In basic homological algebra, the flat and injective dimensions of modules play an important and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions are introduced and studied. W...In basic homological algebra, the flat and injective dimensions of modules play an important and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions are introduced and studied. We show that IFP-fd（M） = IFP-id（M＋） and IFP-fd（M＋）=IFP-id（M） for any R-module M over any ring R. Let ：Z-In （resp., ＂Zgv,~） he the class of all left （resp., right） R-modules of IFP-injective （resp., IFP-flat） dimension at most n. We prove that every right R-module has an IFn- preenvelope, （IFn,IF⊥n） is a perfect cotorsion theory over any ring R, and for any ring R with IFP-id（RR） 〈 n, （IIn,II⊥n） is a perfect cotorsion theory. This generalizes and improves the earlier work （J. Algebra 242 （2001）, 447-459）. Finally, some applications are given.展开更多
For a special class of non-injective maps on Riemannian manifolds an upper bound for the fractal dimension of invariant set in terms of singular values of the tangent map and degree of non-injectivity is given.
Most injection molded parts are three-dimensional, with complex geometrical configurations and thick/thin wall sections. A 3D simulation model will predict more accurately the filling process than a 2.5D model. This p...Most injection molded parts are three-dimensional, with complex geometrical configurations and thick/thin wall sections. A 3D simulation model will predict more accurately the filling process than a 2.5D model. This paper gives a mathematical model and numeric method based on 3D model, in which an equal-order velocity-pressure interpolation method is employed successfully. The relation between velocity and pressure is obtained from the discretized momentum equations in order to derive the pressure equation. A 3D control volume scheme is employed to track the flow front. Th e validity of the model has been tested through the analysis of the flow in cavity.展开更多
In this paper, we investigate Ding projective dimensions and Ding injective di- mensions of modules and rings. Let R be a ring with rDPD（R） = n 〈 ∞, and let YYl = {Mild（M） 〈 ∞}. We prove that （DP,W1） is a co...In this paper, we investigate Ding projective dimensions and Ding injective di- mensions of modules and rings. Let R be a ring with rDPD（R） = n 〈 ∞, and let YYl = {Mild（M） 〈 ∞}. We prove that （DP,W1） is a complete hereditary cotorsion pair such that a module M belongs to DD∩W1 if and only if M is projective, moreover, 1421 = （M[pd（M） 〈 ∞} = {MIfd（M） ≤ n} = {MIpd（M） ≤ n}. Then we introduce and inves- tigate Ding derived functor Dext^i（-, -）, and use it to characterize global Ding dimension. We show that if R is a Ding-Chen ring, or if R is a ring with rDPD（R） 〈≤ and rDID（R） 〈 ≤, then rDPD（R） 〈 n if and only if rDID（R） 〈 n if and only if Dext^n＋i（M,N） = 0 for all modules M and N and all integer i ≥ 1.展开更多
Let R be a noetherian ring and S an excellent extension of R.cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M.We prove that if M S is a right S-module then cid(M S)=...Let R be a noetherian ring and S an excellent extension of R.cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M.We prove that if M S is a right S-module then cid(M S)=cid(M R) and if S M is a left S-module then cfd(S M)=cfd(R M).Moreover,cid-D(S)=cid-D(R) and cfd-D(S)=cfdD(R).展开更多
As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generali...As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generalization of Gorenstein rings. Moreover, a new proof for Bennis and Mahdou's equality of global Gorenstein dimension is given.展开更多
The category consisting of finitely generated modules which are left orthogonal with a cotilting bimodule is shown to be functorially finite. The notion of left orthogonal dimension is introduced , and then a necessar...The category consisting of finitely generated modules which are left orthogonal with a cotilting bimodule is shown to be functorially finite. The notion of left orthogonal dimension is introduced , and then a necessary and sufficient condition of selforthogonal modules having finite injective dimension and a characterization of cotilting modules are given.展开更多
Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.
