We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on theco-multiplication map and requiring that these isomorphisms satisfy certain law of their own,which is called the co...We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on theco-multiplication map and requiring that these isomorphisms satisfy certain law of their own,which is called the copentagonidentity.We also set up a 2-category of 2-coalgebras.The purpose of this study is from the idea of reconsideringthe quasi-Hopf algebras by the categoriScation process,so that we can study the theory of quasi-Hopf algebras and theirrepresentations in some new framework of higher category theory in naturai ways.展开更多
In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain ...In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain a 2-Hom-associative algebra. On the other hand, we introduce the dual Hom-quasi-Hopf algebra and show that any dual Homquasi-Hopf algebras can be viewed as a 2-Hom-associative algebra.展开更多
In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theore...In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.展开更多
In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras and Kp algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of Kp algebras admit...In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras and Kp algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of Kp algebras admit non-pure resolutions. We provide necessary and sufficient conditions for a notherian semiperfect algebra either to be a quasi-δ-Koszul algebra or to be a quasi-Kp algebra.展开更多
The notions of u-quasi-Hopf algebras and the quantum dimension dimuM of a representation M by u are introduced.It is shown that a u-quasi-Hopf algebra H is semisimple if and only if there is a finite-dimensional proje...The notions of u-quasi-Hopf algebras and the quantum dimension dimuM of a representation M by u are introduced.It is shown that a u-quasi-Hopf algebra H is semisimple if and only if there is a finite-dimensional projective H-module P such that dimu P is invertible.展开更多
Let （C,α） and （H, β） be Hom-bialgebras and ω ： C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct （Cω H, γ） and give necessary and sufficient conditions for （Cω H, γ） to be...Let （C,α） and （H, β） be Hom-bialgebras and ω ： C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct （Cω H, γ） and give necessary and sufficient conditions for （Cω H, γ） to be a Hom-bialgebra. We study the quasi-triangular structures over （Cω H, γ） and show the necessary and sufficient conditions for （Cω H, γ R） to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D（H）＊ and construct quasi-triangular structures over D（H）＊.展开更多
In this article, we consider endomorphism algebras of direct sums of some local left ideals over a local algebra and give a construction of quasi-hereditary algebras.
In this paper, first, we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Cheb...In this paper, first, we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Chebyshev. Examples of those algebras are given including the algebras of continuous functions on compact sets. We also see some results in C＊-algebras and Hilbert C＊-modules. Next, by considering some conditions, we study Chebyshev of subalgebras in C＊-algebras.展开更多
We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result...We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.展开更多
Let a, b be two generalized Drazin invertibleelements in a Banach algebra. An explicit expression for thegeneralized Drazin inverse of the sum a ＋ b in terms of a, b,as, bd is given. The generalized Drazin inverse fo...Let a, b be two generalized Drazin invertibleelements in a Banach algebra. An explicit expression for thegeneralized Drazin inverse of the sum a ＋ b in terms of a, b,as, bd is given. The generalized Drazin inverse for the sum oftwo elements in a Banach algebra is studied by means of thesystem of idempotents. It is first proved that a ＋ b ∈ Aqnll underthe condition that a, b ∈ Aqnil, aba = 0 and ab^2 = 0 and then theexplicit expressions for the generalized Drazin inverse of thesum a ＋ b under some new conditions are given. Also, someknown results are extended.展开更多
Proteomics is the study of proteins and their interactions in a cell. With the successful completion of the Human Cenome Project, it comes the postgenome era when the proteomics technology is emerging. This paper stud...Proteomics is the study of proteins and their interactions in a cell. With the successful completion of the Human Cenome Project, it comes the postgenome era when the proteomics technology is emerging. This paper studies protein molecule from the algebraic point of view. The algebraic system （∑, ＋, ＊） is introduced, where ∑ is the set of 64 codons. According to the characteristics of （∑, ＋, ＊）, a novel quasi-amino acids code classification method is introduced and the corresponding algebraic operation table over the set ZU of the 16 kinds of quasi-amino acids is established. The internal relation is revealed about quasi-amino acids. The results show that there exist some very close correlations between the properties of the quasi-amino acids and the codon. All these correlation relationships may play an important part in establishing the logic relationship between codons and the quasi-amino acids during the course of life origination. According to Ma F et al （2003 J. Anhui Agricultural University 30 439）, the corresponding relation and the excellent properties about amino acids code are very difficult to observe. The present paper shows that （ZU, ＋,×） is a field. Furthermore, the operational results display that the eodon tga has different property from other stop codons. In fact, in the mitochondrion from human and ox genomic codon, tga is just tryptophane, is not the stop codon like in other genetic code, it is the case of the Chen W C et al （2002 Acta Biophysiea Siniea 18（1） 87）. The present theory avoids some inexplicable events of the 20 kinds of amino acids code, in other words it solves the problem of ＇the 64 codon assignments of mRNA to amino acids is probably completely wrong＇ proposed by Yang （2006 Progress in Modern Biomedicine 6 3）.展开更多
