We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an actio...We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.展开更多
Let H be a finite-dimensional weak Hopf algebra over a field κ and A an associative algebra, and A#;H a weak crossed product. In this paper, a spectral sequence for Ext is constructed which yields an estimate for cot...Let H be a finite-dimensional weak Hopf algebra over a field κ and A an associative algebra, and A#;H a weak crossed product. In this paper, a spectral sequence for Ext is constructed which yields an estimate for cotorsion dimension of A#;H in terms of the corresponding data for H and A.展开更多
We study the reversible properties of monoid crossed products. The new class of strongly CM-reversible rings is introduced and characterized. This class of rings is a generalization of those of strongly reversible rin...We study the reversible properties of monoid crossed products. The new class of strongly CM-reversible rings is introduced and characterized. This class of rings is a generalization of those of strongly reversible rings, skew strongly reversible rings and strongly M-reversible rings. Some well-known results on this subject are generalized and extended.展开更多
Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left...Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σH, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.展开更多
This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system,and shows that the reduced crossed product is an inverse limit of an inverse...This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system,and shows that the reduced crossed product is an inverse limit of an inverse system of Banach algebra crossed products.Also,the authors show that if the locally compact group is amenable,then the crossed product and the reduced crossed product are isometrically isomorphic.展开更多
In this paper, we show that if H is a finite-dimensional Hopf algebra such that H and H^* are semisimple, then gl.dim(A#σH)=gl.dim(A), where a is a convolution invertible cocycle. We also discuss the relationshi...In this paper, we show that if H is a finite-dimensional Hopf algebra such that H and H^* are semisimple, then gl.dim(A#σH)=gl.dim(A), where a is a convolution invertible cocycle. We also discuss the relationship of global dimensions between the crossed product A^#σH and the algebra A, where A is coacted by H. Dually, we give a sufficient condition for a finite dimensional coalgebra C and a finite dimensional semisimple Hopf algebra H such that gl.dim(C α H)=gl.dim(C).展开更多
Let E be a row-finite directed graph, let G be a locally compact abelian group with dual group G = F, let w be a labeling map from E* to F, and let (C*(E), G,a^w) be the C*-dynamical system defined by w. Some m...Let E be a row-finite directed graph, let G be a locally compact abelian group with dual group G = F, let w be a labeling map from E* to F, and let (C*(E), G,a^w) be the C*-dynamical system defined by w. Some mappings concerning the AF-embedding construction of C* (E) X(aw) G are studied in more detail. Several necessary conditions of AF-embedding and some properties of almost proper labeling map are obtained. Moreover it is proved that if E is constructed by attaching some l-loops to a directed graph T consisting of some rooted directed trees and G is compact, then oJ is k almost proper, that is a sufficient condition for AF-embedding, if and only if ∑j^Kk=1^wγ j ≠fi 1r for any loop γi, γ2 …γk attached to one path in T展开更多
Let г^+ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г+ as endomorphisms of C^*-algebras, and use this to generalize the t...Let г^+ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г+ as endomorphisms of C^*-algebras, and use this to generalize the theorem of Ji.展开更多
When a flow on a C*-algebra has KMS states we study traces on the associated crossed product to show that they are determined by KMS states under a mild assumption on the flow.
