Recent examples of periodic bifurcations in descendant trees of finite p-groups with ?are used to show that the possible p-class tower groups G of certain multiquadratic fields K with p- class group of type (2,2,2) , ...Recent examples of periodic bifurcations in descendant trees of finite p-groups with ?are used to show that the possible p-class tower groups G of certain multiquadratic fields K with p- class group of type (2,2,2) , resp. (3,3), form periodic sequences in the descendant tree of the elementary Abelian root , resp. . The particular vertex of the periodic sequence which occurs as the p-class tower group G of an assigned field K is determined uniquely by the p-class number of a quadratic, resp. cubic, auxiliary field k, associated unambiguously to K. Consequently, the hard problem of identifying the p-class tower group G is reduced to an easy computation of low degree arithmetical invariants.展开更多
Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are...Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E/F, we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups of dihedral fields E with degree 6, which could not be realized up to now.展开更多
采用同位素稀释高分辨气相色谱-高分辨质谱法(isotope dilution high resolution gas chromatography and high resolution mass spectrometry,ID-HRGC-HRMS)测定土壤样品中二恶英类化合物(polychlorinated dibenzo-p-dioxins and diben...采用同位素稀释高分辨气相色谱-高分辨质谱法(isotope dilution high resolution gas chromatography and high resolution mass spectrometry,ID-HRGC-HRMS)测定土壤样品中二恶英类化合物(polychlorinated dibenzo-p-dioxins and dibenzofurans,PCDD/Fs)的等价毒性当量(toxic equivalent quantity,TEQ)。讨论并确定了测定土壤样品中二恶英类化合物2,3,7,8位异构体不确定度的来源并合成了各异构体的相对标准不确定度;在此基础上,计算了3种等价毒性当量因子(toxic equivalent factor,TEF)框架下土壤样品中PCDD/Fs的TEQ浓度及其合成不确定度和扩展不确定度。展开更多
文摘Recent examples of periodic bifurcations in descendant trees of finite p-groups with ?are used to show that the possible p-class tower groups G of certain multiquadratic fields K with p- class group of type (2,2,2) , resp. (3,3), form periodic sequences in the descendant tree of the elementary Abelian root , resp. . The particular vertex of the periodic sequence which occurs as the p-class tower group G of an assigned field K is determined uniquely by the p-class number of a quadratic, resp. cubic, auxiliary field k, associated unambiguously to K. Consequently, the hard problem of identifying the p-class tower group G is reduced to an easy computation of low degree arithmetical invariants.
文摘Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E/F, we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups of dihedral fields E with degree 6, which could not be realized up to now.
文摘采用同位素稀释高分辨气相色谱-高分辨质谱法(isotope dilution high resolution gas chromatography and high resolution mass spectrometry,ID-HRGC-HRMS)测定土壤样品中二恶英类化合物(polychlorinated dibenzo-p-dioxins and dibenzofurans,PCDD/Fs)的等价毒性当量(toxic equivalent quantity,TEQ)。讨论并确定了测定土壤样品中二恶英类化合物2,3,7,8位异构体不确定度的来源并合成了各异构体的相对标准不确定度;在此基础上,计算了3种等价毒性当量因子(toxic equivalent factor,TEF)框架下土壤样品中PCDD/Fs的TEQ浓度及其合成不确定度和扩展不确定度。
