The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- reg...The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.展开更多
A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper ...A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.展开更多
In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight fra...In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for L2 （JRa） by replacing some mother framelets.展开更多
In the extension matrix approach of inductive learning, the minimum formula (MFL) ofa positive example (e^+) against a set of negative examples (NE) and tbe optimal covering(MCV) of a set of positive examples (PE) aga...In the extension matrix approach of inductive learning, the minimum formula (MFL) ofa positive example (e^+) against a set of negative examples (NE) and tbe optimal covering(MCV) of a set of positive examples (PE) against NE are two striking optimization prob-lems. They have been proved to be NP-hard in Ref. [1]. This paper presents four algorithms,named MFL, HFL, MCV and HCV respectively. Algorithms MFL and MCV are complete forsolving the problems MFL and MCV but they opelate in exponential time on the number ofattributes in an example space and polynomial time on the number of examples. AlgorithmsHFL and HCV are two heuristic algorithms homologous to Algorithms MFL and MCV buttheir time complexities are polynomial.展开更多
This paper is concerned with seeking the general solutions of matrix equation M（ξ）M＊ （ξ） = Is for the construction of multiple channel biorthogonal wavelets, provided that some special solution of its is known.
We study structures of endomorphisms and introduce a skew Hochschild 2-cocycles related to Hochschild 2-cocycle. We moreover define skew Hochschild extensions equipped with skew Hochschild 2-cocycles, and then we exam...We study structures of endomorphisms and introduce a skew Hochschild 2-cocycles related to Hochschild 2-cocycle. We moreover define skew Hochschild extensions equipped with skew Hochschild 2-cocycles, and then we examine uniquely clean, Abelian, directly finite, symmetric, and reversible ring properties of skew Hochschild extensions and related ring systems. The results obtained here provide various kinds of examples of such rings. Especially, we give an answer negatively to the question of H. Lin and C. Xi for the corresponding Hochschild extensions of reversible （or semicommutative） rings. Finally, we establish three kinds of Hochschild extensions with Hochschild 2-cocycles and skew Hochschild 2-cocycles.展开更多
基金The Foundation for Excellent Doctoral Dissertationof Southeast University (NoYBJJ0507)the National Natural ScienceFoundation of China (No10571026)the Natural Science Foundation ofJiangsu Province (NoBK2005207)
文摘The concept of the strongly π-regular general ring （with or without unity） is introduced and some extensions of strongly π-regular general rings are considered. Two equivalent characterizations on strongly π- regular general rings are provided. It is shown that I is strongly π-regular if and only if, for each x ∈I, x^n =x^n＋1y = zx^n＋1 for n ≥ 1 and y, z ∈ I if and only if every element of I is strongly π-regular. It is also proved that every upper triangular matrix general ring over a strongly π-regular general ring is strongly π-regular and the trivial extension of the strongly π-regular general ring is strongly clean.
基金The NSF(11471108) of Chinathe NSF(2015JJ2051,2016JJ2050) of Hunan Provincethe Teaching Reform Foundation(G21316) of Hunan Province
文摘A unitary right R-module MR satisfies acc on d-annihilators if for every sequence（a;）;of elements of R the ascending chain AnnM（a;）■ AnnM（a;a;）■AnnM（a;a;a;）■… of submodules of MR stabilizes. In this paper we first investigate some triangular matrix extensions of modules with acc on d-annihilators. Then we show that under some additional conditions,the Ore extension module M[x]R[x;α,δ]over the Ore extension ring R[x;α,δ] satisfies acc on d-annihilators if and only if the module MR satisfies acc on d-annihilators. Consequently, several known results regarding modules with acc on d-annihilators are extended to a more general setting.
文摘In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight frames for L2 （JRa） by replacing some mother framelets.
基金Project supported by the National Natural Science Foundation of China.
文摘In the extension matrix approach of inductive learning, the minimum formula (MFL) ofa positive example (e^+) against a set of negative examples (NE) and tbe optimal covering(MCV) of a set of positive examples (PE) against NE are two striking optimization prob-lems. They have been proved to be NP-hard in Ref. [1]. This paper presents four algorithms,named MFL, HFL, MCV and HCV respectively. Algorithms MFL and MCV are complete forsolving the problems MFL and MCV but they opelate in exponential time on the number ofattributes in an example space and polynomial time on the number of examples. AlgorithmsHFL and HCV are two heuristic algorithms homologous to Algorithms MFL and MCV buttheir time complexities are polynomial.
基金supported in part Professor Yuesheng Xu under the program of"One Hundred Outstanding Young Chinese Scientists" of the Chinese Academy of Sciencesthe Graduate Innovation Foundation of the Chinese Academy of Sciences
文摘This paper is concerned with seeking the general solutions of matrix equation M（ξ）M＊ （ξ） = Is for the construction of multiple channel biorthogonal wavelets, provided that some special solution of its is known.
文摘We study structures of endomorphisms and introduce a skew Hochschild 2-cocycles related to Hochschild 2-cocycle. We moreover define skew Hochschild extensions equipped with skew Hochschild 2-cocycles, and then we examine uniquely clean, Abelian, directly finite, symmetric, and reversible ring properties of skew Hochschild extensions and related ring systems. The results obtained here provide various kinds of examples of such rings. Especially, we give an answer negatively to the question of H. Lin and C. Xi for the corresponding Hochschild extensions of reversible （or semicommutative） rings. Finally, we establish three kinds of Hochschild extensions with Hochschild 2-cocycles and skew Hochschild 2-cocycles.
