设φ(n)是Euler函数,本文给出了短区间上算术序列的Erds-Kac型定理,其中该算术序列与φ(n)分布有关。Assuming φ(n)is an Euler function, this article provides the Erds-Kac type theorem for arithmetic sequences on short interv...设φ(n)是Euler函数,本文给出了短区间上算术序列的Erds-Kac型定理,其中该算术序列与φ(n)分布有关。Assuming φ(n)is an Euler function, this article provides the Erds-Kac type theorem for arithmetic sequences on short intervals, where the arithmetic sequence is related to the Euler function’s distribution.展开更多
Erdős-Kac定理是数论中的一个经典结果,它描述了在自然数范围内,整数的不同素因子个数的分布渐进服从正态分布。本文主要目的是将Erdős-Kac定理在高斯域中进行推广,令K是高斯域,OK是其整数环。设a∈OK,ω(a)表示其不同的素因子个数,τk...Erdős-Kac定理是数论中的一个经典结果,它描述了在自然数范围内,整数的不同素因子个数的分布渐进服从正态分布。本文主要目的是将Erdős-Kac定理在高斯域中进行推广,令K是高斯域,OK是其整数环。设a∈OK,ω(a)表示其不同的素因子个数,τk(a)是高斯域上k重除数函数。我们用围道积分法,推导出ω(a)的加权均值和m阶中心矩,并由此推导出高斯域上权重为τk(a)的Erdős-Kac定理。这一结果不仅丰富了数论中的分布理论,也为进一步研究高斯域中的数论问题提供了新的工具和方法。The Erdős-Kac theorem is a classical result in number theory, which describes that the distribution of the number of distinct prime factors of integers asymptotically follows a normal distribution. The primary aim of this paper is to extend the Erdős-Kac theorem to Gaussian fields. Let Kbe a Gaussian field and OKbe its ring of integers. Let a∈OK, and ω(a)denote the number of distinct prime factors of a. Let τk(a)be the -fold divisor function on the Gaussian field. Using the method of contour integration, we derive the weighted mean and the k-th central moment ofω(a), and from these, we deduce a weighted form of the Erdős-Kac theorem on Gaussian fields with weight τk(a). This result not only enriches the distribution theory in number theory but also provides new tools and methods for further research on number-theoretical problems in Gaussian fields.展开更多
An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is ...An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.展开更多
在脑机接口研究中,针对运动想象脑电信号的特征提取,采用了一种优化的基于小波包的ICA(独立成分分析)法,用于提取大脑在想象动作时产生事件相关去同步/同步(Event Related Desynchronization or Event Related Synchronization ERD/ERS...在脑机接口研究中,针对运动想象脑电信号的特征提取,采用了一种优化的基于小波包的ICA(独立成分分析)法,用于提取大脑在想象动作时产生事件相关去同步/同步(Event Related Desynchronization or Event Related Synchronization ERD/ERS)信号。利用小波包对脑电信号进行分解去除不同脑电信号之间的统计相关性,抽取包含ERD/ERS现象的特征频带,对每个特征频带分别进行ICA分解,获取与ERD/ERS现象相关的μ节律和β节律。最后引入ERD/ERS系数作为量化指标进行想象动作的识别。分类仿真结果表明,上述方法能够显著增强运动想象脑电信号的ERD/ERS特征信息,对比与独立使用某一种方法,两种方法结合更能有效的提取脑电信号特征波。展开更多
在EAST装置上研制了一套边界旋转测量系统（ERD）用于测量边界等离子体环向/极向旋转速度和离子温度分布。前置收光系统采用了嵌入式（plug-in）结构，便于系统调试与维护。光谱仪设计成多入射狭缝结构，可容纳更多的光纤，提高了其利...在EAST装置上研制了一套边界旋转测量系统（ERD）用于测量边界等离子体环向/极向旋转速度和离子温度分布。前置收光系统采用了嵌入式（plug-in）结构，便于系统调试与维护。光谱仪设计成多入射狭缝结构，可容纳更多的光纤，提高了其利用率。探测器选用了高灵敏度和高动态范围的电子倍增 CCD（EMCCD）探测器。使用了含高OH基浓度的石英光纤，可以承受一定剂量的中子辐射。系统设计的测量波段为350~800nm，最高时间分辨为15ms，空间分辨为1cm。低杂波注入下的实验结果与早期 EAST 上二维弯晶谱仪与快速往复探针联合实验的结论一致。展开更多
文摘设φ(n)是Euler函数,本文给出了短区间上算术序列的Erds-Kac型定理,其中该算术序列与φ(n)分布有关。Assuming φ(n)is an Euler function, this article provides the Erds-Kac type theorem for arithmetic sequences on short intervals, where the arithmetic sequence is related to the Euler function’s distribution.
