By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipat...By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipative 3D Lotka-Volterra systems and five classes of maximal stably dissipative graphs were obtained for these systems. Finally, the necessary and sufficient condition of being stably dissipative for every class was studied, under which the matrix associated with the graph is stably dissipative.展开更多
The structures and the vertical profiles of turbulent variance and covariance of the stably stratified boundary layer (SBL) are simulated with a second-order closure turbulence model. The results confirm that the vert...The structures and the vertical profiles of turbulent variance and covariance of the stably stratified boundary layer (SBL) are simulated with a second-order closure turbulence model. The results confirm that the vertical profiles of the dimensionless turbulence variance and covariance can be well represented by the form F = A(1 - Z / h)x. Here h is the height of SBL. and both exponent a and coefficient A are the functions of terrain, baroclinicity, radiation cooling and the state of temporal development of SBL. Comparing with Minnesota and Cabauw experiment data, we have analysed the value of a and expounded the main reasons that great difference in a exists among different literatures.展开更多
Stably stratified flows over a two-dimensional hill are investigated in a channel of finite depth using a three-dimensional direct numerical simulation (DNS). The present study follows onto our previous two-dimensiona...Stably stratified flows over a two-dimensional hill are investigated in a channel of finite depth using a three-dimensional direct numerical simulation (DNS). The present study follows onto our previous two-dimensional DNS studies of stably stratified flows over a hill in a channel of finite depth and provides a more realistic simulation of atmospheric flows than our previous studies. A hill with a constant cross-section in the spanwise (y) direction is placed in a 3-D computational domain. As in the previous 2-D simulations, to avoid the effect of the ground boundary layer that develops upstream of the hill, no-slip conditions are imposed only on the hill surface and the surface downstream of the hill;slip conditions are imposed on the surface upstream of the hill. The simulated 3-D flows are discussed by comparing them to the simulated 2-D flows with a focus on the effect of the stable stratification on the non-periodic separation and reattachment of the flow behind the hill. In neutral (K = 0, where K is a non-dimensional stability parameter) and weakly stable (K = 0.8) conditions, 3-D flows over a hill differ clearly from 2-D flows over a hill mainly because of the three-dimensionality of the flow, that is the development of a spanwise flow component in the 3-D flows. In highly stable conditions (K = 1, 1.3), long-wavelength lee waves develop downstream of the hill in both 2-D and 3-D flows, and the behaviors of the 2-D and 3-D flows are similar in the vicinity of the hill. In other words, the spanwise component of the 3-D flows is strongly suppressed in highly stable conditions, and the flow in the vicinity of the hill becomes approximately two-dimensional in the x and z directions.展开更多
With the support by the National Natural Science Foundation of China and the Strategic Priority Research Program of the Chinese Academy of Sciences,Prof.Chu Haiyan’s laboratory at the Institute of Soil Science,Chines...With the support by the National Natural Science Foundation of China and the Strategic Priority Research Program of the Chinese Academy of Sciences,Prof.Chu Haiyan’s laboratory at the Institute of Soil Science,Chinese Academy of Sciences,reported comparative analysis of bacterial communities in soils that have been subjected to 30years of chemical fertilization(NPK)with the addition of either cow manure,pig manure or wheat straw residues,which was published in Soil Biology&Biochemistry(2015,88:9—18).展开更多
At night, over sloped terrain the drainage flow can be always caused by cooling: of the air near a sloped surface. Its structure differs from that over horizontal planes. Brost and Wyngaard pointed out that even sligh...At night, over sloped terrain the drainage flow can be always caused by cooling: of the air near a sloped surface. Its structure differs from that over horizontal planes. Brost and Wyngaard pointed out that even slight terrain slopes have strong effects on the turbulent structure and the parameters of the boundary layer.展开更多
Let G be a finite group and A be a finite-dimensional selfinjective algebra over an algebraically closed field. Suppose A is a left G-module algebra. Some suficient conditions for the skew group algebra AG to be stabl...Let G be a finite group and A be a finite-dimensional selfinjective algebra over an algebraically closed field. Suppose A is a left G-module algebra. Some suficient conditions for the skew group algebra AG to be stably Calabi-Yau are provided, and some new examples of stably Calabi-Yau algebras are given as well.展开更多
