A presentation of hyperbolic unitary group is an important part in the unitary group. The group KG 2,n (R) plays an elementary role in presentation of unitary group. It is proved that KG 2,n(R)=1 for n≥2 over a...A presentation of hyperbolic unitary group is an important part in the unitary group. The group KG 2,n (R) plays an elementary role in presentation of unitary group. It is proved that KG 2,n(R)=1 for n≥2 over a ring R with division ring of quotients, using a new method, and a presentation of GE n(R) is given.展开更多
A presentation of hyperbolic unitary group is an important part in the unitary group. The group KG 2,n (R) plays an elementary role in presentation of unitary group. It is proved that KG 2,n(R)=1 for n≥2 over a...A presentation of hyperbolic unitary group is an important part in the unitary group. The group KG 2,n (R) plays an elementary role in presentation of unitary group. It is proved that KG 2,n(R)=1 for n≥2 over a ring R with division ring of quotients, using a new method, and a presentation of GE n(R) is given.展开更多
This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study ...This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.展开更多
Mn18Cr18N, the high-nitrogen steel, is the 2nd generation material for manufacturing the retaining ring of firepower generators. In this paper, the hot deformation behavior of the material was investigated by thermo-m...Mn18Cr18N, the high-nitrogen steel, is the 2nd generation material for manufacturing the retaining ring of firepower generators. In this paper, the hot deformation behavior of the material was investigated by thermo-mechanical modeling tests. And the flow stress curves of the steel were obtained for various combinations of the temperature and strain rate. Based on the results of the tests, the complex forming process of a retaining ring including punching, expanding and extrusion with an enclosure was put forward and simulated by means of numerical simulation method. The results indicate that the process is a novel and force-saved practical technology for manufacturing heavy retaining rings.展开更多
A knowledge of the tree-ring stable nitrogen isotope ratio(δ^(15)N)can deepen our understanding of forest ecosystem dynamics by indicating the long-term availability,cycling and sources of nitrogen(N).However,the rad...A knowledge of the tree-ring stable nitrogen isotope ratio(δ^(15)N)can deepen our understanding of forest ecosystem dynamics by indicating the long-term availability,cycling and sources of nitrogen(N).However,the radial mobility of N blurs the interannual variations in the long-term N records.Previous studies of the chemical extraction of tree rings before analysis had produced inconsistent results and it is still unclear whether it is necessary to pre-treat wood samples from specific tree species to remove soluble N compounds before determining theδ^(15)N values.We compared the effects of pre-treatment with organic solvents and hot ultrapure water on the N concentration andδ^(15)N of tree rings from endemic Qinghai spruce(Picea crassifolia)growing in the interior of the central Qilian Mountains,China,during the last 60 a.We assessed the effects of different preparation protocols on the removal of the labile N compounds and investigated the need to pre-treat wood samples before determining theδ^(15)N values of tree rings.Increasing trends of the tree-ring N concentration were consistently observed in both the extracted and unextracted wood samples.The total N removed by extraction with organic solvents was about 17.60%,with a significantly higher amount in the sapwood section(P<0.01).Theδ^(15)N values of tree rings decreased consistently from 1960 to 2019 in both the extracted and unextracted wood samples.Extraction with organic solvents increased theδ^(15)N values markedly by about 5.2‰and reduced the variations in theδ^(15)N series.However,extraction with hot ultrapure water had little effect,with only a slight decrease in theδ^(15)N values of about 0.5‰.Our results showed that the radial pattern in the inter-ring movement of N in Qinghai spruce was not minimized by extraction with either organic solvents or hot ultrapure water.It is unnecessary to conduct hot ultrapure water extraction for the wood samples from Qinghai spruce because of its negligible effect on the removal of the labile N.Theδ^(15)N variation trend of tree rings in the unextracted wood samples was not influenced by the heartwood-sapwood transition zone.We suggest that theδ^(15)N values of the unextracted wood samples of the climate-sensitive Qinghai spruce could be used to explore the ecophysiological dynamics while focusing on the long-term variations.展开更多
Benzoxazoline ring substituted ketene N,O-acetals 3 were synthesized by the reaction of ketene S,S-acetals 2 with 2-aminophenol.The tautomeric equilibrium of some 3 was also observed.
Let R, S be rings, U a flat right .R-rnodule and V a flat right S-module. We show in this paper that (N, (U, V))-lc.dim(R(?) S) = sup((N, U)-lc.dimR, (N, V)-lc.dimS).
