Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

ATML测试资源与测试需求自动匹配方法研究

基于ATML测试描述文档自动生成测试程序过程中,关键是实现测试资源与测试需求的自动匹配。首先对ATML测试描述文档中测试能力、测试需求、开关、端口、能力与资源的映射等基本数据元素的表示方法进行分析研究,定义了与其对应的C 数据类型。然后在研究图论相关理论的基础上,分析了描述文档中测试路径的表示方法,确定了采用邻接矩阵表示测试路径的方法。最后,在以上研究的基础上,提出了以稀疏矩阵和单链表为基础的测试能力与测试需求匹配算法,实现了测试能力与测试需求的自动匹配。该算法在实际测试程序开发中得到了应用,结果表明该算法能够实现基于ATML描述文档的测试资源与测试需求自动匹配,并能极大提供测试程序开发效率。     

Performance of concatenated codes over an APD-based optical system with estimated channel-state information

In this paper, we investigate the efficiency of serially concatenated codes using a BCH (32400, 32208) inner code and an LDPC (64800, 32400) outer code over a free-space optical communication (FSOC) system with APD detectors. Based on the experimental optical signals recorded from a FSO (free-space optical) link with the distance z = 11.8 km, the bit error rate (BER) performance of the concatenated codes is evaluated from the aspect of simulation under weak turbulence conditions (for which the scintillation index σ _I ² = 0.18) and strong turbulence conditions (for which σ _I ² = 1.49). The results indicate that the fade level P _T can be set much lower for the FSOC system using the concatenated codes, leading to shorter fade length and interleavers in smaller size. The concatenated codes are shown to even outperform the (4, 1, 7) convolutional code in both cases. In addition, we analyze the BER performance of these concatenated codes on the basis of pilot-aided channel estimation with different numbers of pilot symbols.     

On the representation of a large integer as the sum of a prime and a square-free number with at most three prime divisors

The Ramanujan Journal - In this paper we prove that every sufficiently large odd integer can be written as a sum of a prime and 2 times a product of at most two distinct odd primes. Together with...