The conceptions of stably free order,stably free rank and power stably free isomorphism are given.The structure of power stably free module categories over a JBN ring (not necessarily commutative) and the K0 groups of...The conceptions of stably free order,stably free rank and power stably free isomorphism are given.The structure of power stably free module categories over a JBN ring (not necessarily commutative) and the K0 groups of power stably free module categories over an IBN ring are investigated through a new route.展开更多
To promote efficient screening of active angiogenic drugs from traditional medicines, we constructed a humanembryonic kidney-293 cell model using vascular endothelial growth factor （VEGF） gene promoter as the drug t...To promote efficient screening of active angiogenic drugs from traditional medicines, we constructed a humanembryonic kidney-293 cell model using vascular endothelial growth factor （VEGF） gene promoter as the drug target. Inthis model, VEGF gene promoter may regulate the expression of the luciferase reporter gene by responding to thestimulation of drug molecules. This cell model allows rapid and efficient screening of vascular-inducing activecomponents from several drug monomer molecules. Furthermore, we used rat bone marrow mesenchymal stem cells（rMSCs） to conduct a preliminary study on the activity of alantolactone. Using simvastatin as a positive control, weinvestigated the effects of alantolactone on the expression of vascular-related cell marker molecules such as VEGF andα-smooth muscle actin （α-SMA） in rMSCs. According to our results, 0.1, 1, 3 and 5 μM of alantolactone upregulated thetranscriptional luciferase gene activity of VEGF promoter, and a significant difference from that in the control group wasobserved. Among them, 3μM of alantolactone showed the better effect than that of 3 μM of simvastatin （P = 0.036） andother concentrations of alantolactone and simvastatin showed similar effects. Compared with that in the control group,rMSCs induced with 1μM alantolactone for 3 days showed a significant increase in the relative mRNA expressions ofVEGF and α-SMA genes. However, these effect of 5 μM alantolactone were weaker than those of 5 μM simvastatin （P 〈0.05）; rMSCs treated with 1 μM alantolactone for 3 days showed brighter green fluorescence （FITC marker） of α-SMAand VEGF in situ expression than that observed in the control group and similar fluorescence intensity than that ofsimvastatin group in an immunoradiometric assay. The above results demonstrate the reliability of the highly efficientsystem for screening of active drug molecules and confirmed the vascular induction function of alantolactone at the geneand protein levels.展开更多
The murine interleukin-2 gene was introduced intomurine melanoma B16 cells by retroviral vector. AfterG418 selection, a clone stably secreting high level ofinterleukin-2 (1038IU per 10~6 cells per 24 hours) wasobtaine...The murine interleukin-2 gene was introduced intomurine melanoma B16 cells by retroviral vector. AfterG418 selection, a clone stably secreting high level ofinterleukin-2 (1038IU per 10~6 cells per 24 hours) wasobtained. The tumorigenicity of this clone decreasedsignificantly as compared with parental tumor cells andtumor cells transferred neomycin gene. There was notumor developed after injection of 5×10~5 IL2-transfectedB16 cells into C57BL/6 mice. However when the展开更多
Myoblast-mediated gene transfer approach has agreat potential to be developed into a durable genetherapy method for various diseases. To increase theexpression level of human factor Ⅸ (hFⅨ) in musclecells, we constr...Myoblast-mediated gene transfer approach has agreat potential to be developed into a durable genetherapy method for various diseases. To increase theexpression level of human factor Ⅸ (hFⅨ) in musclecells, we constructed a series of hFⅨ expression vectorswith the retroviral vector frame and examined their hFⅨexpression in skeletal muscle cells. Firstly, we introducedhFⅨ minigene (hFⅨ ml or hFⅨ m2), which contains atruncated first intron (1. 4 kb or 0. 3 kb) of hFⅨ展开更多
In this paper, the exploitation of single population modelled by Richards model is studied. By choosing the maximum annual-sustainable yield as management objective, we investigate the optimal harvesting policies for ...In this paper, the exploitation of single population modelled by Richards model is studied. By choosing the maximum annual-sustainable yield as management objective, we investigate the optimal harvesting policies for autonomous and periodic exploited Richards model. Further, when the functions in the exploited Richards model are stably bounded functions, we study the ultimately optimal harvesting policy and obtain the corresponding average limiting maximum sustainable yield.展开更多