A rhodium-catalyzed ring opening reaction of N-Boc-azabenzonorbornadiene with heteroatom nucleophiles was described. Piperidine and piperazine＇s derivatives were nucleophiles in this reaction. The yields of the produ...A rhodium-catalyzed ring opening reaction of N-Boc-azabenzonorbornadiene with heteroatom nucleophiles was described. Piperidine and piperazine＇s derivatives were nucleophiles in this reaction. The yields of the products 2a-f are good and the regioselectivity are excellent.展开更多
A rare earth Schiff base complex:lanthanum tris(N-phenylethyl-3,5-di-t-butylsalicylaldiminato)s [La(OPEBS)_3] was successfully applied as single component initiator for the ring-opening polymerization of 1,4-dioxan-2-...A rare earth Schiff base complex:lanthanum tris(N-phenylethyl-3,5-di-t-butylsalicylaldiminato)s [La(OPEBS)_3] was successfully applied as single component initiator for the ring-opening polymerization of 1,4-dioxan-2-one (PDO) in bulk.The influence of reaction conditions,such as polymerization temperature,the molar ratio of the monomer to initiator (M/I) on the monomer conversion and molecular weight of the polymer has been investigated.Poly(1,4-dioxan-2-one) with a viscosity-average molecular weight (My) o...展开更多
This paper describes the synthesis and free radical ring-opening polymerization of 2-methyl-and 2-methyl-9-n-butyl (-7-methylene-1, 4, 6-trioxaspiro (4, 4) nonane). The structures of the two polymers were verified by ...This paper describes the synthesis and free radical ring-opening polymerization of 2-methyl-and 2-methyl-9-n-butyl (-7-methylene-1, 4, 6-trioxaspiro (4, 4) nonane). The structures of the two polymers were verified by IR, 'H and ^(13)C NMR spectra. The substituent on 9-position of 7-methylene-trioxaspiro (4, 4) nonane affects the structure of polymer and polymerization activity. The polymerization mechanism is discussed.展开更多
Let M be a right R-module with endomorphism ring S. We study the left (m, n)-coherence of S. It is shown that S is a left (m, n)-coherent ring if and only if the left annihilator annMn(S)(X)annMn(S)(X) is a finitely g...Let M be a right R-module with endomorphism ring S. We study the left (m, n)-coherence of S. It is shown that S is a left (m, n)-coherent ring if and only if the left annihilator annMn(S)(X)annMn(S)(X) is a finitely generated left ideal of Mn(S) for any M-m-generated submodule X of M^n if and only if every M-(n, m)-presented right R-module has an add M-preenvelope. As a consequence, we investigate when the endomorphism ring S is left coherent, left pseudo-coherent, left semihereditary or von Neumann regular.展开更多
Let R be a ring, n, d be fixed non-negative integers, Jn,d the class of （n, d）- injective left R-modules, and Fn,d the class of （n, d）-flat right R-modules. In this paper, we prove that if R is a left n-coherent r...Let R be a ring, n, d be fixed non-negative integers, Jn,d the class of （n, d）- injective left R-modules, and Fn,d the class of （n, d）-flat right R-modules. In this paper, we prove that if R is a left n-coherent ring and m ≥ 2, then gl-right-Jn,a-dimRM ≤ m if and only if gl-left-Jn,d-dimRM ≤ m -- 2, if and only if Extm＋k（M, N） = 0 for all left R-modules M, N and all k 〉 -1, if and only if Extm-l（M, N） = 0 for all left R-modules M, N. Meanwhile, we prove that if R is a left n-coherent ring, then - - is right balanced on MR ×RM by Fn,d × Jn,d, and investigate the global right Jn,d-dimension of RM and the global right Fn,d-dimension of MR by right derived functors of - -. Some known results are obtained as corollaries.展开更多
文摘A presentation of hyperbolic unitary group is an important part in the unitary group. The group KG 2,n (R) plays an elementary role in presentation of unitary group. It is proved that KG 2,n(R)=1 for n≥2 over a ring R with division ring of quotients, using a new method, and a presentation of GE n(R) is given.
文摘A presentation of hyperbolic unitary group is an important part in the unitary group. The group KG 2,n (R) plays an elementary role in presentation of unitary group. It is proved that KG 2,n(R)=1 for n≥2 over a ring R with division ring of quotients, using a new method, and a presentation of GE n(R) is given.
文摘This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.
文摘Mn18Cr18N, the high-nitrogen steel, is the 2nd generation material for manufacturing the retaining ring of firepower generators. In this paper, the hot deformation behavior of the material was investigated by thermo-mechanical modeling tests. And the flow stress curves of the steel were obtained for various combinations of the temperature and strain rate. Based on the results of the tests, the complex forming process of a retaining ring including punching, expanding and extrusion with an enclosure was put forward and simulated by means of numerical simulation method. The results indicate that the process is a novel and force-saved practical technology for manufacturing heavy retaining rings.