In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, the notion of (α,β)-fuzzy Q-algebras, the level Q-subalgebra is introduced where α,β are any two of {...In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, the notion of (α,β)-fuzzy Q-algebras, the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q. Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras. The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined, and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.展开更多
Let V1 and V2 be two -Banach algebras and Ri be the right operator Banach algebra and Li be the left operator Banach algebra of Vi(i=1,2). We give a characterization of the Jacobson radical for the projective tensor p...Let V1 and V2 be two -Banach algebras and Ri be the right operator Banach algebra and Li be the left operator Banach algebra of Vi(i=1,2). We give a characterization of the Jacobson radical for the projective tensor product V1rV2 in terms of the Jacobson radical for R1rL2. If V1 and V2 are isomorphic, then we show that this characterization can also be given in terms of the Jacobson radical for R2rL1.展开更多
Letαbe a flow on a Banach algebra B, and t 7→ut a continuous function from R into the group of invertible elements of B such that usαs（ut）=us＋t, s, t∈R. Then βt =Adut？αt, t∈R is also a flow on B, where Adut...Letαbe a flow on a Banach algebra B, and t 7→ut a continuous function from R into the group of invertible elements of B such that usαs（ut）=us＋t, s, t∈R. Then βt =Adut？αt, t∈R is also a flow on B, where Adut（B） , utBu-1t for any B ∈ B. β is said to be a cocycle perturbation of α. We show that if α, β are two flows on a nest algebra （or quasi-triangular algebra）, thenβ is a cocycle perturbation ofα. And the flows on a nest algebra （or quasi-triangular algebra） are all uniformly continuous.展开更多
Algebraic solutions of the D-dimensional Schrodinger equation with Killingbeck potential are investigated using the Lie algebraic approach within the framework of quasi-exact solvability. The spectrum and wavefunction...Algebraic solutions of the D-dimensional Schrodinger equation with Killingbeck potential are investigated using the Lie algebraic approach within the framework of quasi-exact solvability. The spectrum and wavefunctions of the system are reported and the allowed values of the potential parameters are obtained through the sl（2） algebraization.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos. 10975102, 11031005 10871135, 10871227, and PHR201007107
文摘We categorify the notion of coalgebras by imposing a co-associative law up to some isomorphisms on theco-multiplication map and requiring that these isomorphisms satisfy certain law of their own,which is called the copentagonidentity.We also set up a 2-category of 2-coalgebras.The purpose of this study is from the idea of reconsideringthe quasi-Hopf algebras by the categoriScation process,so that we can study the theory of quasi-Hopf algebras and theirrepresentations in some new framework of higher category theory in naturai ways.
基金Supported by the National Natural Science Foundation of China（11047030, 11171055） Supported by the Grant from China Scholarship Counci1（2011841026）
文摘In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain a 2-Hom-associative algebra. On the other hand, we introduce the dual Hom-quasi-Hopf algebra and show that any dual Homquasi-Hopf algebras can be viewed as a 2-Hom-associative algebra.
基金supported by the National Natural Science Foundation of China(No.11361064)the project No.174024 of the Ministry of Education,Science and Technological Department of the Republic of Serbia
文摘In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.
基金Supported by the National Natural Science Foundation of China(10971188)the Zhejiang ProvincialNatural Science Foundation of China(J20080154)
文摘In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras and Kp algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of Kp algebras admit non-pure resolutions. We provide necessary and sufficient conditions for a notherian semiperfect algebra either to be a quasi-δ-Koszul algebra or to be a quasi-Kp algebra.
文摘The notions of u-quasi-Hopf algebras and the quantum dimension dimuM of a representation M by u are introduced.It is shown that a u-quasi-Hopf algebra H is semisimple if and only if there is a finite-dimensional projective H-module P such that dimu P is invertible.
基金Supported by the National Natural Science Foundation of China(60873267)the Ningbo Natural Science Foundation of China(2011A610172)K.C.Wang Magna Fund in Ningbo University
文摘Let （C,α） and （H, β） be Hom-bialgebras and ω ： C × H → H × C a linear map. We introduce a Horn-ω-smash coproduct （Cω H, γ） and give necessary and sufficient conditions for （Cω H, γ） to be a Hom-bialgebra. We study the quasi-triangular structures over （Cω H, γ） and show the necessary and sufficient conditions for （Cω H, γ R） to be a quasi-triangular Hom-Hopf algebra. As applications of our results, we introduce the concept of D（H）＊ and construct quasi-triangular structures over D（H）＊.