Because of the widely-used nonlinear loads, the problems of harmonics and low power factor in power systems are becoming more and more serious. In view of the above problems, a shunt three-phase active power filter （...Because of the widely-used nonlinear loads, the problems of harmonics and low power factor in power systems are becoming more and more serious. In view of the above problems, a shunt three-phase active power filter （SAPF） based on discrete sliding mode control to suppress the harmonics was designed and the power factor improved. First, built the mathematical model of SAPF. Then, controlled the switch through analyzing the harmonic current that was controlled signal using discrete sliding mode control. Through simulation using MATLAB, verified the validity of the algorithm. By the simulation waveforms, it can be found that after the load current containing a large number of harmonics passes the active power filter, the waveform of the power current approximately becomes a sine wave and the harmonics is significantly reduced. As a result, it plays a good role in purifying power systems. Moreover, from the waveforms of harmonic current and power current, it can be found that the algorithm has a faster tracking speed. The waveform can fect.展开更多
The article introduces the design of the data acquisition and power supply of multi-step temperature controller. The power supply works stably and reliably. This data acquisition system possess a good linearity stabil...The article introduces the design of the data acquisition and power supply of multi-step temperature controller. The power supply works stably and reliably. This data acquisition system possess a good linearity stability, because we adopt constant current source, temperature amplifier LM301, high precision 12 bit A/D AD574. As general temperature controller can only control a preconcerted temperature, in our actual展开更多
The growing interest to examine the hydroelastic dynamics and stabilities of lightweight and flexible materials requires robust and accurate fluid–structure interaction（FSI）models. Classically, partitioned fluid an...The growing interest to examine the hydroelastic dynamics and stabilities of lightweight and flexible materials requires robust and accurate fluid–structure interaction（FSI）models. Classically, partitioned fluid and structure solvers are easier to implement compared to monolithic methods;however, partitioned FSI models are vulnerable to numerical（“virtual added mass”） instabilities for cases when the solid to fluid density ratio is low and if the flow is incompressible.As a partitioned method, the loosely hybrid coupled（LHC）method, which was introduced and validated in Young et al.（Acta Mech. Sin. 28：1030–1041, 2012）, has been successfully used to efficiently and stably model lightweight and flexible structures. The LHC method achieves its numerical stability by, in addition to the viscous fluid forces, embedding potential flow approximations of the fluid induced forces to transform the partitioned FSI model into a semi-implicit scheme. The objective of this work is to derive and validate the numerical stability boundary of the LHC. The results show that the stability boundary of the LHC is much wider than traditional loosely coupled methods for a variety of numerical integration schemes. The results also show that inclusion of an estimate of the fluid inertial forces is the most critical to ensure the numerical stability when solving for fluid–structure interaction problems involving cases with a solid to fluid-added mass ratio less than one.展开更多
A digital image processing system has been developed to quantitatively analyzemorphometric data on the microcirculatory network.The microvascular image ofmesentry is digitized to 512* 512,8 bit image by PIP-1024B,then...A digital image processing system has been developed to quantitatively analyzemorphometric data on the microcirculatory network.The microvascular image ofmesentry is digitized to 512* 512,8 bit image by PIP-1024B,then the tissue back-ground can be eliminated effectively by a local thresholding procedure that is a func-tion of image position.We use the Safe-Point Thinning Algorithm to extract skele-展开更多
A new electrothermal alloy containing 0.1—1.0 wt% yttrium has been developed by Prof.Li Pei andhis coworkers in Baotou Research Institute of RareEarth.This alloy is characterized by low brittleness,high strength at h...A new electrothermal alloy containing 0.1—1.0 wt% yttrium has been developed by Prof.Li Pei andhis coworkers in Baotou Research Institute of RareEarth.This alloy is characterized by low brittleness,high strength at high temperature,good cold worka-bility,high service temperature,long lifetime and lowoxidation rate.The experts identified that its compre-hensive property had reached an advanced level incomparison with the same kind of alloy in the world.展开更多
Strict feasibility is proved to be an equivalent characterization of （dual） variational inequalities having a nonempty bounded solution set, provided the mappings involved are stably properly quasimonotone. This gen...Strict feasibility is proved to be an equivalent characterization of （dual） variational inequalities having a nonempty bounded solution set, provided the mappings involved are stably properly quasimonotone. This generalizes an earlier result from finite-dimensional Euclidean spaces to infinitedimensional reflexive Banach spaces. Moreover, the monotonicity-type assumptions are also mildly relaxed.展开更多
