After defining the strong tensor product of strong (sub)chain complenes, it is shown that an analogue of the Kunneth theorem holds in strong homology by proving that the kernel (cokernel) of connecting homomorphisms i...After defining the strong tensor product of strong (sub)chain complenes, it is shown that an analogue of the Kunneth theorem holds in strong homology by proving that the kernel (cokernel) of connecting homomorphisms is isomorphic to the direct sum of torsion (tensor) products of strong homology groups. An isomorphism between strong (r-stage) homology groups of inverse systems is also constructed.展开更多
This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor ,4 such that the tensor complementarity problem （q, A）： finding an x ∈R^n such that x ≥ 0, q＋Axm-1 ≥ 0, and xT（q＋Ax^m-1） = 0...This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor ,4 such that the tensor complementarity problem （q, A）： finding an x ∈R^n such that x ≥ 0, q＋Axm-1 ≥ 0, and xT（q＋Ax^m-1） = 0, has a solution for each vector q ∈R^n. Several subclasses of Q-tensors are given： F-tensors, R-tensors, strictly semi-positive tensors and semi-positive R0-tensors. We prove that a nonnegative tensor is a Q-tensor if and only if all of its principal diagonal entries are positive, and so the equivalence of Q-tensor, R-tensors, strictly semi-positive tensors was showed if they are nonnegative tensors. We also show that a tensor is an R0-tensor if and only if the tensor complementarity problem （0, A） has no non-zero vector solution, and a tensor is a R-tensor if and only if it is an R0-tensor and the tensor complementarity problem （e,A） has no non-zero vector solution, where e = （1, 1…. , 1）T展开更多
We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We investigate some properties of this new construction, for...We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We investigate some properties of this new construction, for instance, we prove a result of the type ＂invariance under twisting＂ and we show that under certain circumstances L-R- twisted tensor products of algebras may be iterated.展开更多
文摘After defining the strong tensor product of strong (sub)chain complenes, it is shown that an analogue of the Kunneth theorem holds in strong homology by proving that the kernel (cokernel) of connecting homomorphisms is isomorphic to the direct sum of torsion (tensor) products of strong homology groups. An isomorphism between strong (r-stage) homology groups of inverse systems is also constructed.
基金supported by the National Natural Science Foundation of China(Grant No.11571095,11601134)the Hong Kong Research Grant Council(Grant No.PolyU502111,501212,501913 and 15302114)
文摘This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor ,4 such that the tensor complementarity problem （q, A）： finding an x ∈R^n such that x ≥ 0, q＋Axm-1 ≥ 0, and xT（q＋Ax^m-1） = 0, has a solution for each vector q ∈R^n. Several subclasses of Q-tensors are given： F-tensors, R-tensors, strictly semi-positive tensors and semi-positive R0-tensors. We prove that a nonnegative tensor is a Q-tensor if and only if all of its principal diagonal entries are positive, and so the equivalence of Q-tensor, R-tensors, strictly semi-positive tensors was showed if they are nonnegative tensors. We also show that a tensor is an R0-tensor if and only if the tensor complementarity problem （0, A） has no non-zero vector solution, and a tensor is a R-tensor if and only if it is an R0-tensor and the tensor complementarity problem （e,A） has no non-zero vector solution, where e = （1, 1…. , 1）T
文摘We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We investigate some properties of this new construction, for instance, we prove a result of the type ＂invariance under twisting＂ and we show that under certain circumstances L-R- twisted tensor products of algebras may be iterated.