基金Supported by the National Natural Science Foundation of China(10801117)
文摘In this article, we consider endomorphism algebras of direct sums of some local left ideals over a local algebra and give a construction of quasi-hereditary algebras.
文摘In this paper, first, we consider closed convex and bounded subsets of infinite-dimensional unital Banach algebras and show with regard to the general conditions that these sets are not quasi-Chebyshev and pseudo-Chebyshev. Examples of those algebras are given including the algebras of continuous functions on compact sets. We also see some results in C＊-algebras and Hilbert C＊-modules. Next, by considering some conditions, we study Chebyshev of subalgebras in C＊-algebras.
文摘We shall generalize the results of [9] about characterization of isomorphisms on quasi-Banach algebras by providing integral type conditions. Also, we shall give some new results in this way and finally, give a result about hybrid fixed point of two homomorphisms on quasi-Banach algebras.
基金The National Natural Science Foundation of China(No.11371089,11371165)the Natural Science Foundation of Jilin Province(No.20160101264JC)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020)the Natural Science Foundation of Jiangsu Province(No.BK20141327)the Fundamental Research Funds for the Central Universities,the Foundation of Graduate Innovation Program of Jiangsu Province(No.KYZZ15-0049)
文摘Let a, b be two generalized Drazin invertibleelements in a Banach algebra. An explicit expression for thegeneralized Drazin inverse of the sum a ＋ b in terms of a, b,as, bd is given. The generalized Drazin inverse for the sum oftwo elements in a Banach algebra is studied by means of thesystem of idempotents. It is first proved that a ＋ b ∈ Aqnll underthe condition that a, b ∈ Aqnil, aba = 0 and ab^2 = 0 and then theexplicit expressions for the generalized Drazin inverse of thesum a ＋ b under some new conditions are given. Also, someknown results are extended.
基金Project supported in part by the International Technology Collaboration Research Program of China (Grant No 2007DFA706700)
文摘Proteomics is the study of proteins and their interactions in a cell. With the successful completion of the Human Cenome Project, it comes the postgenome era when the proteomics technology is emerging. This paper studies protein molecule from the algebraic point of view. The algebraic system （∑, ＋, ＊） is introduced, where ∑ is the set of 64 codons. According to the characteristics of （∑, ＋, ＊）, a novel quasi-amino acids code classification method is introduced and the corresponding algebraic operation table over the set ZU of the 16 kinds of quasi-amino acids is established. The internal relation is revealed about quasi-amino acids. The results show that there exist some very close correlations between the properties of the quasi-amino acids and the codon. All these correlation relationships may play an important part in establishing the logic relationship between codons and the quasi-amino acids during the course of life origination. According to Ma F et al （2003 J. Anhui Agricultural University 30 439）, the corresponding relation and the excellent properties about amino acids code are very difficult to observe. The present paper shows that （ZU, ＋,×） is a field. Furthermore, the operational results display that the eodon tga has different property from other stop codons. In fact, in the mitochondrion from human and ox genomic codon, tga is just tryptophane, is not the stop codon like in other genetic code, it is the case of the Chen W C et al （2002 Acta Biophysiea Siniea 18（1） 87）. The present theory avoids some inexplicable events of the 20 kinds of amino acids code, in other words it solves the problem of ＇the 64 codon assignments of mRNA to amino acids is probably completely wrong＇ proposed by Yang （2006 Progress in Modern Biomedicine 6 3）.
文摘In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets, the notion of (α,β)-fuzzy Q-algebras, the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q. Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras. The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined, and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.
文摘Let V1 and V2 be two -Banach algebras and Ri be the right operator Banach algebra and Li be the left operator Banach algebra of Vi(i=1,2). We give a characterization of the Jacobson radical for the projective tensor product V1rV2 in terms of the Jacobson radical for R1rL2. If V1 and V2 are isomorphic, then we show that this characterization can also be given in terms of the Jacobson radical for R2rL1.
文摘Letαbe a flow on a Banach algebra B, and t 7→ut a continuous function from R into the group of invertible elements of B such that usαs（ut）=us＋t, s, t∈R. Then βt =Adut？αt, t∈R is also a flow on B, where Adut（B） , utBu-1t for any B ∈ B. β is said to be a cocycle perturbation of α. We show that if α, β are two flows on a nest algebra （or quasi-triangular algebra）, thenβ is a cocycle perturbation ofα. And the flows on a nest algebra （or quasi-triangular algebra） are all uniformly continuous.
文摘Algebraic solutions of the D-dimensional Schrodinger equation with Killingbeck potential are investigated using the Lie algebraic approach within the framework of quasi-exact solvability. The spectrum and wavefunctions of the system are reported and the allowed values of the potential parameters are obtained through the sl（2） algebraization.