Observations of the EUV and the soft X-ray of the sun have revealed many loop-like structures, which are rooted near the region with strong magnetic field in the photosphere, with their upper part extending out into t...Observations of the EUV and the soft X-ray of the sun have revealed many loop-like structures, which are rooted near the region with strong magnetic field in the photosphere, with their upper part extending out into the corona. Observations also show that some loop-like structures stably lasted for hours or even days. The diame-展开更多
Suppose R be a commutative ring with an identity element 1. Tong Wenting hasstudied PF rings in ref.[1]. A ring R is called a PF ring if every finitely generatedprojective R-module is free. In this note, we construct ...Suppose R be a commutative ring with an identity element 1. Tong Wenting hasstudied PF rings in ref.[1]. A ring R is called a PF ring if every finitely generatedprojective R-module is free. In this note, we construct a new abelian group X(R). Asa ring, we will prove X(R) is a PF ring.展开更多
New groups: X-groups are constructed. These groups are easy to calculateand they reflect more general properties of rings than K0-groups. As their applications, some characteristics of group rings with torsion-free K0...New groups: X-groups are constructed. These groups are easy to calculateand they reflect more general properties of rings than K0-groups. As their applications, some characteristics of group rings with torsion-free K0-groups are obtained.展开更多
基金The Natural Science Foundation of Yun-nan Province of China (2001A0001M)
文摘By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipative 3D Lotka-Volterra systems and five classes of maximal stably dissipative graphs were obtained for these systems. Finally, the necessary and sufficient condition of being stably dissipative for every class was studied, under which the matrix associated with the graph is stably dissipative.
文摘The structures and the vertical profiles of turbulent variance and covariance of the stably stratified boundary layer (SBL) are simulated with a second-order closure turbulence model. The results confirm that the vertical profiles of the dimensionless turbulence variance and covariance can be well represented by the form F = A(1 - Z / h)x. Here h is the height of SBL. and both exponent a and coefficient A are the functions of terrain, baroclinicity, radiation cooling and the state of temporal development of SBL. Comparing with Minnesota and Cabauw experiment data, we have analysed the value of a and expounded the main reasons that great difference in a exists among different literatures.
文摘Stably stratified flows over a two-dimensional hill are investigated in a channel of finite depth using a three-dimensional direct numerical simulation (DNS). The present study follows onto our previous two-dimensional DNS studies of stably stratified flows over a hill in a channel of finite depth and provides a more realistic simulation of atmospheric flows than our previous studies. A hill with a constant cross-section in the spanwise (y) direction is placed in a 3-D computational domain. As in the previous 2-D simulations, to avoid the effect of the ground boundary layer that develops upstream of the hill, no-slip conditions are imposed only on the hill surface and the surface downstream of the hill;slip conditions are imposed on the surface upstream of the hill. The simulated 3-D flows are discussed by comparing them to the simulated 2-D flows with a focus on the effect of the stable stratification on the non-periodic separation and reattachment of the flow behind the hill. In neutral (K = 0, where K is a non-dimensional stability parameter) and weakly stable (K = 0.8) conditions, 3-D flows over a hill differ clearly from 2-D flows over a hill mainly because of the three-dimensionality of the flow, that is the development of a spanwise flow component in the 3-D flows. In highly stable conditions (K = 1, 1.3), long-wavelength lee waves develop downstream of the hill in both 2-D and 3-D flows, and the behaviors of the 2-D and 3-D flows are similar in the vicinity of the hill. In other words, the spanwise component of the 3-D flows is strongly suppressed in highly stable conditions, and the flow in the vicinity of the hill becomes approximately two-dimensional in the x and z directions.
文摘With the support by the National Natural Science Foundation of China and the Strategic Priority Research Program of the Chinese Academy of Sciences,Prof.Chu Haiyan’s laboratory at the Institute of Soil Science,Chinese Academy of Sciences,reported comparative analysis of bacterial communities in soils that have been subjected to 30years of chemical fertilization(NPK)with the addition of either cow manure,pig manure or wheat straw residues,which was published in Soil Biology&Biochemistry(2015,88:9—18).
