Let S be a semigroup and let A be an S-act. Some necessary and sufficient conditions that S-subacts of A are maximal S-subacts are given. A relation B which is similar to the Green relation in semigroups is defined. B...Let S be a semigroup and let A be an S-act. Some necessary and sufficient conditions that S-subacts of A are maximal S-subacts are given. A relation B which is similar to the Green relation in semigroups is defined. By the relation B, it is proved that a non-empty set L of A is a maximal S-subact if and only if A／L is a （maximal） B-class. Finally, the concept of a C-subact is defined, some properties of C-subacts are discussed, and it is proved that A contains no maximal S-subacts if and only if every cyclic S-subact of A is a C-subact. Consequently, the results obtained by Imrich Fabrici that semigroups contain no maximal （left） ideals are the corollary of this paper.展开更多
Let S be a semigroup with zero and an S-act be a centered left S-act. This paper is devoted to the study of chain conditions on PS-acts. We prove that a PS-act having finite decomposition has ACC （DCC） on all subact...Let S be a semigroup with zero and an S-act be a centered left S-act. This paper is devoted to the study of chain conditions on PS-acts. We prove that a PS-act having finite decomposition has ACC （DCC） on all subacts if it has ACC （DCC） on essential subacts. Moreover, a PS-act with ACC （DCC） on essential subacts has ACC （DCC） on all subacts if and only if it has finite decomposition. We characterize the structure of a PS-act and generalize some results of the Goldie dimension and semisimple S-acts.展开更多
In this paper, we tackle the problem of segmenting out a sequence of actions from videos. The videos contain background and actions which are usually composed of ordered sub-actions. We refer the sub-actions and the b...In this paper, we tackle the problem of segmenting out a sequence of actions from videos. The videos contain background and actions which are usually composed of ordered sub-actions. We refer the sub-actions and the background as semantic units. Considering the possible overlap between two adjacent semantic units, we propose a bidirectional sliding window method to generate the label distributions for various segments in the video. The label distribution covers a certain number of semantic unit labels, representing the degree to which each label describes the video segment. The mapping from a video segment to its label distribution is then learned by a Label Distribution Learning (LDL) algorithm. Based on the LDL model, a soft video parsing method with segmental regular grammars is proposed to construct a tree structure for the video. Each leaf of the tree stands for a video clip of background or sub-action. The proposed method shows promising results on the THUMOST4, MSR-II and UCF101 datasets and its computational complexity is much less than the compared state-of-the-art video parsing method.展开更多
基金The National Natural Science Foundation of China(No10626012), Jiangsu Planned Projects for Postdoctoral ResearchFund(No0502022B)
文摘Let S be a semigroup and let A be an S-act. Some necessary and sufficient conditions that S-subacts of A are maximal S-subacts are given. A relation B which is similar to the Green relation in semigroups is defined. By the relation B, it is proved that a non-empty set L of A is a maximal S-subact if and only if A／L is a （maximal） B-class. Finally, the concept of a C-subact is defined, some properties of C-subacts are discussed, and it is proved that A contains no maximal S-subacts if and only if every cyclic S-subact of A is a C-subact. Consequently, the results obtained by Imrich Fabrici that semigroups contain no maximal （left） ideals are the corollary of this paper.
基金The NSF (10571181,10471045) of Chinathe NSF (021073, Z02017) of Guangdong Province
文摘Let S be a semigroup with zero and an S-act be a centered left S-act. This paper is devoted to the study of chain conditions on PS-acts. We prove that a PS-act having finite decomposition has ACC （DCC） on all subacts if it has ACC （DCC） on essential subacts. Moreover, a PS-act with ACC （DCC） on essential subacts has ACC （DCC） on all subacts if and only if it has finite decomposition. We characterize the structure of a PS-act and generalize some results of the Goldie dimension and semisimple S-acts.
基金the National Key Research & Development Plan of China (2017YFB1002801)the National Science Foundation of China (61622203, 61232007)the Jiangsu Natural Science Funds for Distinguished Young Scholar (BK20140022).
文摘In this paper, we tackle the problem of segmenting out a sequence of actions from videos. The videos contain background and actions which are usually composed of ordered sub-actions. We refer the sub-actions and the background as semantic units. Considering the possible overlap between two adjacent semantic units, we propose a bidirectional sliding window method to generate the label distributions for various segments in the video. The label distribution covers a certain number of semantic unit labels, representing the degree to which each label describes the video segment. The mapping from a video segment to its label distribution is then learned by a Label Distribution Learning (LDL) algorithm. Based on the LDL model, a soft video parsing method with segmental regular grammars is proposed to construct a tree structure for the video. Each leaf of the tree stands for a video clip of background or sub-action. The proposed method shows promising results on the THUMOST4, MSR-II and UCF101 datasets and its computational complexity is much less than the compared state-of-the-art video parsing method.
