绝对值损失下单边截断型分布族参数的经验Bayes估计

本文在绝对值损失下,构造了单边截断型分布族参数的EB估计,并证明了在一组条件下,其Bayes风险的收敛速度为0((ln n/n)~(λγ/(2r+))·M_n),其中0<λ,γ≤1,M_n≤ln ln n(n充分大),M_n为一无穷大量。     

巧解含绝对值的一元二次不等式

一元二次不等式和含绝对值不等式都是中学数学的重要内容针对含绝对值的一元二次不等式的三种题型进行探讨采取有针对性的巧妙办法去掉绝对值,然后进行求解,教学效果较好.     

绝对值不等式的性质如何用？

同学们知道，绝对值不等式有性质：     

由错误引发的再思考

｜x｜≥ax≤-a或x≥a,这一等价形式是我们在中学数学中非常熟悉的,可是在处理含绝对值不等式恒成立的问题时我们却常常被误导,在此本人以一题说明,以供参考.题目已知函数f（x）=ln（2＋3x）-3/2x2,若对任意x∈[1/6,1/3],不等式｜a-lnx｜＋ln[f′（x）＋3x]〉0恒成立,求a的取值范围.     

On a discrete version of alexandrov’s projection theorem

In this paper, we consider a discrete version of Aleksandrov＇s projection theorem. We prove that an origin-symmetric convex lattice set, whose lattice＇s y-coordinates＇ absolute values are not bigger than 2, can be uniquely determined by its lattice projection counts if its cardinality is not 11. This partly answers a question on the discrete version of Aleksandrov＇s projection theorem which was proposed by Gardner, Gronchi and Zong in 2005.     

旋转锥面$l_\infty$拟合的截断光滑化牛顿法

In this paper, the rotated cone fitting problem is considered. In case the measured data are generally accurate and it is needed to fit the surface within expected error bound, it is more appropriate to use l∞ norm than 12 norm. l∞ fitting rotated cones need to minimize, under some bound constraints, the maximum function of some nonsmooth functions involving both absolute value and square root functions. Although this is a low dimensional problem, in some practical application, it is needed to fitting large amount of cones repeatedly, moreover, when large amount of measured data are to be fitted to one rotated cone, the number of components in the maximum function is large. So it is necessary to develop efficient solution methods. To solve such optimization problems efficiently, a truncated smoothing Newton method is presented. At first, combining aggregate smoothing technique to the maximum function as well as the absolute value function and a smoothing function to the square root function, a monotonic and uniform smooth approximation to the objective function is constructed. Using the smooth approximation, a smoothing Newton method can be used to solve the problem. Then, to reduce the computation cost, a truncated aggregate smoothing technique is applied to give the truncated smoothing Newton method, such that only a small subset of component functions are aggregated in each iteration point and hence the computation cost is considerably reduced.     

数字多波束系统检测性能的研究

本义讨论时域数字多分层、多波束系统的检测性能.首先指出,在有强干扰存在时,一比特量化的限幅系统检测性能将严重下降.进而分析了分层比特数对单波束检测性能的影响.文中提出估计数字式多波束系统检测性能的系统总增益的概念.指出系统均匀性在检测弱信号时的作用.从理论上说明数字多波束系统的模/数转换、后置积累时间以及输出动态的选取准则.     

绝对值教学中的多项思维

绝对值是中学数学中的一个很重要的概念。分布于中学数学的各个分支,也可说贯穿于整个中学数学教材之中。从初中开始主要以其代数意义来解决数学中出现的各种绝对值问题。但进入到高中,随着教材内容的深入提高,     

求解广义绝对值方程的交替牛顿矩阵多分裂方法

本文针对广义绝对值方程,提出了基于牛顿法的矩阵多分裂方法.并在该方法的基础上进一步改进,得到了基于牛顿法的交替矩阵多分裂方法.给出两种算法在一定条件下的全局收敛性,并分析当分裂为H分裂时,基于牛顿法的矩阵多分裂方法的收敛条件.通过数值实验验证了所提出的算法的可行性和有效性.