In this paper,the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras(see[13]).They show that every congruence relationθon a de...In this paper,the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras(see[13]).They show that every congruence relationθon a decomposable MS-algebra L can be uniquely determined by a congruence pair(θ_(1),θ_(2)),whereθ_(1)is a congruence on the de Morgan subalgebra L^(∞)of L andθ_(2)is a lattice congruence on the sublattice D(L)of L.They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L.Moreover,they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs.展开更多
For every simple graph G,a class of multiple clique cluster-whiskered graphs G^(eπm)is introduced,and it is shown that all such graphs are vertex decomposable;thus,the independence simplicial complex Ind G^(eπm)is s...For every simple graph G,a class of multiple clique cluster-whiskered graphs G^(eπm)is introduced,and it is shown that all such graphs are vertex decomposable;thus,the independence simplicial complex Ind G^(eπm)is sequentially Cohen-Macaulay.The properties of the graphs G^(eπm)and G^(π)constructed by Cook and Nagel are studied,including the enumeration of facets of the complex Ind G^(π)and the calculation of Betti numbers of the cover ideal Ic(G^(eπm).We also prove that the complex△=IndH is strongly shellable and pure for either a Boolean graph H=Bn or the full clique-whiskered graph H=G^(W)of C,which is obtained by adding a whisker to each vertex of G.This implies that both the facet ideal I(△)and the cover ideal Ic(H)have linear quotients.展开更多
As important applications of minimax-type inequalities for a family of functions in [3], in the present paper there are given a number of existence theorems on simultaneous solutions to fixed point and minimax-type in...As important applications of minimax-type inequalities for a family of functions in [3], in the present paper there are given a number of existence theorems on simultaneous solutions to fixed point and minimax-type inequality problems and to fixed point and variational-type inequality problems. not only abolishing the paracompactness hypothesis on the underlying space and weak- ening the others in the results in[1], but also making them still nicer in form with still more concise and straightforward proofs.展开更多
In the present paper there are given a number of minimax-type inequalities for a family of functions,involving two multivalued mappings,one being strongly decomposable and the other monotone.Hence some applications to...In the present paper there are given a number of minimax-type inequalities for a family of functions,involving two multivalued mappings,one being strongly decomposable and the other monotone.Hence some applications to the variational-type inequality theory and to the fixed point theory.展开更多
In this paper we give 4 futher generalization of the KKM theorem in tying up with a strongly decomposable mapping, hence some equivalent forms such as KKM-type theorems, matching theorems and coincidence theorems.
基金supported by 2nd International Conference for Mathematics,Statistics and Information Technology(ICMSIT for short)that held in the Faculty of ScienceTanta UniversityEgypt,18-20December,2018。
文摘In this paper,the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras(see[13]).They show that every congruence relationθon a decomposable MS-algebra L can be uniquely determined by a congruence pair(θ_(1),θ_(2)),whereθ_(1)is a congruence on the de Morgan subalgebra L^(∞)of L andθ_(2)is a lattice congruence on the sublattice D(L)of L.They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L.Moreover,they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs.
基金Supported by the Natural Science Foundation of Shanghai(No.19ZR1424100)the National Natural Science Foundation of China(No.11271250,11971338).
文摘For every simple graph G,a class of multiple clique cluster-whiskered graphs G^(eπm)is introduced,and it is shown that all such graphs are vertex decomposable;thus,the independence simplicial complex Ind G^(eπm)is sequentially Cohen-Macaulay.The properties of the graphs G^(eπm)and G^(π)constructed by Cook and Nagel are studied,including the enumeration of facets of the complex Ind G^(π)and the calculation of Betti numbers of the cover ideal Ic(G^(eπm).We also prove that the complex△=IndH is strongly shellable and pure for either a Boolean graph H=Bn or the full clique-whiskered graph H=G^(W)of C,which is obtained by adding a whisker to each vertex of G.This implies that both the facet ideal I(△)and the cover ideal Ic(H)have linear quotients.
基金Supported both by the National Natural Science Foundation of Chinaby the Institute of Mathematics. Academia Sinica
文摘As important applications of minimax-type inequalities for a family of functions in [3], in the present paper there are given a number of existence theorems on simultaneous solutions to fixed point and minimax-type inequality problems and to fixed point and variational-type inequality problems. not only abolishing the paracompactness hypothesis on the underlying space and weak- ening the others in the results in[1], but also making them still nicer in form with still more concise and straightforward proofs.
基金Supported both by the National Natural Science Foundation of China and by the Institute of Mathematics,Academia Sinica
文摘In the present paper there are given a number of minimax-type inequalities for a family of functions,involving two multivalued mappings,one being strongly decomposable and the other monotone.Hence some applications to the variational-type inequality theory and to the fixed point theory.
文摘In this paper we give 4 futher generalization of the KKM theorem in tying up with a strongly decomposable mapping, hence some equivalent forms such as KKM-type theorems, matching theorems and coincidence theorems.
