Numerical calculation of the density of prime numbers with a given least primitive root

In this paper the densities of prime numbers having the least primitive root , where is equal to one of the initial positive integers less than 32, have been numerically calculated. The computations were carried out under the assumption of the Generalised Riemann Hypothesis. The results of these computations were compared with the results of numerical frequency estimations.

     

On the least prime primitive root modulo a prime

We derive a conditional formula for the natural density of prime numbers having its least prime primitive root equal to , and compare theoretical results with the numerical evidence.

     

观测来自银道面的TeV γ射线

给出来自银经79.3866°的银道面的TeV γ射线的观测结果.数据是在1995年10月至1998年11月间的晴朗无月夜,用兴隆站的大气契伦科夫望远镜ACT2和ACT3以向源–背景(ON–OFF)观测方式取得的,总观测时间为224.4h.在望远镜计数服从高斯分布的情况下,导出了最大似然比λ的表达式,它直接给出显著性水平的概率.用它分析观测资料,在统计误差范围内没发现有来自银道面的TeV γ射线.     

双参数指数分布位置参数的统计推断

通过次序统计量 ,得到了双参数指数分布 E(μ,λ)中位置参数μ的一致最小方差无偏估计为nn-1 T(1) -1n-1 T,推导出了 ( T-μ) / ( T-T(1) )的分布与参数μ,λ无关 ,从而得到了μ的置信区间与检验统计量 .     

组合预测的权估计及其显著性检验

提出了组合预测权系数的另一种算法,即从统计角度给出了权重的LS估计及其假设检验,旨在提高预测的精度。     

空间网架结构在地震作用下的损伤累积分析

本文从连续介质损伤力学的基础理论出发，提出了弹性模量等价性假设，并在这一假设的基础上建立了考虑损伤累积效应的空间网架结构分析的有限元列式。最后，以空间网架结构在地震作用下的损伤累积分析为例，给出了本文方法的具体实施步骤。     

动态最优滤波系统的粗差探测

观测粗差是影响动态系统最优滤波效果的重要因素，本文以静态平差理论为基础，研究了动态滤波系统粗差探测的理论和方法，简单的应用实例说明，文中介绍的粗差探测方法是有效的     

基于试验熵的火工品可靠性评估理论与方法研究

为了降低可靠性评估试验样本量,避免计量法评估试验中由于刻度参数的估计偏差所带来的风险,研究了火工品可靠性验证试验中数据的统计分析方法,引入了熵,给出了试验熵等值方程,提出了结合产品的感度分布函数,通过计数和计量相结合评估火工品可靠性的试验熵等值方法,并结合某火工品的大小样本对比试验验证了该方法的正确性及可行性。研究结果表明,使用该方法可以用较少的试验样本量,实现对高可靠性指标要求的火工品进行可靠性评估。     

Some checks of Taylor''s hypothesis in a slightly heated turbulent circular jet

Taylor's hypothesis has been examined by comparing temporal variations of the temperature fluctuation θ with the corresponding spatial variations. The comparison is made on the axis of a circular jet in the self-preserving region of the flow for streamwise separations extending to about 10 Kolmogorov microscales. The use of the hypothesis yields reliable estimates of streamwise temperature correlations and also of second- and third-order moments of streamwise temperature increments. Fourth-order moments of these increments are estimated less accurately. Departures from the hypothesis are smaller than in the plane jet; consistently, local isotropy appears to be more closely satisfied in the circular jet.