“M矩阵的Hadamard不等式”的注记

文献[1]研究了具有广泛实际背景的M矩阵的不等式。本文指出了文献[1]的主要结果,即其定理1和定理3为著名的Hadamard-Fischer不等式的特款。     

变号系数一阶非线性泛函微分方程的解的渐近性与振动性

本文对一类变号系数的一阶非线性泛函微分方程的解的渐近性与振动性进行研究,得出方程渐近性与振动性的几个充分法则。     

关于已知函数对中间变量的导数求函数的一种方法

本文提出了若干类函数对中间变量的导数,借用微积分的方法,运用变量替换的技巧,找到了求这几类函数的有效方法.给出了所求函数的表达式,其结论是有关文献例题的推广.直接利用所得结论解题,使求解过程大为简化,文中列举了实例.     

SHARP BOUNDS FOR EXPECTATIONS OF kTH RECORD INCREMENTS

This paper presents sharp bounds for expectations of non‐adjacent increments of kth record statistics, measured in various scale units, for a sequence of independent identically distributed random variables with continuous cumulative distribution function. The results for kth record spacings are considered as special cases. The paper also characterizes probability distributions for which the bounds are attained.     

初始点任意优化问题的广义梯度投影法

利用广义投影与罚函数技巧和辅助规划处理带等式和不等式约束问题以及采用二阶段搜索方法，给出了一个初始点可任意的带不等式和等式约束的优化问题的广义梯度投影算法，并证明了该算法具有全局收敛性。文中削弱了文献［１］的条件，保持了它的优越性，罚参数在计算过程中自动调整且只需适当大，因此，在实际运用中不会有太大的困难。     

A new ranked set sample estimator of variance

Summary. We develop an unbiased estimator of the variance of a population based on a ranked set sample. We show that this new estimator is better than estimating the variance based on a simple random sample and more efficient than the estimator based on a ranked set sample proposed by Stokes. Also, a test to determine the effectiveness of the judgment ordering process is proposed.     

一种差分跳频系统的频率转移函数

根据差分跳频系统的特点推导并归纳了频率转移函数的构造原则和优化目标,提出了一种有效的频率转移函数构造方法,并从理论上证明了该方法在提高系统误码率和频率随机性方面的优良性能。该方法基于多维空间变换,构造频率转移函数简单方便,而且便于跳频密钥的管理和控制。     

逐字符和多字符频域差分OFDM的性能比较

通过仿真试验对使用了逐字符和多字符频域差分检测OFDM系统的误码率性能进行了比较。结果表明:当信道的相干带宽远大于多个差分编码字符的所占带宽时,多字符频域差分检测的性能优于逐字符差分;信道的相干带宽与多个字符所占带宽比较接近时,逐字符差分检测的性能好于多字符差分检测。     

3×3一阶线性微分方程组的积分解法

讨论3×3一阶线性微分方程组的积分解法,并给出其通解公式。     

Minimax Rates for Estimating the Variance and its Derivatives in Non–Parametric Regression

In this paper the van Trees inequality is applied to obtain lower bounds for the quadratic risk of estimators for the variance function and its derivatives in non–parametric regression models. This approach yields a much simpler proof compared to previously applied methods for minimax rates. Furthermore, the informative properties of the van Trees inequality reveal why the optimal rates for estimating the variance are not affected by the smoothness of the signal g . A Fourier series estimator is constructed which achieves the optimal rates. Finally, a second–order correction is derived which suggests that the initial estimator of g must be undersmoothed for the estimation of the variance.