文摘At night, over sloped terrain the drainage flow can be always caused by cooling: of the air near a sloped surface. Its structure differs from that over horizontal planes. Brost and Wyngaard pointed out that even slight terrain slopes have strong effects on the turbulent structure and the parameters of the boundary layer.
基金supported by National Natural Science Foundation of China (GrantNo. 10971188)
文摘Let G be a finite group and A be a finite-dimensional selfinjective algebra over an algebraically closed field. Suppose A is a left G-module algebra. Some suficient conditions for the skew group algebra AG to be stably Calabi-Yau are provided, and some new examples of stably Calabi-Yau algebras are given as well.
文摘The conceptions of stably free order,stably free rank and power stably free isomorphism are given.The structure of power stably free module categories over a JBN ring (not necessarily commutative) and the K0 groups of power stably free module categories over an IBN ring are investigated through a new route.
文摘To promote efficient screening of active angiogenic drugs from traditional medicines, we constructed a humanembryonic kidney-293 cell model using vascular endothelial growth factor （VEGF） gene promoter as the drug target. Inthis model, VEGF gene promoter may regulate the expression of the luciferase reporter gene by responding to thestimulation of drug molecules. This cell model allows rapid and efficient screening of vascular-inducing activecomponents from several drug monomer molecules. Furthermore, we used rat bone marrow mesenchymal stem cells（rMSCs） to conduct a preliminary study on the activity of alantolactone. Using simvastatin as a positive control, weinvestigated the effects of alantolactone on the expression of vascular-related cell marker molecules such as VEGF andα-smooth muscle actin （α-SMA） in rMSCs. According to our results, 0.1, 1, 3 and 5 μM of alantolactone upregulated thetranscriptional luciferase gene activity of VEGF promoter, and a significant difference from that in the control group wasobserved. Among them, 3μM of alantolactone showed the better effect than that of 3 μM of simvastatin （P = 0.036） andother concentrations of alantolactone and simvastatin showed similar effects. Compared with that in the control group,rMSCs induced with 1μM alantolactone for 3 days showed a significant increase in the relative mRNA expressions ofVEGF and α-SMA genes. However, these effect of 5 μM alantolactone were weaker than those of 5 μM simvastatin （P 〈0.05）; rMSCs treated with 1 μM alantolactone for 3 days showed brighter green fluorescence （FITC marker） of α-SMAand VEGF in situ expression than that observed in the control group and similar fluorescence intensity than that ofsimvastatin group in an immunoradiometric assay. The above results demonstrate the reliability of the highly efficientsystem for screening of active drug molecules and confirmed the vascular induction function of alantolactone at the geneand protein levels.
文摘The murine interleukin-2 gene was introduced intomurine melanoma B16 cells by retroviral vector. AfterG418 selection, a clone stably secreting high level ofinterleukin-2 (1038IU per 10~6 cells per 24 hours) wasobtained. The tumorigenicity of this clone decreasedsignificantly as compared with parental tumor cells andtumor cells transferred neomycin gene. There was notumor developed after injection of 5×10~5 IL2-transfectedB16 cells into C57BL/6 mice. However when the
文摘Myoblast-mediated gene transfer approach has agreat potential to be developed into a durable genetherapy method for various diseases. To increase theexpression level of human factor Ⅸ (hFⅨ) in musclecells, we constructed a series of hFⅨ expression vectorswith the retroviral vector frame and examined their hFⅨexpression in skeletal muscle cells. Firstly, we introducedhFⅨ minigene (hFⅨ ml or hFⅨ m2), which contains atruncated first intron (1. 4 kb or 0. 3 kb) of hFⅨ
文摘In this paper, the exploitation of single population modelled by Richards model is studied. By choosing the maximum annual-sustainable yield as management objective, we investigate the optimal harvesting policies for autonomous and periodic exploited Richards model. Further, when the functions in the exploited Richards model are stably bounded functions, we study the ultimately optimal harvesting policy and obtain the corresponding average limiting maximum sustainable yield.
