A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e＋u＋（1-e）rx or x=-e＋uq-（1-e）rx where e is an idempotent and u is a invertible element. These ringsare shown to...A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e＋u＋（1-e）rx or x=-e＋uq-（1-e）rx where e is an idempotent and u is a invertible element. These ringsare shown to be a unifying generalization of skew power series ring R[[x;σ]], Hurwitz series ring H（R） andT（R,a）. The pseudo weak cleanness of the ring o[ triangular matrices is discussed as well. Furthermore, thispaper proves that the following are equivalent： that is R is pseudo weakly clean; there is an integer n such thatR[x]/（x^n） is pseudo weakly clean; there is an integer n such that R[[x]]/（x^n） is pseudo weakly clean.展开更多
The exchange rings without unity, first introduced by Ara, are further investigated. Some new characterizations and properties of exchange general rings are given. For example, a general ring I is exchange if and only...The exchange rings without unity, first introduced by Ara, are further investigated. Some new characterizations and properties of exchange general rings are given. For example, a general ring I is exchange if and only if for any left ideal L of I and a^-= a^-2 ∈I/L, there exists w ∈ r. ureg（I） such that w^- = a^-; E（R, I） （ the ideal extension of a ring R by its ideal I） is an exchange ring if and only if R and I are both exchange. Furthermore, it is presented that if I is a two-sided ideal of a unital ring R and I is an exchange general ring, then every central element of I is a clean element in 1.展开更多
In this paper,we investigate the comparability structure over exchange rings.It is shown that the subdirect product of an exchange ring with stable range one and an exchange ring satisfying the comparability is also a...In this paper,we investigate the comparability structure over exchange rings.It is shown that the subdirect product of an exchange ring with stable range one and an exchange ring satisfying the comparability is also an exchange ring satisfying the comparability.This provides a new class of exchange rings satisfying the comparability.Furthermore,we investigate the s-comparability over exchange rings.This generalizes the corresponding results of Goodearl and Chen.展开更多
The comparison between the carbon isotope and the index of ring width of a pine disc from the Tuomuer Peak region in Xinjiang shows that the effects of climate changes on the tree-ring growth and carbon isotopic fract...The comparison between the carbon isotope and the index of ring width of a pine disc from the Tuomuer Peak region in Xinjiang shows that the effects of climate changes on the tree-ring growth and carbon isotopic fractionation varies with time. The reason is probably relative to the characters of climate changes and adaptability of the tree-ring growth to climate changes. The relationships between the atmospheric CO2 level and the revised δ13Cair by the tree-ring carbon isotope indicate that the carbon cycle is not in a steady state, but under a stage-change condition in this area. It also can be concluded that the ratio of CO2 from the terrestrial eco-system has increased, and the flux of CO2 exchange between the atmosphere and the biosphere was gradually increasing over the past century. In addition, the results also confirm the validity and superiority of the carbon isotope to the research of the water-use efficiency.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
We obtain the structure of the rings in which every element is either a sum or a difference of a nilpotent and an idempotent that commute. This extends the structure theorems of a commutative weakly nil-clean ring, of...We obtain the structure of the rings in which every element is either a sum or a difference of a nilpotent and an idempotent that commute. This extends the structure theorems of a commutative weakly nil-clean ring, of an abelian weakly nil-clean ring, and of a strongly nil-clean ring. As applications, this result is used to determine the 2-primal rings R such that the matrix ring Mn（R） is weakly nil-clean, and to show that the endomorphism ring EndD（V） over a vector space VD is weakly nil-clean if and only if it is nil-clean or dim（V） = 1 with D Z3.展开更多
Planar ring resonator waveguides are fabricated in thin films of As2S3 chalcogenide glass,deposited on silicaon-silicon substrates.Waveguide cores are directly written by scanning the focused illumination of a femtose...Planar ring resonator waveguides are fabricated in thin films of As2S3 chalcogenide glass,deposited on silicaon-silicon substrates.Waveguide cores are directly written by scanning the focused illumination of a femtosecond Ti:sapphire laser at a central wavelength of 810 nm,through a two-photon photo-darkening process.A large photoinduced index change of 0.3–0.4 refractive index units is obtained.The radius of the ring resonator is 1.9 mm,corresponding to a transmission free spectral range of 9.1 GHz.A high loaded（intrinsic） Q value of 110,000（180,000） is achieved.The thermal dependence of the resonator transfer function is characterized.The results provide the first report,to the best of our knowledge,of directly written high-Q ring resonators in chalcogenide glass films,and demonstrate the potential of this simple technique towards the fabrication of planar lightguide circuits in these materials.展开更多
文摘A ring R is called a pseudo weakly clean ring i[ every element xE R can be written in the form of x=e＋u＋（1-e）rx or x=-e＋uq-（1-e）rx where e is an idempotent and u is a invertible element. These ringsare shown to be a unifying generalization of skew power series ring R[[x;σ]], Hurwitz series ring H（R） andT（R,a）. The pseudo weak cleanness of the ring o[ triangular matrices is discussed as well. Furthermore, thispaper proves that the following are equivalent： that is R is pseudo weakly clean; there is an integer n such thatR[x]/（x^n） is pseudo weakly clean; there is an integer n such that R[[x]]/（x^n） is pseudo weakly clean.
