关于有限域上一类特殊的对偶基

设q为素数幂,F=Fqn为有限域Fq的n次扩张,N={αq^i|i=0,…,n-1}为F到Fq上的一组正规基,T=(ti,j)为其乘法表,B={βq^i|=0,…,n-1}为N的对偶基,H=(hi,j)为其乘法表．本文作者给出了：a,b∈Fq使β=a ba的两个充分必要条件,以及在该假设之下乘法表T与H之间的运算关系。     

On the complexity of the normal bases via prime Gauss period over finite fields

A formula on the complexity of the normal bases generated by prime Gauss period over finite fields is presented in terms of cyclotomic numbers. Then, the authors determine explicitly the complexity of such normal bases and their dual bases in several cases where the related cyclotomic numbers have been calculated. Particularly, the authors ˉnd several series of such normal bases with low complexity. This research is supported by the National Fundamental Science Research Program 973 of China under Grant No. 2004 CB3180000 and the State Key Lab. (Information Security) of China.     

Application of improved equivalent edge currents in synthetic aperture radar imaging

Target modeling and scattering function calculating are important prerequisites and groundwork for the synthetic aperture radar (SAR) imaging simulation. According to the difficult problems that normal methods cannot calculate the scattering function of electrically large object under the condition to wideband, an effective method of improved equivalent edge currents is presented and applied to SAR imaging simulation for the first time. This method improves calculating velocity and has relatively high precision. The concrete steps of applying the method are given. By way of the simulation experiment, the effectiveness of the method is verified.     

Optimum design of equivalent accelerated life testing plans based on proportional hazards-proportional odds model

The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented.The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix.The equivalent test plan of step stress accelerated life testing(SSALT) to a baseline optimum constant stress accelerated life testing(CSALT) plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan.Numerical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.     

基于NSTPNT的风电系统可靠性对风电预测误差灵敏度

研究电力系统可靠性对风电预测误差的灵敏度,量化风电预测误差对可靠性的影响,可为风电并网系统的优化调度与备用规划提供参考依据.实际风电预测误差的分布未知,给灵敏度计算带来困难.本文首次提出非标准三阶多项式正态变换方法,推导非标准正态假设下多项式系数的解析表达式,实现将风电预测误差转换为同期望,标准差正态随机变量的多项式形式.将转换后的风电预测误差,代入含备用最优负荷削减模型,评估风电系统可靠性.提出可靠性指标对风电预测误差期望,标准差的灵敏度解析算法.算例验证了非标准三阶多项式正态变换方法与预测误差分布参数可靠性灵敏度算法的准确性.分析备用容量与标准差变化对预测误差可靠性灵敏度的影响.     

非平稳性条件下设计洪水地区组成分析

针对非平稳性条件下不同区域洪水间组合设计值计算难题,采用Copula函数构建了可综合考虑不同区域洪水边缘分布非平稳性和洪水间相依结构非平稳性的变参数Copula模型,分析了不同区域洪水间联合分布规律随时间的演变特征。基于等可靠度法和条件期望组合法,提出了变化环境下设计洪水地区组成分析方法,实现了非平稳性条件下不同区域洪水组合设计值的计算。以寸滩站和宜昌站年最大15 d洪量系列为例,分析了两站洪量及其区间洪量的变化特征。结果表明,寸滩站和宜昌站的洪量系列均具有减少趋势,两站洪量的联合分布随时间变化,指定重现期对应的宜昌站、寸滩站及寸滩—宜昌区间洪水设计值随使用年限的增加而减小。     

西太平洋俯冲带岩石圈变形研究

全球海洋岩石圈的最大弯曲与大地震发生在俯冲带。当弯曲应力超过岩石承受范围,就会产生正断层和地震,海水沿着正断层进入上地幔并发生蛇纹石化,引发浅源地震并可能造成灾难性海啸。选取西太平洋最具代表性的日本、伊豆-小笠原、马里亚纳和雅浦俯冲带以及汤加-克马德克俯冲带,归纳近些年的地球物理观测及地球动力学模拟的结果,对比分析了不同俯冲带挠曲正断层的分布特征,并探讨了俯冲板块变形与地震之间的相关性,以揭示俯冲板片弯曲变形及相应的正断层与潜在板块水化特征。     

考虑吊杆断裂的拱梁组合桥动力响应分析

针对拱梁组合桥吊杆断裂动力响应问题,建立一种考虑吊杆断裂作用的拱梁组合桥等效静力计算方法.通过构建具有代表性的标准拱梁组合桥,采用有限元软件ANSYS/LS-DYNA进行吊杆断裂冲击作用下拱梁组合桥动力分析.分析结果显示,拱梁组合桥的长、短吊杆断裂,对剩余吊杆与系梁的影响较大,对拱肋的影响较小;短吊杆对剩余吊杆应力的影响程度更大,长吊杆对系梁的动力响应影响更大.采用考虑吊杆断裂作用的等效静力法计算拱梁组合桥动力响应时,短吊杆断裂时动力系数可偏安全地取为0.8,长吊杆断裂时动力系数根据跨径按公式取值.     

一种求简谐振动频率的新方法

本文完全使用初等数学的知识，通过类推法导出简谐振动的频率公式利用该公式和简谐振动系统的机械能守恒，可以一分简捷地求出各类谐振动的频率。     

方法论随笔

本文论述了数学方法论的有无,数学方法论的应用以及如何研究方法论。