Given a fixed prime number p, the multiplet of abelian type invariants of the p-class groups of all unramified cyclic degree p extensions of a number field K is called its IPAD (index-p abeliani- zation data). These i...Given a fixed prime number p, the multiplet of abelian type invariants of the p-class groups of all unramified cyclic degree p extensions of a number field K is called its IPAD (index-p abeliani- zation data). These invariants have proved to be a valuable information for determining the Galois group of the second Hilbert p-class field and the p-capitulation type of K. For p=3 and a number field K with elementary p-class group of rank two, all possible IPADs are given in the complete form of several infinite sequences. Iterated IPADs of second order are used to identify the group of the maximal unramified pro-p extension of K.展开更多
【目的】探究不同植棉密度对新疆南疆棉花株型与产量的影响,为优化栽培技术提供理论依据。【方法】2023―2024年,在新疆尉犁县开展大田试验,设计5个植棉密度:28万株·hm^(-2)(D1)、22万株·hm^(-2)(D2)、18万株·hm^(-2)(D3...【目的】探究不同植棉密度对新疆南疆棉花株型与产量的影响,为优化栽培技术提供理论依据。【方法】2023―2024年,在新疆尉犁县开展大田试验,设计5个植棉密度:28万株·hm^(-2)(D1)、22万株·hm^(-2)(D2)、18万株·hm^(-2)(D3)、13万株·hm^(-2)(D4)和9万株·hm^(-2)(D5),以筒形(新陆中79号,T1)和塔形(欣试518,T2)棉花品种为研究对象,分析不同植棉密度对棉花株高、果枝节间长度、果枝和叶片的倾角及方位角、叶面积指数(leaf area index,LAI)和产量性状的影响。【结果】T1品种的株高在D3或D4处理下最大,T2品种的株高在D4处理下最大。随植棉密度减小,T1与T2品种的平均果枝节间长度逐渐增加,下部、中部、上部果枝的倾角整体呈增大趋势。D4或D5处理下,2个品种的下部、中部、上部叶片倾角最大。不同植棉密度下,T1品种的下部、中部、上部叶片倾角无显著差异;T1、T2品种的下部果枝方位角以及中部、上部叶片的方位角均无显著差异。T1、T2品种的LAI分别在D4、D3处理下最大。随植棉密度增大,单株铃数降低。T1、T2品种分别在D3、D1处理下籽棉产量最高。【结论】不同植棉密度对筒形和塔形棉花品种的株型与产量具有一定影响。南疆植棉区新陆中79号和欣试518的适宜种植密度分别为18万株·hm^(-2)和28万株·hm^(-2)。展开更多
Let p be a prime and K be a number field with non-trivial p-class group ClpK. A crucial step in identifying the Galois group G∞p of the maximal unramified pro-p extension of K is to determine its two-stage approximat...Let p be a prime and K be a number field with non-trivial p-class group ClpK. A crucial step in identifying the Galois group G∞p of the maximal unramified pro-p extension of K is to determine its two-stage approximation M=G2pk, that is the second derived quotient M≃G/Gn. The family τ1K of abelian type invariants of the p-class groups ClpL of all unramified cyclic extensions L/K of degree p is called the index- abelianization data (IPAD) of K. It is able to specify a finite batch of contestants for the second p-class group M of K. In this paper we introduce two different kinds of generalized IPADs for obtaining more sophisticated results. The multi-layered IPAD (τ1Kτ(2)K) includes data on unramified abelian extensions L/K of degree p2 and enables sharper bounds for the order of M in the case Clpk≃(p,p,p), where current im-plementations of the p-group generation algorithm fail to produce explicit contestants for M , due to memory limitations. The iterated IPAD of second order τ(2)K contains information on non-abelian unramified extensions L/K of degree p2, or even p3, and admits the identification of the p-class tower group G for various infinite series of quadratic fields K=Q(√d) with ClpK≃(p,p) possessing a p-class field tower of exact length lpK=3 as a striking novelty.展开更多
文摘Given a fixed prime number p, the multiplet of abelian type invariants of the p-class groups of all unramified cyclic degree p extensions of a number field K is called its IPAD (index-p abeliani- zation data). These invariants have proved to be a valuable information for determining the Galois group of the second Hilbert p-class field and the p-capitulation type of K. For p=3 and a number field K with elementary p-class group of rank two, all possible IPADs are given in the complete form of several infinite sequences. Iterated IPADs of second order are used to identify the group of the maximal unramified pro-p extension of K.
文摘【目的】探究不同植棉密度对新疆南疆棉花株型与产量的影响,为优化栽培技术提供理论依据。【方法】2023―2024年,在新疆尉犁县开展大田试验,设计5个植棉密度:28万株·hm^(-2)(D1)、22万株·hm^(-2)(D2)、18万株·hm^(-2)(D3)、13万株·hm^(-2)(D4)和9万株·hm^(-2)(D5),以筒形(新陆中79号,T1)和塔形(欣试518,T2)棉花品种为研究对象,分析不同植棉密度对棉花株高、果枝节间长度、果枝和叶片的倾角及方位角、叶面积指数(leaf area index,LAI)和产量性状的影响。【结果】T1品种的株高在D3或D4处理下最大,T2品种的株高在D4处理下最大。随植棉密度减小,T1与T2品种的平均果枝节间长度逐渐增加,下部、中部、上部果枝的倾角整体呈增大趋势。D4或D5处理下,2个品种的下部、中部、上部叶片倾角最大。不同植棉密度下,T1品种的下部、中部、上部叶片倾角无显著差异;T1、T2品种的下部果枝方位角以及中部、上部叶片的方位角均无显著差异。T1、T2品种的LAI分别在D4、D3处理下最大。随植棉密度增大,单株铃数降低。T1、T2品种分别在D3、D1处理下籽棉产量最高。【结论】不同植棉密度对筒形和塔形棉花品种的株型与产量具有一定影响。南疆植棉区新陆中79号和欣试518的适宜种植密度分别为18万株·hm^(-2)和28万株·hm^(-2)。
文摘Let p be a prime and K be a number field with non-trivial p-class group ClpK. A crucial step in identifying the Galois group G∞p of the maximal unramified pro-p extension of K is to determine its two-stage approximation M=G2pk, that is the second derived quotient M≃G/Gn. The family τ1K of abelian type invariants of the p-class groups ClpL of all unramified cyclic extensions L/K of degree p is called the index- abelianization data (IPAD) of K. It is able to specify a finite batch of contestants for the second p-class group M of K. In this paper we introduce two different kinds of generalized IPADs for obtaining more sophisticated results. The multi-layered IPAD (τ1Kτ(2)K) includes data on unramified abelian extensions L/K of degree p2 and enables sharper bounds for the order of M in the case Clpk≃(p,p,p), where current im-plementations of the p-group generation algorithm fail to produce explicit contestants for M , due to memory limitations. The iterated IPAD of second order τ(2)K contains information on non-abelian unramified extensions L/K of degree p2, or even p3, and admits the identification of the p-class tower group G for various infinite series of quadratic fields K=Q(√d) with ClpK≃(p,p) possessing a p-class field tower of exact length lpK=3 as a striking novelty.
