Let K2 be the Milnor functor and let Фn （x）∈ Q[X] be the n-th cyclotomic polynomial. Let Gn（Q） denote a subset consisting of elements of the form {a, Фn（a）}, where a ∈ Q^＊ and {, } denotes the Steinberg sym...Let K2 be the Milnor functor and let Фn （x）∈ Q[X] be the n-th cyclotomic polynomial. Let Gn（Q） denote a subset consisting of elements of the form {a, Фn（a）}, where a ∈ Q^＊ and {, } denotes the Steinberg symbol in K2Q. J. Browkin proved that Gn（Q） is a subgroup of K2Q if n = 1,2, 3, 4 or 6 and conjectured that Gn（Q） is not a group for any other values of n. This conjecture was confirmed for n =2^T 3S or n = p^r, where p ≥ 5 is a prime number such that h（Q（ζp）） is not divisible by p. In this paper we confirm the conjecture for some n, where n is not of the above forms, more precisely, for n = 15, 21,33, 35, 60 or 105.展开更多
Based on the analysis of core,logging,and testing data,the fourth member of the Cretaceous Quantou Formation(K_(2)q^(4))in the Sanzhao depression,Songliao Basin,is investigated in order to understand the sedimentary c...Based on the analysis of core,logging,and testing data,the fourth member of the Cretaceous Quantou Formation(K_(2)q^(4))in the Sanzhao depression,Songliao Basin,is investigated in order to understand the sedimentary characteristics and hydrocarbon exploration significance of a retrograding shallow-water delta.The results show that during the sedimentary period of K_(2)q^(4),the Sanzhao depression with a gentle basement experienced stable tectonic subsidence and suffered a long-term lake level rise caused by paleoclimate changes(from semiarid to semihumid),the K_(2)q^(4)in the study area were dominated by a fining-upward deltaic succession and had relatively stable thickness.From the bottom to the top,the color of mudstone gradually changes from purplish-red to gray and grayish-green,the contents of caliche nodules decrease gradually,while the presence of pyrite in sediments becomes frequent.Channel sandstones mainly composed of siltstone and fine sandstone with developed high-energy sedimentary structures constitute the main sand bodies of deltaic deposits,but the scale of channel sandstones decrease upward.Despite the long-term lake level rise and fining-upward sedimentary succession,purplish-red mudstone,caliche nodules and thin channel sandstones are still broadly distributed in the study area,and thin channel sandstones can be found at the top of K_(2)q^(4)covered by the black oil shale of Qingshankou Formation.These assertations suggest that the study area was dominated by retrograding shallow-water delta deposits during the sedimentary period of K_(2)q^(4).In comparison with modern Poyang Lake,we infer that during the sedimentary period of K_(2)q^(4),the study area experienced frequent lake level fluctuations triggered by paleoclimate changes despite the long-term lake level rise,and the lake level fluctuations control the deposition of retrograding shallow-water delta.In addition,most of the thin channel sandstones distributed at the top of K_(2)q^(4)and covered by black oil shale are generally immersed in展开更多
基金This work is supported by SRFDP,the 973 Grant,the National Natural Science Foundation of China 10471118the Jiangsu Natural Science Foundation Bk2002023
文摘Let K2 be the Milnor functor and let Фn （x）∈ Q[X] be the n-th cyclotomic polynomial. Let Gn（Q） denote a subset consisting of elements of the form {a, Фn（a）}, where a ∈ Q^＊ and {, } denotes the Steinberg symbol in K2Q. J. Browkin proved that Gn（Q） is a subgroup of K2Q if n = 1,2, 3, 4 or 6 and conjectured that Gn（Q） is not a group for any other values of n. This conjecture was confirmed for n =2^T 3S or n = p^r, where p ≥ 5 is a prime number such that h（Q（ζp）） is not divisible by p. In this paper we confirm the conjecture for some n, where n is not of the above forms, more precisely, for n = 15, 21,33, 35, 60 or 105.
基金financially supported by the National Science and Technology Major Project of China(H.M.Y.,grant number 2016ZX05013006-006)Natural Science Foundation of Hubei Province of China(L.H.,grant number 2020CFB745)
文摘Based on the analysis of core,logging,and testing data,the fourth member of the Cretaceous Quantou Formation(K_(2)q^(4))in the Sanzhao depression,Songliao Basin,is investigated in order to understand the sedimentary characteristics and hydrocarbon exploration significance of a retrograding shallow-water delta.The results show that during the sedimentary period of K_(2)q^(4),the Sanzhao depression with a gentle basement experienced stable tectonic subsidence and suffered a long-term lake level rise caused by paleoclimate changes(from semiarid to semihumid),the K_(2)q^(4)in the study area were dominated by a fining-upward deltaic succession and had relatively stable thickness.From the bottom to the top,the color of mudstone gradually changes from purplish-red to gray and grayish-green,the contents of caliche nodules decrease gradually,while the presence of pyrite in sediments becomes frequent.Channel sandstones mainly composed of siltstone and fine sandstone with developed high-energy sedimentary structures constitute the main sand bodies of deltaic deposits,but the scale of channel sandstones decrease upward.Despite the long-term lake level rise and fining-upward sedimentary succession,purplish-red mudstone,caliche nodules and thin channel sandstones are still broadly distributed in the study area,and thin channel sandstones can be found at the top of K_(2)q^(4)covered by the black oil shale of Qingshankou Formation.These assertations suggest that the study area was dominated by retrograding shallow-water delta deposits during the sedimentary period of K_(2)q^(4).In comparison with modern Poyang Lake,we infer that during the sedimentary period of K_(2)q^(4),the study area experienced frequent lake level fluctuations triggered by paleoclimate changes despite the long-term lake level rise,and the lake level fluctuations control the deposition of retrograding shallow-water delta.In addition,most of the thin channel sandstones distributed at the top of K_(2)q^(4)and covered by black oil shale are generally immersed in