Let A be a left and right Noetherian ring and let x be a central regular element of A. A_x denotes the localization of A at the central multiplicatively closed subset {1,x,x^2,…}. Suppose M is an A-module such that x...Let A be a left and right Noetherian ring and let x be a central regular element of A. A_x denotes the localization of A at the central multiplicatively closed subset {1,x,x^2,…}. Suppose M is an A-module such that x is a nonzero divisor in. M. It is shown that there is an equality relation among three iniective dimensions ld_A(M), IdA_x(M_x), and I_dA/xA(M/xM). Then the result is applied to the case of Rees rings of filtered rings and an improved and uniform form of the two results of E. K. Ekstrm is obtained. Moreover, the results in this paper generalize the relevant results of Li Huishi, M. Van den Bergh and F. Van Oystaeyen.展开更多
The concern of this paper is to derive formulas for the injective dimension of the n-th Weyl algebra A_n(R)in case k is a field of characteristic zero and R is a commutative affine k-algebra of finite injective dimens...The concern of this paper is to derive formulas for the injective dimension of the n-th Weyl algebra A_n(R)in case k is a field of characteristic zero and R is a commutative affine k-algebra of finite injective dimension.For the case n=1 we prove a more general result from which the above result follows.Such formulas can be viewed as generalizations of the corresponding results given by J.C.McConnell in the case R has finite global dimension.展开更多
Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR（ω） ∞ implies G-dimω（M） ∞,w...Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR（ω） ∞ implies G-dimω（M） ∞,where M ∈ modR.This result generalizes the result by Huang and Tang about the relationship between the FP-injective dimension and the generalized Gorenstein dimension in 2001.In addition,we get that the left orthogonal dimension is equal to the generalized Gorenstein dimension when G-dimω（M） is finite.展开更多
The tight tuff reservoir is an unusual type of unconventional reservoir with strong heterogeneity.However,there is a lack of research on the microscopic pore structure that causes the heterogeneity of tuff reservoirs....The tight tuff reservoir is an unusual type of unconventional reservoir with strong heterogeneity.However,there is a lack of research on the microscopic pore structure that causes the heterogeneity of tuff reservoirs.Using the Chang 7 Formation in Ordos Basin,China as a case study,carbon-dioxide gas adsorption,nitrogen gas adsorption and high-pressure mercury injection are integrated to investigate the multi-scale pore structure characteristics of tuff reservoirs.Meanwhile,the fractal dimension is introduced to characterize the complexity of pore structure in tuff reservoirs.By this multi-experimental method,the quantitative characterizations of the full-range pore size distribution of four tuff types were obtained and compared in the size ranges of micropores,mesopores and macropores.Fractal dimension curves derived from full-range pores are divided into six segments as D1,D2,D3,D4,D5 and D6 corresponding to fractal characteristics of micropores,smaller mesopores,larger mesopores,smaller macropores,medium macropores and larger macropores,respectively.The macropore volume,average macropore radius and fractal dimension D5 significantly control petrophysical properties.The larger macropore volume,average macropore radius and D5 correspond to favorable pore structure and good reservoir quality,which provides new indexes for the tuff reservoir evaluation.This study enriches the understanding of the heterogeneity of pore structures and contributes to unconventional oil and gas exploration and development.展开更多
基金supported by National Natural Science Foundation of China(10961021,11001222)
文摘In basic homological algebra, the flat and injective dimensions of modules play an important and fundamental role. In this paper, the closely related IFP-flat and IFP-injective dimensions are introduced and studied. We show that IFP-fd（M） = IFP-id（M＋） and IFP-fd（M＋）=IFP-id（M） for any R-module M over any ring R. Let ：Z-In （resp., ＂Zgv,~） he the class of all left （resp., right） R-modules of IFP-injective （resp., IFP-flat） dimension at most n. We prove that every right R-module has an IFn- preenvelope, （IFn,IF⊥n） is a perfect cotorsion theory over any ring R, and for any ring R with IFP-id（RR） 〈 n, （IIn,II⊥n） is a perfect cotorsion theory. This generalizes and improves the earlier work （J. Algebra 242 （2001）, 447-459）. Finally, some applications are given.
文摘For a special class of non-injective maps on Riemannian manifolds an upper bound for the fractal dimension of invariant set in terms of singular values of the tangent map and degree of non-injectivity is given.
基金This work was supported by research foundation for PH. D candidates of universities (20020487032)
文摘Most injection molded parts are three-dimensional, with complex geometrical configurations and thick/thin wall sections. A 3D simulation model will predict more accurately the filling process than a 2.5D model. This paper gives a mathematical model and numeric method based on 3D model, in which an equal-order velocity-pressure interpolation method is employed successfully. The relation between velocity and pressure is obtained from the discretized momentum equations in order to derive the pressure equation. A 3D control volume scheme is employed to track the flow front. Th e validity of the model has been tested through the analysis of the flow in cavity.
基金Supported by the National Natural Science Foundation of China(11201424)the Zhejiang Natural Science Foundation of China(LY12A01026)
文摘In this paper, we investigate Ding projective dimensions and Ding injective di- mensions of modules and rings. Let R be a ring with rDPD（R） = n 〈 ∞, and let YYl = {Mild（M） 〈 ∞}. We prove that （DP,W1） is a complete hereditary cotorsion pair such that a module M belongs to DD∩W1 if and only if M is projective, moreover, 1421 = （M[pd（M） 〈 ∞} = {MIfd（M） ≤ n} = {MIpd（M） ≤ n}. Then we introduce and inves- tigate Ding derived functor Dext^i（-, -）, and use it to characterize global Ding dimension. We show that if R is a Ding-Chen ring, or if R is a ring with rDPD（R） 〈≤ and rDID（R） 〈 ≤, then rDPD（R） 〈 n if and only if rDID（R） 〈 n if and only if Dext^n＋i（M,N） = 0 for all modules M and N and all integer i ≥ 1.