基金Supported by the National Natural Science Foundation of China （50375026, 50375028）
文摘Because of the widely-used nonlinear loads, the problems of harmonics and low power factor in power systems are becoming more and more serious. In view of the above problems, a shunt three-phase active power filter （SAPF） based on discrete sliding mode control to suppress the harmonics was designed and the power factor improved. First, built the mathematical model of SAPF. Then, controlled the switch through analyzing the harmonic current that was controlled signal using discrete sliding mode control. Through simulation using MATLAB, verified the validity of the algorithm. By the simulation waveforms, it can be found that after the load current containing a large number of harmonics passes the active power filter, the waveform of the power current approximately becomes a sine wave and the harmonics is significantly reduced. As a result, it plays a good role in purifying power systems. Moreover, from the waveforms of harmonic current and power current, it can be found that the algorithm has a faster tracking speed. The waveform can fect.
文摘The article introduces the design of the data acquisition and power supply of multi-step temperature controller. The power supply works stably and reliably. This data acquisition system possess a good linearity stability, because we adopt constant current source, temperature amplifier LM301, high precision 12 bit A/D AD574. As general temperature controller can only control a preconcerted temperature, in our actual
基金the financial support received from the Office of Naval Research (ONR) (Grants N00014-11-1-0833 and N00014-13-1-0383)
文摘The growing interest to examine the hydroelastic dynamics and stabilities of lightweight and flexible materials requires robust and accurate fluid–structure interaction（FSI）models. Classically, partitioned fluid and structure solvers are easier to implement compared to monolithic methods;however, partitioned FSI models are vulnerable to numerical（“virtual added mass”） instabilities for cases when the solid to fluid density ratio is low and if the flow is incompressible.As a partitioned method, the loosely hybrid coupled（LHC）method, which was introduced and validated in Young et al.（Acta Mech. Sin. 28：1030–1041, 2012）, has been successfully used to efficiently and stably model lightweight and flexible structures. The LHC method achieves its numerical stability by, in addition to the viscous fluid forces, embedding potential flow approximations of the fluid induced forces to transform the partitioned FSI model into a semi-implicit scheme. The objective of this work is to derive and validate the numerical stability boundary of the LHC. The results show that the stability boundary of the LHC is much wider than traditional loosely coupled methods for a variety of numerical integration schemes. The results also show that inclusion of an estimate of the fluid inertial forces is the most critical to ensure the numerical stability when solving for fluid–structure interaction problems involving cases with a solid to fluid-added mass ratio less than one.
文摘A digital image processing system has been developed to quantitatively analyzemorphometric data on the microcirculatory network.The microvascular image ofmesentry is digitized to 512* 512,8 bit image by PIP-1024B,then the tissue back-ground can be eliminated effectively by a local thresholding procedure that is a func-tion of image position.We use the Safe-Point Thinning Algorithm to extract skele-
文摘A new electrothermal alloy containing 0.1—1.0 wt% yttrium has been developed by Prof.Li Pei andhis coworkers in Baotou Research Institute of RareEarth.This alloy is characterized by low brittleness,high strength at high temperature,good cold worka-bility,high service temperature,long lifetime and lowoxidation rate.The experts identified that its compre-hensive property had reached an advanced level incomparison with the same kind of alloy in the world.
基金NSFC(Grant A0324638)Sichuan Youth Science and Technology Foundation(06ZQ026-013)SZD0406 from Sichuan Province
文摘Strict feasibility is proved to be an equivalent characterization of （dual） variational inequalities having a nonempty bounded solution set, provided the mappings involved are stably properly quasimonotone. This generalizes an earlier result from finite-dimensional Euclidean spaces to infinitedimensional reflexive Banach spaces. Moreover, the monotonicity-type assumptions are also mildly relaxed.
文摘Observations of the EUV and the soft X-ray of the sun have revealed many loop-like structures, which are rooted near the region with strong magnetic field in the photosphere, with their upper part extending out into the corona. Observations also show that some loop-like structures stably lasted for hours or even days. The diame-
文摘Suppose R be a commutative ring with an identity element 1. Tong Wenting hasstudied PF rings in ref.[1]. A ring R is called a PF ring if every finitely generatedprojective R-module is free. In this note, we construct a new abelian group X(R). Asa ring, we will prove X(R) is a PF ring.
基金Project supported by the National Natural Science Foundation of China.
文摘New groups: X-groups are constructed. These groups are easy to calculateand they reflect more general properties of rings than K0-groups. As their applications, some characteristics of group rings with torsion-free K0-groups are obtained.
