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
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 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
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
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.
This paper aims to confirm the optimal pruning intensity to promote paulownia growth. Annualdynamic of 8 growth indicators for pruning of three-year-old Paulownia to promote trunk extension weresimulated under 7 treat...This paper aims to confirm the optimal pruning intensity to promote paulownia growth. Annualdynamic of 8 growth indicators for pruning of three-year-old Paulownia to promote trunk extension weresimulated under 7 treatments. The results showed that annual growth process could be modeled reliably byRichards function. Eight growth parameters were developed including fast-growing point (t0), initialpoint of fast-growing period (t1), final point of fast-growing period (t2), fast-growing period (t), growthperiod (Dg), maximum day increment (AGRmax), maximum annual increment (A). Effects of pruning topromote trunk extension on growth parameters were analyzed. Paulownia remaining 3~6 lower branchesafter pruning had relatively longer fast-growing period (t), growth period (Dg), higher average day increment(Am), maximum day increment (AGRmax) and maximum annual increment (A). Therefore, lower diametergrowth of original trunk did not decrease significantly, and upper diameter growth increased to someextent. Height and diameter growth of grafting trunk, and form ratio of grafting trunk were relatively higher.Total stock volume increment was improved significantly under the condition that stock volume incrementof original trunk did not decrease.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
Inorder to carry out trunk extension by lateral buds ,the laws of trunk extension and branching sprouted from lateral buds were investigated in 1-year-old seedlings of P.tomentosaxP,fortunei 33 under natural condition...Inorder to carry out trunk extension by lateral buds ,the laws of trunk extension and branching sprouted from lateral buds were investigated in 1-year-old seedlings of P.tomentosaxP,fortunei 33 under natural conditions.The results indicated：（1）Under conditions of high density and extensive management,42%of individuals in P.tomentosaxP.fortunei 33 showed pseudo dichotomous branching characteristics and could not extend their trunks in the second year.But other individuals showed the characteristics of sympodial branching and pseudo monopodial branching （not from terminal buds ）and could realize natural trunk extension.All the 3types of branching could be called branching of pseudo asis;（2）The stem form quotieties of extended trunk in all individuals wrer larger in the second year ,but only 14%of them could straight extend their trunks and 86%of them needed2-3years to reach straight trunk estension;（3）Among individuals which could extend their trunks ,from upper lateral buds to lower lateral buds on trunks ,the lengths and diameters of branches sprouted from lateral buds became smaller and smaller ,but the angles of branching up to trunk became larger and larger ,and the fourth pair of lateral branches reached to the largest,Under the fourth pair ,the angles of branches became smaller again and those branches all died.展开更多
An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We exten...An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.展开更多
Let R be a ring with an automorphismφof order two.We introduce the definition ofφ-centrosymmetric matrices.Denote by M_(n)(R)the ring of all n X n matrices over R,and by Sn(φ,R)the set of all p-centrosymmetric n...Let R be a ring with an automorphismφof order two.We introduce the definition ofφ-centrosymmetric matrices.Denote by M_(n)(R)the ring of all n X n matrices over R,and by Sn(φ,R)the set of all p-centrosymmetric n×n matrices over R for any positive integer n.We show that Sn(φ,R)■M_(n)(R)is a separable Frobenius extension.If R is commutative,then Sn(φ,R)is a cellular algebra over the invariant subring R^(φ)of R.展开更多
This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the g...This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.展开更多
Extensive aneurysms involving the ascending aorta, aortic arch, and the descending aorta stand as a therapeutic dilemma in simultaneous management of multiple sites of pathology of the aortic arch and the descending t...Extensive aneurysms involving the ascending aorta, aortic arch, and the descending aorta stand as a therapeutic dilemma in simultaneous management of multiple sites of pathology of the aortic arch and the descending thoracic aorta. We systematically reviewed about literatures of stented elephant trunk operation （SET） identified through searches of the electronic databasesEMBASE and Medline, and aimed to summarize studies of patients undergoing SET for extensive aneurysms. Since 1996, Kato Mintroduced a hybrid technique by using stented graft implantation to the descending aorta for treatment of thoracic aortic aneurysm or dissection. It has been describe a good option for extensive thoracic aortic aneurysms and in a fashion similar to the elephant trunk technique.展开更多
A ring R is said to be satisfying P-stable range provided that whenever aR ＋ bR = R, there exists y ∈ P（R） such that a ＋ by is a unit of R, where P（R） is the subset of R which satisfies the property that up, pu...A ring R is said to be satisfying P-stable range provided that whenever aR ＋ bR = R, there exists y ∈ P（R） such that a ＋ by is a unit of R, where P（R） is the subset of R which satisfies the property that up, pu∈ P（R） for every unit u of R and p ∈P（R）. By studying this ring, some known results of rings satisfying unit-1 stable range, （ S, 2） -stable range, weakly unit 1- stable range and stable range one are unified. An element of a ring is said to be UR if it is the sum of a unit and a regular dement and a ring is said to be satisfying UR-stable range if R has P-stable range and P（R） is the set of all UR-elements of R, Some properties of this ring are studied and it is proven that if R satisfies UR-stahle range then so does any n × n matrix ring over R.展开更多
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.
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.