文摘Let R be a noetherian ring and S an excellent extension of R.cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M.We prove that if M S is a right S-module then cid(M S)=cid(M R) and if S M is a left S-module then cfd(S M)=cfd(R M).Moreover,cid-D(S)=cid-D(R) and cfd-D(S)=cfdD(R).
基金Supported by the National Natural Science Foundation of China（11401476） Supported by the Project for Universities of Gansu Province（2015A-019）
文摘As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generalization of Gorenstein rings. Moreover, a new proof for Bennis and Mahdou's equality of global Gorenstein dimension is given.
文摘The category consisting of finitely generated modules which are left orthogonal with a cotilting bimodule is shown to be functorially finite. The notion of left orthogonal dimension is introduced , and then a necessary and sufficient condition of selforthogonal modules having finite injective dimension and a characterization of cotilting modules are given.
基金supported by National Natural Science Foundation of China (Grant Nos. 11026141,11071111)the Zhejiang Provincial Natural Science Foundation of China (Grant Nos. D7080064,Y6100173)
文摘Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.
文摘Let A be a left and right Noetherian ring and let x be a central regular element of A. A_x denotes the localization of A at the central multiplicatively closed subset {1,x,x^2,…}. Suppose M is an A-module such that x is a nonzero divisor in. M. It is shown that there is an equality relation among three iniective dimensions ld_A(M), IdA_x(M_x), and I_dA/xA(M/xM). Then the result is applied to the case of Rees rings of filtered rings and an improved and uniform form of the two results of E. K. Ekstrm is obtained. Moreover, the results in this paper generalize the relevant results of Li Huishi, M. Van den Bergh and F. Van Oystaeyen.
基金Project supported in part by the National Natural Science Foundation for Youth
文摘The concern of this paper is to derive formulas for the injective dimension of the n-th Weyl algebra A_n(R)in case k is a field of characteristic zero and R is a commutative affine k-algebra of finite injective dimension.For the case n=1 we prove a more general result from which the above result follows.Such formulas can be viewed as generalizations of the corresponding results given by J.C.McConnell in the case R has finite global dimension.
基金Supported by the Ph. D. Program Foundation of Ministry of Education of China (Grant No.200803570003)
文摘Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR（ω） ∞ implies G-dimω（M） ∞,where M ∈ modR.This result generalizes the result by Huang and Tang about the relationship between the FP-injective dimension and the generalized Gorenstein dimension in 2001.In addition,we get that the left orthogonal dimension is equal to the generalized Gorenstein dimension when G-dimω（M） is finite.
基金supported by the Strategic Cooperation Technology Projects of CNPC and CUPB(No.ZLZX2020-02)the National Science and Technology Special(No.2017ZX05049-006-001)+1 种基金the National Natural Science Foundation of China(No.41602137)Science Foundation of China University of Petroleum,Beijing(No.2462020YXZZ022).
文摘The tight tuff reservoir is an unusual type of unconventional reservoir with strong heterogeneity.However,there is a lack of research on the microscopic pore structure that causes the heterogeneity of tuff reservoirs.Using the Chang 7 Formation in Ordos Basin,China as a case study,carbon-dioxide gas adsorption,nitrogen gas adsorption and high-pressure mercury injection are integrated to investigate the multi-scale pore structure characteristics of tuff reservoirs.Meanwhile,the fractal dimension is introduced to characterize the complexity of pore structure in tuff reservoirs.By this multi-experimental method,the quantitative characterizations of the full-range pore size distribution of four tuff types were obtained and compared in the size ranges of micropores,mesopores and macropores.Fractal dimension curves derived from full-range pores are divided into six segments as D1,D2,D3,D4,D5 and D6 corresponding to fractal characteristics of micropores,smaller mesopores,larger mesopores,smaller macropores,medium macropores and larger macropores,respectively.The macropore volume,average macropore radius and fractal dimension D5 significantly control petrophysical properties.The larger macropore volume,average macropore radius and D5 correspond to favorable pore structure and good reservoir quality,which provides new indexes for the tuff reservoir evaluation.This study enriches the understanding of the heterogeneity of pore structures and contributes to unconventional oil and gas exploration and development.