Let G be a second countable groupoid with Haar system {λ~u}, A be an abelian group which left invariant acts on G. Then we have a C*-dynamic system (C*(G), A, β). In this paper we have studied the existence of quasi...Let G be a second countable groupoid with Haar system {λ~u}, A be an abelian group which left invariant acts on G. Then we have a C*-dynamic system (C*(G), A, β). In this paper we have studied the existence of quasi-invariant measure with certain properties; using these measures some important results about crossed products and groupoid C*-algebras have been obtained.展开更多
In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash produc...In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash products, two-sided smash products and two-sided crossed products and prove that they are all associative algebras. Then we show the isomorphic relations of them.展开更多
This article originates from the observation that field lines are drawn using distinctive rules in magnetic field and electrostatic fields. It aims at reconciliating the definitions of these fields and thus reaching a...This article originates from the observation that field lines are drawn using distinctive rules in magnetic field and electrostatic fields. It aims at reconciliating the definitions of these fields and thus reaching a consensus on the interpretation of field lines. Our unified field definition combines three orthogonal vectors and a unique scalar value. Field lines are then defined as isovalue lines of the scalar value, rendering it simpler to interpret in both field types. Specific to our field definition is the use of square root of vector’s cross product so that all vectors have the same physical unit. This enhanced field definition also enables a more efficient calculation of Biot-Savart law. This article is the first of a series allowing the drawing of isovalue contour lines.展开更多
Within the framework of isospin-dependent Boltzmann-Langevin model,the production cross sections of proton-rich nuclei with Z=20-25 are investigated.According to the reaction results for different isospin of projectil...Within the framework of isospin-dependent Boltzmann-Langevin model,the production cross sections of proton-rich nuclei with Z=20-25 are investigated.According to the reaction results for different isospin of projectiles^(48)Ni,^(49)Ni,and^(50)Ni,proton-rich fragments tend to be more easily produced in reactions with the protonrich projectile^(48)Ni.The production cross sections of the unknown nuclei in the vicinity of the projectile are sensitive to incident energy.It is observed that incident energy of 345 MeV/u is appropriate for producing proton-rich nuclei with Z=20-25.In projectile fragmentation reactions based on the radioactive ion beam of48Ni at 345MeV/u,several unknown proton-rich nuclei near the proton drip line are generated in the simulations.All these new nuclei are near-projectile elements near Z=28.The production cross sections of the new nuclei^(34)Ca,37,38Sc,^(38)Ti,^(40,41,42)V,^(40,41)Cr,and^(42,43,44,45)Mn are in the range of 10-2-102mb.Hence,projectile fragmentation of radioactive ion beams of Ni is a potential method for generating new proton-rich nuclei with Z=20-25.展开更多
A quasi-classical trajectory(QCT) calculation is used to investigate the vector and scalar properties of the D + Br O → DBr + O reaction based on an ab initio potential energy surface(X1A state) with collision ...A quasi-classical trajectory(QCT) calculation is used to investigate the vector and scalar properties of the D + Br O → DBr + O reaction based on an ab initio potential energy surface(X1A state) with collision energy ranging from 0.1 kcal/mol to 6 kcal/mol. The reaction probability, the cross section, and the rate constant are studied. The probability and the cross section show decreasing behaviors as the collision energy increases. The distribution of the rate constant indicates that the reaction favorably occurs in a relatively low-temperature region(T 〈 100 K). Meanwhile, three product angular distributions P(θr), P(φr), and P(θr, φr) are presented, which reflect the positive effect on the rotational angular momentum j' polarization of the DBr product molecule. In addition, two of the polarization-dependent generalized differential cross sections(PDDCSs), PDDCS00 and PDDCS20, are computed as well. Our results demonstrate that both vector and scalar properties have strong energy dependence.展开更多
In the wireless guidance system, the signals that receiver received has obvious Doppler shift for the high dynamic characteristic of the carrier. A new solution of carrier frequency tracking loop with frequency modify...In the wireless guidance system, the signals that receiver received has obvious Doppler shift for the high dynamic characteristic of the carrier. A new solution of carrier frequency tracking loop with frequency modifying system is put forward. The characteristic of cross product auto frequency control and the second order loop filter in this loop are analyzed. The simulation shows that this loop can accomplish frequency tracking well in high dynamic circumstance.展开更多