基金The National Natural Science Foundation of China(No10571026),the Natural Science Foundation of Jiangsu Province(NoBK2005207), the Teaching and Research Award Program for Out-standing Young Teachers in Higher Education Institutions of MOE,PRC
文摘The exchange rings without unity, first introduced by Ara, are further investigated. Some new characterizations and properties of exchange general rings are given. For example, a general ring I is exchange if and only if for any left ideal L of I and a^-= a^-2 ∈I/L, there exists w ∈ r. ureg（I） such that w^- = a^-; E（R, I） （ the ideal extension of a ring R by its ideal I） is an exchange ring if and only if R and I are both exchange. Furthermore, it is presented that if I is a two-sided ideal of a unital ring R and I is an exchange general ring, then every central element of I is a clean element in 1.
基金This work is supported by the National Natural Science Foundation of China (Grant No.19801012)the Ministry of Education of China.
文摘In this paper,we investigate the comparability structure over exchange rings.It is shown that the subdirect product of an exchange ring with stable range one and an exchange ring satisfying the comparability is also an exchange ring satisfying the comparability.This provides a new class of exchange rings satisfying the comparability.Furthermore,we investigate the s-comparability over exchange rings.This generalizes the corresponding results of Goodearl and Chen.
基金The work was supported by the National NaturalScience Foundation of China (Grant Nos.49333040 and 49903007).
文摘The comparison between the carbon isotope and the index of ring width of a pine disc from the Tuomuer Peak region in Xinjiang shows that the effects of climate changes on the tree-ring growth and carbon isotopic fractionation varies with time. The reason is probably relative to the characters of climate changes and adaptability of the tree-ring growth to climate changes. The relationships between the atmospheric CO2 level and the revised δ13Cair by the tree-ring carbon isotope indicate that the carbon cycle is not in a steady state, but under a stage-change condition in this area. It also can be concluded that the ratio of CO2 from the terrestrial eco-system has increased, and the flux of CO2 exchange between the atmosphere and the biosphere was gradually increasing over the past century. In addition, the results also confirm the validity and superiority of the carbon isotope to the research of the water-use efficiency.
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...
文摘We obtain the structure of the rings in which every element is either a sum or a difference of a nilpotent and an idempotent that commute. This extends the structure theorems of a commutative weakly nil-clean ring, of an abelian weakly nil-clean ring, and of a strongly nil-clean ring. As applications, this result is used to determine the 2-primal rings R such that the matrix ring Mn（R） is weakly nil-clean, and to show that the endomorphism ring EndD（V） over a vector space VD is weakly nil-clean if and only if it is nil-clean or dim（V） = 1 with D Z3.
基金the support of the Israeli Science Foundation (ISF),under grant 635/10
文摘Planar ring resonator waveguides are fabricated in thin films of As2S3 chalcogenide glass,deposited on silicaon-silicon substrates.Waveguide cores are directly written by scanning the focused illumination of a femtosecond Ti:sapphire laser at a central wavelength of 810 nm,through a two-photon photo-darkening process.A large photoinduced index change of 0.3–0.4 refractive index units is obtained.The radius of the ring resonator is 1.9 mm,corresponding to a transmission free spectral range of 9.1 GHz.A high loaded（intrinsic） Q value of 110,000（180,000） is achieved.The thermal dependence of the resonator transfer function is characterized.The results provide the first report,to the best of our knowledge,of directly written high-Q ring resonators in chalcogenide glass films,and demonstrate the potential of this simple technique towards the fabrication of planar lightguide circuits in these materials.
基金supported by the Chinese Ministry of Education via the Program for New Century Excellent Talents in University (NCET-12-0079)the Fundamental Research Funds for the Central Universities (DUT12LK51)~~
