New results on rendezvous search on the interval

In a rendezvous search problem, two players are placed in a network and must try to meet each other in the least possible expected time. We look at rendezvous search on a discrete interval in which the players are initially placed using independent draws (usually assumed to be from the same distribution). Some optimal solutions are known if this distribution is uniform, and also for certain other special types of distribution. In this article, we present two new results. First, we characterize the complete set of solutions for the uniform case, showing that all optimal strategies must have two specific properties (namely, of being swept and strictly geodesic). Second, we relate search strategies on the interval to proper binary trees, and use this correspondence to derive a recurrence relation for solutions to the symmetric rendezvous problem for any initial distribution. This relation allows us to solve any such problem computationally by dynamic programming. Finally, some ideas for future research are discussed. © Wiley Periodicals, Inc. Naval Research Logistics 60: 454–467, 2013     

Inequality‐based reliability estimates for complex systems

Full‐system testing for large‐scale systems is often infeasible or very costly. Thus, when estimating system reliability, it is desirable to use a method that uses subsystem tests, which are often less expensive and more feasible. This article presents a method for bounding full‐system reliabilities based on subsystem tests and, if available, full‐system tests. The method does not require that subsystems be independent. It accounts for dependencies through the use of certain probability inequalities. The inequalities provide the basis for valid reliability calculations while not requiring independent subsystems or full‐system tests. The inequalities allow for test information on pairwise subsystem failure modes to be incorporated, thereby improving the bound on system reliability. We illustrate some of the properties of the estimates via an example application. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

基于时频单源点检测和聚类验证技术的欠定混合盲辨识算法

针对欠定混合盲辨识问题,提出了一种基于时频单源点检测及聚类验证的盲辨识算法。检测各个源信号的时频单源点,利用奇异值分解的方法求解不同单源点集合对应的混合矢量,利用基于k均值的聚类验证技术完成源信号数目和混合矩阵的联合估计。算法放宽了已有方法对时频单源区域的假设,不需要假设信号存在时频单源区域,可以完成仅存在离散的时频单源点条件下的欠定混合盲辨识;同时克服了传统算法需要假设源信号个数已知的不足,可以有效地估计源信号数目。仿真结果验证了算法的有效性。     

战时装备保障阵地选址不确定决策方法

针对战时选址属性信息为区间数的情形,提出了一种基于模糊偏序关系的装备保障阵地选址决策方法.首先,建立战时装备保障点选址的评估值模型,并对其进行预处理;然后建立了模糊偏序关系模型,将混合型评估值模型转化为评估关系模型,得到各备选点之间的偏序关系;最后,对偏序关系进行集结,得到全序关系,从而获取方案的优劣排序.这为战时装备保障阵地选址提供了一种新的有效途径.     

《初等数论》课程渗透数学文化教学研究与实践

数学课程是实施数学文化教育的主渠道和主阵地,是学生触摸、体悟数学本质,感受、体验数学内在文化气息的畅享地。本文重点从课程导言、核心概念、符号语言及命题、定理、法则教学等方面来探讨数学文化在《初等数论》课程教学中的渗透和实施。     

舰艇辐射噪声仿真信号应用风险评估模型

为了克服传统风险评估中定性分析方法客观性较差等缺点,定义了与仿真信号特征参数一致性相关联的后果系数,对仿真信号风险事件所导致的后果进行了定量分析,并在此基础上提出了基于一致性分析的仿真信号应用风险评估模型,最后给出了该模型应用于舰艇辐射噪声仿真的评估实例。评估实例表明,该模型不仅有助于充分挖掘信号仿真中阶段性数据的有用信息,同时也能为仿真信号的风险评估提供实用工具。     

防空火力配系在敌机投弹线前的射击次数分析

防空兵对空作战的本质是在敌机投弹线或制导武器发射阵位线前击毁来袭敌机,这就要求防空火力在敌机投弹线或制导武器发射阵位线前有相当的射击次数以保证足够大的击毁概率。建立了防空火力配系对空袭兵器射击次数的模型,并分析提出了增加防空火力配系对空袭兵器射击次数的方法途径。     

整数线性规划问题的一个新算法

本文给出求解整数线性规划问题的一个算法。基本思想是通过求出其伴随线性规划问题的最优单纯形表,把整数线性规划化成正整数系数的不定方程,然后从不定方程的非负整数解集中选取一组满足整数线性规划的约束条件的解,作为整数线性规划的最优解。     

一种新的自适应粒子滤波算法*

在对实时性要求高的系统中,粒子数的选择对粒子滤波至关重要,需要在滤波精度与计算复杂度乏间取折衷.提出了一种基于决策规则的自适应粒子滤波算法,在定义综合性能代价函数的基础上,推导出粒子数与滤波误差方差之间的关系,使得在粒子滤波过程中,可以根据实际滤波情况在线调节粒子数,以使滤波的综合性能达到最优.通过Monte Carlo仿真实验表明,新算法在与基本粒子滤波算法(PF)保持同等精度的条件下,大大降低了算法的计算量,约为PF的六分之一.     

基于一乘准则的LMR在声音转换中的应用

线性多变量回归中聚类数的选择对转换效果有很大影响,通过研究聚类数与类内均方差、类间均方差的关系确定最佳聚类数。针对传统二乘规则的 LMR 的转换语音在听觉上自然度较差的缺陷,提出了基于一乘规则的 LMR,采用遗传算法解决绝对值条件下转换矩阵的求解问题,实验仿真表明,基于一乘规则的 LMR 的转换语音在主观听觉上优于基于二乘规则的 LMR,ABX 测试识别率平均提高了12.5%,MOS 分提高了0.24。