文摘Erdős-Kac定理是数论中的一个经典结果,它描述了在自然数范围内,整数的不同素因子个数的分布渐进服从正态分布。本文主要目的是将Erdős-Kac定理在高斯域中进行推广,令K是高斯域,OK是其整数环。设a∈OK,ω(a)表示其不同的素因子个数,τk(a)是高斯域上k重除数函数。我们用围道积分法,推导出ω(a)的加权均值和m阶中心矩,并由此推导出高斯域上权重为τk(a)的Erdős-Kac定理。这一结果不仅丰富了数论中的分布理论,也为进一步研究高斯域中的数论问题提供了新的工具和方法。The Erdős-Kac theorem is a classical result in number theory, which describes that the distribution of the number of distinct prime factors of integers asymptotically follows a normal distribution. The primary aim of this paper is to extend the Erdős-Kac theorem to Gaussian fields. Let Kbe a Gaussian field and OKbe its ring of integers. Let a∈OK, and ω(a)denote the number of distinct prime factors of a. Let τk(a)be the -fold divisor function on the Gaussian field. Using the method of contour integration, we derive the weighted mean and the k-th central moment ofω(a), and from these, we deduce a weighted form of the Erdős-Kac theorem on Gaussian fields with weight τk(a). This result not only enriches the distribution theory in number theory but also provides new tools and methods for further research on number-theoretical problems in Gaussian fields.
文摘An edge coloring of hypergraph H is a function such that holds for any pair of intersecting edges . The minimum number of colors in edge colorings of H is called the chromatic index of H and is denoted by . Erdös, Faber and Lovász proposed a famous conjecture that holds for any loopless linear hypergraph H with n vertices. In this paper, we show that is true for gap-restricted hypergraphs. Our result extends a result of Alesandroni in 2021.
文摘在脑机接口研究中,针对运动想象脑电信号的特征提取,采用了一种优化的基于小波包的ICA(独立成分分析)法,用于提取大脑在想象动作时产生事件相关去同步/同步(Event Related Desynchronization or Event Related Synchronization ERD/ERS)信号。利用小波包对脑电信号进行分解去除不同脑电信号之间的统计相关性,抽取包含ERD/ERS现象的特征频带,对每个特征频带分别进行ICA分解,获取与ERD/ERS现象相关的μ节律和β节律。最后引入ERD/ERS系数作为量化指标进行想象动作的识别。分类仿真结果表明,上述方法能够显著增强运动想象脑电信号的ERD/ERS特征信息,对比与独立使用某一种方法,两种方法结合更能有效的提取脑电信号特征波。
文摘在EAST装置上研制了一套边界旋转测量系统（ERD）用于测量边界等离子体环向/极向旋转速度和离子温度分布。前置收光系统采用了嵌入式（plug-in）结构，便于系统调试与维护。光谱仪设计成多入射狭缝结构，可容纳更多的光纤，提高了其利用率。探测器选用了高灵敏度和高动态范围的电子倍增 CCD（EMCCD）探测器。使用了含高OH基浓度的石英光纤，可以承受一定剂量的中子辐射。系统设计的测量波段为350~800nm，最高时间分辨为15ms，空间分辨为1cm。低杂波注入下的实验结果与早期 EAST 上二维弯晶谱仪与快速往复探针联合实验的结论一致。