Some useful layered cross product decompositons are derived both for general bit permutation networks and for(2n-1)-stage multistage interconnection networks.Several issues in related works are clarified and the rearr...Some useful layered cross product decompositons are derived both for general bit permutation networks and for(2n-1)-stage multistage interconnection networks.Several issues in related works are clarified and the rearrangeability of some interesting networks are considered.In particular, the rearrangeability of one class of networks is formulated as a new type of combinatorial design problmes.展开更多
Kr L X-ray and Au M X-ray emission for Kr13+ ions with energies of 1.5 MeV and 3.9 MeV impacting on an Au target are investigated at heavy ion research facility in Lanzhou (HIRFL). The L-shell X-ray yield per ion o...Kr L X-ray and Au M X-ray emission for Kr13+ ions with energies of 1.5 MeV and 3.9 MeV impacting on an Au target are investigated at heavy ion research facility in Lanzhou (HIRFL). The L-shell X-ray yield per ion of Kr is measured as a function of incident energy. In addition, Kr L X-ray production cross section is extracted from the yield and compared with the result obtained from the classical binary-encounter approximation (BEA) model. Furthermore, the intensity ratio of the Au M/33 to Ma1 X-ray is investigated as a function of incident energy.展开更多
In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve ...In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.展开更多
Let X={X_(p)}p∈Pbe a product system over a lattice ordered group(G,P)with coefficients in a C*-algebra A.In this paper,we study the reduced crossed product of the gauge coactionδof G on the Cuntz-Pimsner algebra NO_...Let X={X_(p)}p∈Pbe a product system over a lattice ordered group(G,P)with coefficients in a C*-algebra A.In this paper,we study the reduced crossed product of the gauge coactionδof G on the Cuntz-Pimsner algebra NO_(X)^(r).When X is a product system of Morita equivalence bimodules,we show that the reduced crossed product of the gauge coaction is Morita equivalent to the C*-algebra A.展开更多
Let K be a normal subgroup of the finite group H. To a point of a K-interior H-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to the point given by th...Let K be a normal subgroup of the finite group H. To a point of a K-interior H-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to the point given by the Brauer homomorphism. This may be regarded as a generalization and an alternative treatment of Dade's results [2, Section 12].展开更多
文摘We introduce a special tracial Rokhlin property for unital C~*-algebras. Let A be a unital tracial rank zero C~*-algebra(or tracial rank no more than one C~*-algebra). Suppose that α : G → Aut(A) is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~*-algebra. Then, the crossed product C~*-algebra C~*(G, A, α) has tracia rank zero(or has tracial rank no more than one). In fact,we get a more general results.
基金The NSF(KJ2016A545,KJ2015B12,2017ZR08zd)of Anhui Provincethe key projectsoutstanding young talent support program(gxyq ZD2016353)of Anhui Province
文摘Let H be a finite-dimensional weak Hopf algebra over a field κ and A an associative algebra, and A#;H a weak crossed product. In this paper, a spectral sequence for Ext is constructed which yields an estimate for cotorsion dimension of A#;H in terms of the corresponding data for H and A.
基金The NSF(11601005) of Chinathe Jiangsu Planned Projects(1601151C) for Postdoctoral Research Funds+1 种基金the Provincial NSF(KJ2017A040) of Anhui Provincethe Graduate Students Innovation Projects(2016141) of Anhui University of Technology
文摘We study the reversible properties of monoid crossed products. The new class of strongly CM-reversible rings is introduced and characterized. This class of rings is a generalization of those of strongly reversible rings, skew strongly reversible rings and strongly M-reversible rings. Some well-known results on this subject are generalized and extended.
基金Foundationitem:The NSF(10271081)of Chinathe NSF(1042004)of Beijing City
文摘Let H be a finite dimensional cocommutative Hopf algebra and A an H-module algebra. In this paper, we characterize the projectivity (injectivity) of M as a left A#σH-module when it is projective (injective) as a left A-module. The sufficient and necessary condition for A#σH, the crossed product, to have finite global homological dimension is given, in terms of the global homological dimension of A and the surjectivity of trace maps, provided that H is cocommutative and A is commutative.
基金supported by the National Natural Science Foundation of China(No.11971277)the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province(Nos.2019L0742,2019L0747)+1 种基金the Science and Technology Plan Project of Datong City(Nos.2021155,2019156)the Doctoral Scientific Research Foundation of Shanxi Datong University(No.2015-B-09)
文摘This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system,and shows that the reduced crossed product is an inverse limit of an inverse system of Banach algebra crossed products.Also,the authors show that if the locally compact group is amenable,then the crossed product and the reduced crossed product are isometrically isomorphic.