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This paper aims to confirm the optimal pruning intensity to promote paulownia growth. Annualdynamic of 8 growth indicators for pruning of three-year-old Paulownia to promote trunk extension weresimulated under 7 treatments. The results showed that annual growth process could be modeled reliably byRichards function. Eight growth parameters were developed including fast-growing point (t0), initialpoint of fast-growing period (t1), final point of fast-growing period (t2), fast-growing period (t), growthperiod (Dg), maximum day increment (AGRmax), maximum annual increment (A). Effects of pruning topromote trunk extension on growth parameters were analyzed. Paulownia remaining 3~6 lower branchesafter pruning had relatively longer fast-growing period (t), growth period (Dg), higher average day increment(Am), maximum day increment (AGRmax) and maximum annual increment (A). Therefore, lower diametergrowth of original trunk did not decrease significantly, and upper diameter growth increased to someextent. Height and diameter growth of grafting trunk, and form ratio of grafting trunk were relatively higher.Total stock volume increment was improved significantly under the condition that stock volume incrementof original trunk did not decrease.
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Foundation of Research Startup for Returned Student From Abroad Science Foundation of Henan Province forDistinguished Young Scholars(No.002).
文摘Inorder to carry out trunk extension by lateral buds ,the laws of trunk extension and branching sprouted from lateral buds were investigated in 1-year-old seedlings of P.tomentosaxP,fortunei 33 under natural conditions.The results indicated：（1）Under conditions of high density and extensive management,42%of individuals in P.tomentosaxP.fortunei 33 showed pseudo dichotomous branching characteristics and could not extend their trunks in the second year.But other individuals showed the characteristics of sympodial branching and pseudo monopodial branching （not from terminal buds ）and could realize natural trunk extension.All the 3types of branching could be called branching of pseudo asis;（2）The stem form quotieties of extended trunk in all individuals wrer larger in the second year ,but only 14%of them could straight extend their trunks and 86%of them needed2-3years to reach straight trunk estension;（3）Among individuals which could extend their trunks ,from upper lateral buds to lower lateral buds on trunks ,the lengths and diameters of branches sprouted from lateral buds became smaller and smaller ,but the angles of branching up to trunk became larger and larger ,and the fourth pair of lateral branches reached to the largest,Under the fourth pair ,the angles of branches became smaller again and those branches all died.
基金National Natural Science Foundation of Chian(No.60272042)Natural Science Foundation of Henan Province(No.211050300)Natural Science Foundation of Henan University(No.XK01069)
文摘In this paper, we give a survey of matrix approach in wavelet theory , and describe some related results which were obtained by ourselves.
基金Acknowledgements The authors express their gratitude to the anonymous referees for their kind suggestions and useful comments on the original manuscript, which resulted in this final version. This work was supported by the National Natural Science Foundation of China （No. 61071189）, the Natural Science Foundation for the Education Department of Henan Province of China （No. 13A110072）, and the Natural Science Foundation of Henan University （No. 2011YBZR001）.
文摘An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.
基金supported by Beijing Nova Program(Z181100006218010)by Research Ability Improvement Program of BUCEA(Grant No.X22026).
文摘Let R be a ring with an automorphismφof order two.We introduce the definition ofφ-centrosymmetric matrices.Denote by M_(n)(R)the ring of all n X n matrices over R,and by Sn(φ,R)the set of all p-centrosymmetric n×n matrices over R for any positive integer n.We show that Sn(φ,R)■M_(n)(R)is a separable Frobenius extension.If R is commutative,then Sn(φ,R)is a cellular algebra over the invariant subring R^(φ)of R.
基金This research is supported by the Natural Science Foundation of the Educational Committee of Jiang Su Province.
文摘This paper presents the matrix representation for extension of inverse of restriction of a linear operator to a subspace, on the basis of which we establish useful representations in operator and matrix form for the generalized inverse A(T,S)^(2) and give some of their applications.
文摘Extensive aneurysms involving the ascending aorta, aortic arch, and the descending aorta stand as a therapeutic dilemma in simultaneous management of multiple sites of pathology of the aortic arch and the descending thoracic aorta. We systematically reviewed about literatures of stented elephant trunk operation （SET） identified through searches of the electronic databasesEMBASE and Medline, and aimed to summarize studies of patients undergoing SET for extensive aneurysms. Since 1996, Kato Mintroduced a hybrid technique by using stented graft implantation to the descending aorta for treatment of thoracic aortic aneurysm or dissection. It has been describe a good option for extensive thoracic aortic aneurysms and in a fashion similar to the elephant trunk technique.
基金Foundation items:The National Natural Science Foundation of China (No.10571026)the Specialized Research Fund for the Doctoral Program ofHigher Education (No.20060286006)
文摘A ring R is said to be satisfying P-stable range provided that whenever aR ＋ bR = R, there exists y ∈ P（R） such that a ＋ by is a unit of R, where P（R） is the subset of R which satisfies the property that up, pu∈ P（R） for every unit u of R and p ∈P（R）. By studying this ring, some known results of rings satisfying unit-1 stable range, （ S, 2） -stable range, weakly unit 1- stable range and stable range one are unified. An element of a ring is said to be UR if it is the sum of a unit and a regular dement and a ring is said to be satisfying UR-stable range if R has P-stable range and P（R） is the set of all UR-elements of R, Some properties of this ring are studied and it is proven that if R satisfies UR-stahle range then so does any n × n matrix ring over R.
