公历置闰年方法的解析

历法的本质是对时间的度量问题,公历的核心问题是置闰年,公历是借助置闰协调历年与回归年之间的误差.利用辗转相除法将公历历年中的平年与回归年的误差同1作辗转相除,并按相除结果将0.242 2表为连分式.依次截取连分式,得到0.242 2的渐近分数序列.在其中选取8/33与31/128近似表示0.242 2,得33年8闰与128年31闰的置闰方法.在此基础上利用单位分数来表示31/128,得到一种复合周期置闰法,这便是公历的置闰规律.     

中国传统夏历及其置闰

中国传统夏历是严格按照太阳、月亮的视位置逐年推算编排的置闰极为复杂的历法.在望远镜发明之前,中国古人对历法推算所必须的许多天文基本数据的观测精度在当时是世界领先的;在牛顿-莱布兹发明微积分之前,中国古人对历法推算的数学手段及其运算技巧在当时也是世界领先的;至于中国夏历复杂的置闰规律,是更加值得后人用现代的数学手段去研究分析的,以便让这份精妙绝伦的科学遗产发扬光大、流芳百世.     

太初历特殊置闰问题

《史记·历书》和《汉书·律历志》分别记述了具有同一起算点,但朔望月与回归年平均值根本不同的两种历.按照两部史书所记载的数据及算法分别排算出完整的历谱,并根据出土文物(汉简)对排算结果进行比较研究,结果表明,按《汉书·律历志》排算出的"太初历谱"确实是当时颁行过的.在这一过程中,发现了太初历具有长期未被揭示的特殊置闰问题.     

中国古代的置闰法：一个概率问题

概述了中国传统历法中置闰算法的沿革,特别是比较了早期历法中置闰算法的异同。指出在推算闰月可能发生的位置时,《三统历》（公元前１０４年）采用以中气推闰,《后汉四分历》（８５年）选择以经朔推闰,而《大衍历》（７２４年）则设计出以气盈朔虚推闰,并推导出按照平气平朔置闰时,闰月出现位置的概率计算公式,对于大闰周或无闰财的历法而言按推算结果得本月置闰的概率为０．４５３５,前一个月置闰的概率为０．５４１３,前两个月置闰的概率为０．００５２。     

今年农历闰二月是如何确定的

2004，年我国农历是甲申年。申是地支第九位，对应十二生肖的猴，因此甲申年亦称猴年。人们也许已经注意到日历上，甲申年是从阳历2004年1月22日至2005年2月8日，共计384天，有13个月，     

日历中一种周期现象的解析

指出日历中的国庆日与中秋节重合这种现象发生的周期性.从公历和农历的历法依据——回归年和朔望月出发,利用辗转相除法以及连分数等数学方法对农历的置闰月规律加以推演,进而得出两种历法运行的会合周期.同时对其会合周期的差异性加以分析.     

基于C＋＋实现中国历史编年表公历农历互换

为了方便非历史专业人员阅读历史资料，明确历史事件发生的具体时间，针对我国古代采用的千支纪年方法的特点，建立了公历与干支纪年的转化方法，并利用C＋＋语言，设计了公历农历相互转换的软件。     

有理数的连分数展开及其渐近分数的矩阵同步求解方法探讨

用矩阵初等变换的方法可以方便的研究初等数论中的不少问题,文[1]、[2]等分别介绍了它在同余方程、不定方程,最大公约数等方面的应用,本文探讨它在有理数的连分数表示及其渐近分数求法上的应用。     

渐近周期函数和渐近周期序列的一些性质

利用概周期型函数的理论,得出了渐近周期函数和渐近周期序列二者的关系定理,以及R 上的向量值渐近周期函数与概周期函数的等价关系.研究了渐近强周期函数空间、渐近周期序列空间的可分性质.     

月球车立体视觉系统现场标定方法

针对星球探测任务中星球漫游车自主避障和导航的要求，建立了一种基于平面模板的现场标定方法，实现月球车视觉系统的现场标定．针对月球车视觉系统的广角畸变的特点，引入径向和离心畸变模型，利用最大似然估计（MLE）对内、外参数进行非线性优化求精，并对图像进行畸变校正；计算摄像机间相对位置，实现了紧凑的双目视觉外极线校正．实验表明，该方法快速、简便，获得了较高的标定精度．     

Steering mechanical analysis for lunar rover wheel

Facing the requirement of establishing a steering mechanical model for the wheel configuration design, selection of steering motors, dynamic analysis and simulation of the lunar rover, shear force beneath the steering wheel, bulldozing resistance acting on steering wheel rims and side surfaces respectively are conducted on the basis of the wheel-loose soil interaction. The quantitative relation between steering resistance moment (SRM) and steering radius, dimension of the wheel, soil parameters is established. To validate the model, a single-wheel test bed is employed to test the steering performance of a wheel with 015735m radius and 0165m width when the steering radius is 000m, 004m, 008m, 012m and 016m, respectively. The SRM is approached asymptotically with the increasing steering angle and almost proportional to the steering radius. The theoretical results of SRM are compact with the experimental results, which shows that the steering model can predict the experimental results well.     