基金supported by the National Natural Science Foundation of China (41971104)the Open Foundation of the State Key Laboratory of Loess and Quaternary Geology,Institute of Earth Environment+1 种基金Chinese Academy of Sciences (CASSKLLQG1817)the Qilian Mountain National Park Research Center (Qinghai)(GKQ2019-01)。
文摘A knowledge of the tree-ring stable nitrogen isotope ratio(δ^(15)N)can deepen our understanding of forest ecosystem dynamics by indicating the long-term availability,cycling and sources of nitrogen(N).However,the radial mobility of N blurs the interannual variations in the long-term N records.Previous studies of the chemical extraction of tree rings before analysis had produced inconsistent results and it is still unclear whether it is necessary to pre-treat wood samples from specific tree species to remove soluble N compounds before determining theδ^(15)N values.We compared the effects of pre-treatment with organic solvents and hot ultrapure water on the N concentration andδ^(15)N of tree rings from endemic Qinghai spruce(Picea crassifolia)growing in the interior of the central Qilian Mountains,China,during the last 60 a.We assessed the effects of different preparation protocols on the removal of the labile N compounds and investigated the need to pre-treat wood samples before determining theδ^(15)N values of tree rings.Increasing trends of the tree-ring N concentration were consistently observed in both the extracted and unextracted wood samples.The total N removed by extraction with organic solvents was about 17.60%,with a significantly higher amount in the sapwood section(P<0.01).Theδ^(15)N values of tree rings decreased consistently from 1960 to 2019 in both the extracted and unextracted wood samples.Extraction with organic solvents increased theδ^(15)N values markedly by about 5.2‰and reduced the variations in theδ^(15)N series.However,extraction with hot ultrapure water had little effect,with only a slight decrease in theδ^(15)N values of about 0.5‰.Our results showed that the radial pattern in the inter-ring movement of N in Qinghai spruce was not minimized by extraction with either organic solvents or hot ultrapure water.It is unnecessary to conduct hot ultrapure water extraction for the wood samples from Qinghai spruce because of its negligible effect on the removal of the labile N.Theδ^(15)N variation trend of tree rings in the unextracted wood samples was not influenced by the heartwood-sapwood transition zone.We suggest that theδ^(15)N values of the unextracted wood samples of the climate-sensitive Qinghai spruce could be used to explore the ecophysiological dynamics while focusing on the long-term variations.
基金This work was supported by the National Natural Science Foundation of China
文摘Benzoxazoline ring substituted ketene N,O-acetals 3 were synthesized by the reaction of ketene S,S-acetals 2 with 2-aminophenol.The tautomeric equilibrium of some 3 was also observed.
基金National Natural Science Foundation of China(10171082)by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE.
文摘Let R, S be rings, U a flat right .R-rnodule and V a flat right S-module. We show in this paper that (N, (U, V))-lc.dim(R(?) S) = sup((N, U)-lc.dimR, (N, V)-lc.dimS).
文摘A rhodium-catalyzed ring opening reaction of N-Boc-azabenzonorbornadiene with heteroatom nucleophiles was described. Piperidine and piperazine＇s derivatives were nucleophiles in this reaction. The yields of the products 2a-f are good and the regioselectivity are excellent.
基金supported by the National Natural Science Foundation of China (Key program,Nos.G20434020 and G20774078).
文摘A rare earth Schiff base complex:lanthanum tris(N-phenylethyl-3,5-di-t-butylsalicylaldiminato)s [La(OPEBS)_3] was successfully applied as single component initiator for the ring-opening polymerization of 1,4-dioxan-2-one (PDO) in bulk.The influence of reaction conditions,such as polymerization temperature,the molar ratio of the monomer to initiator (M/I) on the monomer conversion and molecular weight of the polymer has been investigated.Poly(1,4-dioxan-2-one) with a viscosity-average molecular weight (My) o...
基金Supported by National Natural Science Foundation of China
文摘This paper describes the synthesis and free radical ring-opening polymerization of 2-methyl-and 2-methyl-9-n-butyl (-7-methylene-1, 4, 6-trioxaspiro (4, 4) nonane). The structures of the two polymers were verified by IR, 'H and ^(13)C NMR spectra. The substituent on 9-position of 7-methylene-trioxaspiro (4, 4) nonane affects the structure of polymer and polymerization activity. The polymerization mechanism is discussed.
文摘Let M be a right R-module with endomorphism ring S. We study the left (m, n)-coherence of S. It is shown that S is a left (m, n)-coherent ring if and only if the left annihilator annMn(S)(X)annMn(S)(X) is a finitely generated left ideal of Mn(S) for any M-m-generated submodule X of M^n if and only if every M-(n, m)-presented right R-module has an add M-preenvelope. As a consequence, we investigate when the endomorphism ring S is left coherent, left pseudo-coherent, left semihereditary or von Neumann regular.
文摘Let R be a ring, n, d be fixed non-negative integers, Jn,d the class of （n, d）- injective left R-modules, and Fn,d the class of （n, d）-flat right R-modules. In this paper, we prove that if R is a left n-coherent ring and m ≥ 2, then gl-right-Jn,a-dimRM ≤ m if and only if gl-left-Jn,d-dimRM ≤ m -- 2, if and only if Extm＋k（M, N） = 0 for all left R-modules M, N and all k 〉 -1, if and only if Extm-l（M, N） = 0 for all left R-modules M, N. Meanwhile, we prove that if R is a left n-coherent ring, then - - is right balanced on MR ×RM by Fn,d × Jn,d, and investigate the global right Jn,d-dimension of RM and the global right Fn,d-dimension of MR by right derived functors of - -. Some known results are obtained as corollaries.
