On the Number of Integral Ideals in Two Different Quadratic Number Fields

Let K be an algebraic number field of finite degree over the rational field ~, and aK （n） the number of integral ideals in K with norm n. When K is a Galois extension over Q, many authors contribute to the integral power sums of aK（n）,This paper is interested in the distribution of integral ideals concerning different number fields. The author is able to establish asymptotic formulae for the convolution sumwhere K1 and K2 are two different quadratic fields.

On the Distribution of Integral Ideals and Hecke Grssencharacters

The author uses analytic methods to study the distribution of integral ideals and Hecke Grossencharacters in algebraic number fields. Nowak＇s results on the distribution of integral ideals, and Chandrasekharan and Good＇s results on the distribution of Hecke GrSssencharacters are improved.

Evaluation on Ideal Test Sites and Regional Characteristics of Cotton Fiber Quality in Jiangsu Province

[Objective] The aim of this study was to explore the dominant fiber quality traits of test sites in cotton regional trials, by analyzing the regional characteristics of cotton fiber quality in Jiangsu province, in order to provide the theory background for cotton fiber quality improvement. [Method] The dominant fiber quality traits of test locations were analyzed with eight main fiber quality indexes of hybrid cotton regional trials during 2009-2013 in Jiangsu province by use of the "ideal test site" view of GGE biplot. [Result] The test locations with the best integrative fiber quality were proved to be Yanliang, and followed by Dongxin and Guanyun; The better test locations in terms of the major fiber quality indexes, including fiber strength, fiber Length and micronaire value, were Guanyun, Xinyang and Yanliang; To sum up, the best test location with balanced fiber quality was Yanliang. The test locations with specialties in fiber quality index were listed as bellow: Dafeng, Xinghua and Dongtai performance better in fiber length; Qidong, Liuhe and Yanhai locations were of better fiber length uniformity; Sheyang and Dongxin were better in micronaire value;while Sheyang along was better in fiber elongation and reflectance. Moreover, the correlation between fiber yellowness and other traits was significant(P<0.01). [Conclusion] The regional characteristic of cotton fiber quality index in Jiangsu province was obvious and fiber yellowness was worthy an indicator trait to assist the comprehensive improvement of cotton fiber quality.

On the Normality of One-fibered Monomial Ideals

This paper presents a generalization to the higher-dimensional situation of the main results of the first author about the normality of one-fibered monomial ideals [2, Theoremes 2.4 and 3.8]. Precisely, we show that if I is a monomial ideal of R = k[x1, x2,..., Xd], then I is normal one-fibered if and only if for all positive integers n and all x, y in R such that xy ∈ I2n, either x or y belongs to In.