月神及月崇拜探微

古人膜拜天体自然,并演绎了不少神话传说,对月亮的崇拜也是如此。古代月神话与月崇拜大致包括三个方面的内容：古人月神观念产生的原因,认为月神观念的产生和发展,与早期农牧业生产和农牧业社会是分不开的;中国古代神话中的几种月神形象：月母常羲,月神西王母,嫦娥奔月等;月神话的寓意。     

一种基于特征空间的月球撞击坑自动识别算法

撞击坑不仅是月球表面常见的一种地质单元,也是研究月表地质年龄的一个重要因素,所以准确的识别撞击坑就很重要．本文提出了一种基于特征空间的对撞击坑进行自动识别的算法．新算法先将CCD图像转换成特征空间图像,在特征空间中通过自适应的区域检测寻找撞击坑候选区域．再对候选的区域进行椭圆拟合以进一步确认撞击坑,最后统计得到撞击坑个数．新算法在嫦娥一号采集的月球CCD图像上进行测试,测试结果显示该算法对月球中小撞击坑有较高的识别能力．     

Experimental research and statistical analysis on the dielectric properties of lunar soil simulators

To support the microwave brightness data retrieval of future China space-borne lunar exploration microwave radiometer, based on the collection of plentiful terrestrial basalts and anorthosites and their chemical compositions got by X-ray fluorescence, nine lunar soil simulators were prepared and made respectively into 0.8, 1.0, 1.2, 1.4 and 1.6 g/cm3 five densities each. We measured their relative dielectric constants over the range of 0.5-20 GHz with open-ended coaxial line model on the HP8722C Network Analyzer and then processed and analyzed the measurement data. This study shows that among the three parameters of density, frequency and composition, density has the strongest effect on the relative dielectric constants, frequency comes second, composition the least. The three parameters account for 45%, 33% and 22% respectively of the changed real part of a relative dielectric constant, and 55%, 27% and 19% respectively of the changed imaginary part. The real parts of the relative dielectric constants are linearly linearly correlated with density or frequency, and the imaginary parts have a linear relation with both approximately over the range of 0.5-10 GHz and tend to be poorly correlated with them in 10-20 GHz. The effect of composition on a relative dielectric constant seems very complicated, both probably do not follow a simple function relation, with the least correlation. Multiple regression analysis indicates that major element oxides SiO2, Al2O3, CaO, MgO, TiO2 and AFe are correspondent to a one-order polynomial, and TiO2 or AFe or TiO2 ΔFe has not been proven to be the indicators in the contribution to the relative dielectric constants.     

历年中国运动员获世界冠军数的时序分析

运用时间序列分析方法,对我国1978～2006年运动员获金牌数进行了建模,并以此来预测我国2007～2011年可能获得的金牌数,为有关部门制定培养竞技型运动员计划提供有力的理论依据.     

The modeling analysis of microwave emission from stratified media of non-uniform lunar cratered terrain surface for Chinese Chang-E 1 observation

In China’s first lunar exploration project,Chang-E 1,the multi-channel (3.0,7.8,19.35,37 GHz) microwave radiometers were aboard the satellite,with the purpose of measuring microwave brightness temperature from lunar surface and surveying the global distribution of lunar regolith layer thickness,and global evaluation of 3He content.To analyze the modeling of microwave radiative transfer from three-layered media of lunar surface,some factors,such as the cratered lunar surface roughness,scattering of regolith particulate medium with temperature profile,are discussed.Based on the statistics of the lunar cratered terrain and using Monte Carlo (MC) method,the cratered lunar surfaces are numerically generated.The triangulated network is utilized to divide the undulated lunar surface into discrete triangle meshes with the size 10 m as a digital surface topography.The reflectivities of each plane mesh are calculated,and the average reflectivity for all MC-realized lunar surfaces is obtained.It is found that under the spatial resolution of 30 km×30 km of Chang-E 1 radiometer observation,the lunar surface can be well modeled as a flat surface.It makes the predominance of the parameters,such as the regolith layer thickness and stratified structures,to be studied.Using the radiative transfer equation of stratified media with dense scatterers,the scattering coefficient of the regolith particulate medium is found negligible,and the emission is mainly governed by the absorptive property of the medium.Brightness temperature of multi-layered media,i.e.lunar soil,regolith layer with temperature profile and underlying rock media,are derived and calculated,and relevant main factors to affect the modeling and emission simulation are analyzed.     

《授时历》中的招差法和弧矢割圆术研究

研究了《授时历》中的招差法和弧矢割圆术的构建原理。结果表明，前者即现在的三次内插法，古代是从一些实测数据出发，利用代数方法构造一个确定天体在每一时段所处位置的算法，并用表格和公式的形式表示出来；后者是中国历法计算中首次使用的球面几何方法，系应用古代的勾股算术和沈括的“会圆术”并结合高次方程来解决天文测量问题。通过中外比较认为，牛顿内插法晚于中国招差示近400年，而弧矢割圆术的使用标志着中国数学上的球面三角法思想的出现。