互相关

Additivity of average mutual communication is proved, based on this, inequality for general correlation coefficients is derived, and the necessary and sufficient condition is obtained for equality.

证明了平均互信息的可加性，在此基础上得到了广义相关系数不等式，并给出了等式成立的充要条件。

Main work follows:(1) In the first part of this paper, a historical development of the number theory before Gauss is reviewed.Based on the systematic analysis of Gauss"s work in science and mathematics, inquiry into the mathematical background that Disquisitiones Arithmeticae appeals and Gauss"s congruent theory;(2) The development process of Fermat"s little theorem and its important function in the compositeness test is elaborated through original literature.we think that the first three section of Disquisitiones Arithmeticae is a summary and development for ancestors" work about Fermat"s little theorem,show that Fermat"s little theorem played an important role in the elementary number theory;(3) With the two main sources of the quadratic reciprocity law, investigating Fermat,Euler,Lagrange,Legendre, until the related work of Gauss,the way to realize the laws huge push to the development of algebraic number theory in 19 centuries.

本文主要做了以下工作：(1)首先回顾了高斯之前的数论研究状况，在系统分析高斯的科学与数学成就的基础上，探讨了《算术研究》出现的数学背景和高斯的同余理论；(2)通过对原始文献的系统解读，深入分析了费马小定理发现发展的历程以及在素性检验中的重要作用，指出《算术研究》前三节是高斯在总结并发展了前人对该定理研究的基础上形成的，并揭示了费马小定理在初等数论定理证明中的核心地位；(3)以二次互反律的两个主要来源为线索，详细考察了费马，欧拉，拉格朗目，勒让德，直到高斯的相关工作，揭示了该定律对十九世纪数论发展的巨大推动作用。

Based on this, to the recent years the related questions which appear frequently in the middle school mathematics competition, nimble utilization the aliquot concept, the relative prime nature, the combinatorial nature, the factorization, as well as the conclusion of the continual integer product nimbly can by aliquot knowledge and the methods, and so on, carried on the proof and the explanation.

在此基础上，对近年来在中学数学竞赛中频繁出现的相关问题，灵活运用整除概念、互素性质、组合性质、因式分解以及个连续整数的乘积能被整除的结论等知识和方法，来进行证明与解答。

The equations above model the synchronisation channel as orthogonal, while only the α fraction of common channel power is experienced as intracell interference.

上述等式所模拟的同步信道的模型是不相关的，而只有公共信道功率的不相关因数涉及到互区干扰。

The content involves Digital Filter, Auto Correlation, Cross Correlation, mean and standard deviation, probability density and probability distribution statistic, as well as Auto Power Spectrum based on Fast Flourier Transfer, Correct Power Spectrum, Cestrum and Frequency Response. The Short-time Flourier Transfer and Wavelet Transfer are included in the analysis program.

具体内容包括：数字滤波、时域加窗、自相关计算与互相关处理、均值和方差计算、概率密度和概率分布统计，快速傅立叶变换基础上的自功率谱、互功率谱、频率响应函数、相关函数、倒频谱分析；基于短时傅立叶分析的联合时频分析、小波变换等。

As for digenic interaction, 18 pairs of epistatic loci with R2≥5% were resolved with a mean R2 of 6.9%, ranging from 5.1% to 11.8%, which was slightly larger than that of the main-effect QTLs identified for the traits. The majority of the main-effect and epistatic loci detected for seedling vigor related traits were clustered in a few chromosome regions.

种子活力相关性状的大多数主效应和互作QTLs成串分布于少数几个染色体区段（chromosome regions， CRs），并且成串分布在同一染色体区段的QTLs效应的方向总是一致，该结果与这些性状在表型上的正相关相一致。

As for digenic interaction, 18 pairs of epistatic loci with R2 ≥5 were resolved with a mean R2 of 6.9 ,ranging from 5.1 to 11.8 ,which was slightly larger than that of the main-effect QTL identified for the traits.The majority of the main-effect and epistatic loci detected for seedling vigor related traits were clustered in a few chromo-some regions.

种子活力相关性状的大多数主效应和互作QTL成串分布于少数几个染色体区段(Chromosome Regions，CRs)，并且成串分布在同一染色体区段的QTL效应的方向总是一致，该结果与这些性状在表型上的正相关相一致。

Genetic main correlation between number of flowers and bolls at different fruiting sites and final number of bolls were significantly positive, and also for GE interaction correlation coefficients at most fruiting sites.

6不同果枝节位的单株开花数和单株成铃数与最终铃数的遗传主效相关均达到显著或极显著水平的正相关，基因型×环境互作在大部分果枝节位达到显著水平的正相关。

ACA = anterior communicating artery; BA = basilar artery; LACA = left anterior cerebral artery; LCCA = left common carotid artery; LECA = left external carotid artery; LICA = left internal carotid artery; LMCA = left middle cerebral artery; LPCA = left posterior cerebral artery; LSA = left subclaian artery; LA = left ertebral artery; RACA = right anterior cerebral artery; RCCA = right common carotid artery; RECA = right external carotid artery; RICA = right internal carotid artery; RMCA = right middle cerebral artery; RPCA = right posterior cerebral artery; RSA = right subclaian artery; RA = right ertebral artery.

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Genes involved in interactions among plants and pathogens,pathogenicity related genes,and the genes encoding bactericidal peptide,which have been studied in order to promote resistance to soft rot.

目前已有大量研究证实，利用植物与病原菌互作的相关基因、病原菌致病性的相关基因以及杀菌肽基因可以或有望提高植物对软腐病的抗性。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。