基金Supported by the National Natural Science Foundation of China (Grant No. 10771182)Nantong University Foundation (Grant No. xj06Z009)
文摘In this paper, we show that if H is a finite-dimensional Hopf algebra such that H and H^* are semisimple, then gl.dim(A#σH)=gl.dim(A), where a is a convolution invertible cocycle. We also discuss the relationship of global dimensions between the crossed product A^#σH and the algebra A, where A is coacted by H. Dually, we give a sufficient condition for a finite dimensional coalgebra C and a finite dimensional semisimple Hopf algebra H such that gl.dim(C α H)=gl.dim(C).
基金Supported by National Natural Science Foundation of China (Grant Nos. 10771161, 11071188)
文摘Let E be a row-finite directed graph, let G be a locally compact abelian group with dual group G = F, let w be a labeling map from E* to F, and let (C*(E), G,a^w) be the C*-dynamical system defined by w. Some mappings concerning the AF-embedding construction of C* (E) X(aw) G are studied in more detail. Several necessary conditions of AF-embedding and some properties of almost proper labeling map are obtained. Moreover it is proved that if E is constructed by attaching some l-loops to a directed graph T consisting of some rooted directed trees and G is compact, then oJ is k almost proper, that is a sufficient condition for AF-embedding, if and only if ∑j^Kk=1^wγ j ≠fi 1r for any loop γi, γ2 …γk attached to one path in T
基金the Academy of Sciences of Malaysia through SAGA Projectthe Indonesian Research Fund for Doctorate Sandwich Programs(URGE)
文摘Let г^+ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г+ as endomorphisms of C^*-algebras, and use this to generalize the theorem of Ji.
文摘When a flow on a C*-algebra has KMS states we study traces on the associated crossed product to show that they are determined by KMS states under a mild assumption on the flow.
基金This work is supported by National Natural Science Foundation of China
文摘Let G be a second countable groupoid with Haar system {λ~u}, A be an abelian group which left invariant acts on G. Then we have a C*-dynamic system (C*(G), A, β). In this paper we have studied the existence of quasi-invariant measure with certain properties; using these measures some important results about crossed products and groupoid C*-algebras have been obtained.
基金Foundation item: Supported by the Scientific Research Foundation for Doctoral Scientists of Henan University of Science and Technology(09001303) Supported by the National Natural Science Foundation of China(11101128)
文摘In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash products, two-sided smash products and two-sided crossed products and prove that they are all associative algebras. Then we show the isomorphic relations of them.
文摘This article originates from the observation that field lines are drawn using distinctive rules in magnetic field and electrostatic fields. It aims at reconciliating the definitions of these fields and thus reaching a consensus on the interpretation of field lines. Our unified field definition combines three orthogonal vectors and a unique scalar value. Field lines are then defined as isovalue lines of the scalar value, rendering it simpler to interpret in both field types. Specific to our field definition is the use of square root of vector’s cross product so that all vectors have the same physical unit. This enhanced field definition also enables a more efficient calculation of Biot-Savart law. This article is the first of a series allowing the drawing of isovalue contour lines.
基金Supported by the National Natural Science Foundation of China(No.12135004,No.11635003 and No.11961141004)。
文摘Within the framework of isospin-dependent Boltzmann-Langevin model,the production cross sections of proton-rich nuclei with Z=20-25 are investigated.According to the reaction results for different isospin of projectiles^(48)Ni,^(49)Ni,and^(50)Ni,proton-rich fragments tend to be more easily produced in reactions with the protonrich projectile^(48)Ni.The production cross sections of the unknown nuclei in the vicinity of the projectile are sensitive to incident energy.It is observed that incident energy of 345 MeV/u is appropriate for producing proton-rich nuclei with Z=20-25.In projectile fragmentation reactions based on the radioactive ion beam of48Ni at 345MeV/u,several unknown proton-rich nuclei near the proton drip line are generated in the simulations.All these new nuclei are near-projectile elements near Z=28.The production cross sections of the new nuclei^(34)Ca,37,38Sc,^(38)Ti,^(40,41,42)V,^(40,41)Cr,and^(42,43,44,45)Mn are in the range of 10-2-102mb.Hence,projectile fragmentation of radioactive ion beams of Ni is a potential method for generating new proton-rich nuclei with Z=20-25.
