（kx ＋ y） ＋ f（kx - y） = kf（x ＋ y） ＋ kf（x - y） ＋ 2f（kx） - 2kf（x） in Banach modules over a unital Banach algebra.
基金the National Natural Science Foundation of China (No.10961021)the Teaching and Research Award Program for Outsanding Young Teachers in Higher Education Institutions of Ministry of Education(No.NCET-02-080)
文摘Let (S,≤) be a strictly totally ordered monoid which is also artinian, and R a right noetherian ring. Assume that M is a finitely generated right R-module and N is a left Rmodule. Denote by [[MS,≤]] and [NS,≤] the module of generalized power series over M, and the generalized Macaulay-Northcott module over N, respectively. Then we show that there exists an isomorphism of Abelian groups:Tori[[ RS,≤]]([[MS,≤]],[NS,≤])≌ s∈S ToriR (M,N).
文摘In this paper, we study the ring #(D,B) and obtain two very interesting results. First we prove in Theorem 3 that the category of rational left BU-modules is equivalent to both the category of #-rational left modules and the category of all (B,D)-Hopf modules D . Cai and Chen have proved this result in the case B = D = A. Secondly they have proved that if A has a nonzero left integral then A#A *rat is a dense subring of End k (A). We prove that #(A,A) is a dense subring of End k (Q), where Q is a certain subspace of #(A,A) under the condition that the antipode is bijective (see Theorem 18). This condition is weaker than the condition that A has a nonzero integral. It is well known the antipode is bijective in case A has a nonzero integral. Furthermore if A has nonzero left integral, Q can be chosen to be A (see Corollary 19) and #(A,A) is both left and right primitive. Thus A#A *rat ? #(A,A) ? End k (A). Moreover we prove that the left singular ideal of the ring #(A,A) is zero. A corollary of this is a criterion for A with nonzero left integral to be finite-dimensional, namely the ring #(A,A) has a finite uniform dimension.
基金The National Natural Science Foundation of China(No.11371088)the Fundamental Research Funds for the Central Universities(No.3207013906)the Natural Science Foundation of Jiangsu Province(No.BK2012736)
文摘Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD（H） is considered, where YD （H） means the disjoint union of the category of generalized Yetter-Drinfeld modules nYD^H（ α, β） for any α, β E Aut Hopf（H）. First, the fact that YD（H） is closed under Mor is proved. Secondly, based on the properties of finitely generated projective modules and semisimplicity of H, YD（H） satisfies the exact condition. Thus each object in YD（H） can be decomposed into simple ones since H is noetherian and cosemisimple. Finally, it is proved that YD （H） is a sernisimple category.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.51505343 and 51705374)the China Postdoctoral Science Foundation(Grant No.2017M622509)The authors would like to thank the editors and the reviewers for their insightful comments and helpful suggestions to improve the manuscript.
文摘The distributed parameterized intelligent product platform(DPIPP)contains many agents of a product minimum approximate autonomous subsystem(generalized module).These distributed agents communicate,coordinate,and cooperate using their knowledge and skills and eventually accomplish the design for mass customization in a loosely coupled environment.In this study,a new method of isomorphism analysis on generalized modules oriented to DPIPP is proposed.First,on the basis of the bill of material partition and generalized module mining,the parameters of the main characteristics are extracted to construct the main characteristic parameter matrix.Second,similarity calculation of generalized modules is realized by improving the clustering using representatives algorithm,and isomorphism model sets are obtained.Generalized modules with a similar structure are combined to complete the isomorphism analysis.The effectiveness of the proposed method is verified by taking high-and medium-pressure valve data as an example.
基金The National Natural Science Foundation of China(No.10871042)the Natural Science Foundation of Jiangsu Province(No.BK2009258)
文摘The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.