基金supported by the Jilin University,China(Grant No.419080106440)the Chinese National Fusion Project for the International Thermonuclear Experimental Reactor(ITER)(Grant No.2010GB104003)the National Natural Science Foundation of China(Grant No.10974069)
文摘A quasi-classical trajectory(QCT) calculation is used to investigate the vector and scalar properties of the D + Br O → DBr + O reaction based on an ab initio potential energy surface(X1A state) with collision energy ranging from 0.1 kcal/mol to 6 kcal/mol. The reaction probability, the cross section, and the rate constant are studied. The probability and the cross section show decreasing behaviors as the collision energy increases. The distribution of the rate constant indicates that the reaction favorably occurs in a relatively low-temperature region(T 〈 100 K). Meanwhile, three product angular distributions P(θr), P(φr), and P(θr, φr) are presented, which reflect the positive effect on the rotational angular momentum j' polarization of the DBr product molecule. In addition, two of the polarization-dependent generalized differential cross sections(PDDCSs), PDDCS00 and PDDCS20, are computed as well. Our results demonstrate that both vector and scalar properties have strong energy dependence.
文摘In the wireless guidance system, the signals that receiver received has obvious Doppler shift for the high dynamic characteristic of the carrier. A new solution of carrier frequency tracking loop with frequency modifying system is put forward. The characteristic of cross product auto frequency control and the second order loop filter in this loop are analyzed. The simulation shows that this loop can accomplish frequency tracking well in high dynamic circumstance.
文摘Some useful layered cross product decompositons are derived both for general bit permutation networks and for(2n-1)-stage multistage interconnection networks.Several issues in related works are clarified and the rearrangeability of some interesting networks are considered.In particular, the rearrangeability of one class of networks is formulated as a new type of combinatorial design problmes.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.11075135,11075192,and 11075125)the Scientific Research Foundation of the Education Department of Shaanxi Province,China (Grant No.2010JK895)the Special Foundation of Xianyang Normal University,China (Grant No.11XSYK308)
文摘Kr L X-ray and Au M X-ray emission for Kr13+ ions with energies of 1.5 MeV and 3.9 MeV impacting on an Au target are investigated at heavy ion research facility in Lanzhou (HIRFL). The L-shell X-ray yield per ion of Kr is measured as a function of incident energy. In addition, Kr L X-ray production cross section is extracted from the yield and compared with the result obtained from the classical binary-encounter approximation (BEA) model. Furthermore, the intensity ratio of the Au M/33 to Ma1 X-ray is investigated as a function of incident energy.
基金supported by Chinese Universities Scientific Fund(Grant No.WK0010000031)supported by National Natural Science Foundation of China(Grant Nos.11231390,11371222,11301511)
文摘In this paper, we will estimate an upper bound for the similarity degree of the crossed product of a hyperfinite finite von Neumann algebra by weakly compact action of an infinite discrete group. We will also improve some upper bounds for similarity degrees of some finite von Neumann algebras.
基金Wang was supported in part by NSF of China(Grant Nos.11871303,11971463,11671133)NSF of Shandong Province(Grant No.ZR2019MA039)Yuan was supported in part by NSF of China(Grant Nos.11871303,11871127,11971463)。
文摘Let X={X_(p)}p∈Pbe a product system over a lattice ordered group(G,P)with coefficients in a C*-algebra A.In this paper,we study the reduced crossed product of the gauge coactionδof G on the Cuntz-Pimsner algebra NO_(X)^(r).When X is a product system of Morita equivalence bimodules,we show that the reduced crossed product of the gauge coaction is Morita equivalent to the C*-algebra A.
基金supported by a grant of the Ministry of National Education,Romania,CNCS-UEFISCDI,project number PN-II-ID-PCE-2012-4-0100
文摘Let K be a normal subgroup of the finite group H. To a point of a K-interior H-algebra we associate a group extension, and we prove that this extension is isomorphic to an extension associated to the point given by the Brauer homomorphism. This may be regarded as a generalization and an alternative treatment of Dade's results [2, Section 12].