故障树分析法在装甲车辆电源系统故障诊断中的应用

为了能够准确地进行装甲车辆电源系统的故障诊断,深入地研究了故障树分析法在其中的应用;首先,以某型装甲车辆电源系统为研究对象,根据系统失效模型和故障机理,将故障树分析法运用于装甲车辆电源系统故障诊断中,建立电源系统故障树模型,进行故障分析与诊断;其次利用电源系统故障诊断平台对电源系统4个模块进行故障模拟仿真研究,可看出故障树分析法能够准确地诊断出电源系统各个模块的故障,检测精度可达94%,取得了预期效果。     

非齐次树上马氏信源的一类Shannon-McMillan定理

通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,给出了非齐次树上m重非齐次马氏信源的一类Shannon-McMillan定理.     

Farey maps,Diophantine approximation and Bruhat–Tits tree

Based on Broise-Alamichel and Paulin's work on the Gauss map corresponding to the principal convergents via the symbolic coding of the geodesic flow of the continued fraction algorithm for formal power series with coefficients in a finite field, we continue the study of the Gauss map via Farey maps to contain all the intermediate convergents. We define the geometric Farey map, which is given by time-one map of the geodesic flow. We also define algebraic Farey maps, better suited for arithmetic properties, which produce all the intermediate convergents. Then we obtain the ergodic invariant measures for the Farey maps and the convergent speed.     

Knowledge‐based scenario tree generation methods and application in multiperiod portfolio selection problem

A scenario tree is an efficient way to represent a stochastic data process in decision problems under uncertainty. This paper addresses how to efficiently generate appropriate scenario trees. A knowledge‐based scenario tree generation method is proposed; the new method is further improved by accounting for subjective judgements or expectations about the random future. Compared with existing approaches, complicated mathematical models and time‐consuming estimation, simulation and optimization problem solution are avoided in our knowledge‐based algorithms, and large‐scale scenario trees can be quickly generated. To show the advantages of the new algorithms, a multiperiod portfolio selection problem is considered, and a dynamic risk measure is adopted to control the intermediate risk, which is superior to the single‐period risk measure used in the existing literature. A series of numerical experiments are carried out by using real trading data from the Shanghai stock market. The results show that the scenarios generated by our algorithms can properly represent the underlying distribution; our algorithms have high performance, say, a scenario tree with up to 10,000 scenarios can be generated in less than a half minute. The applications in the multiperiod portfolio management problem demonstrate that our scenario tree generation methods are stable, and the optimal trading strategies obtained with the generated scenario tree are reasonable, efficient and robust. Copyright © 2013 John Wiley & Sons, Ltd.     

Depth in bucket recursive trees with variable capacities of buckets

We consider bucket recursive trees of sizen consisting of all buckets with variable capacities1,2,...,b and with a specifc stochastic growth rule.This model can be considered as a generalization of random recursive trees like bucket recursive trees introduced by Mahmoud and Smythe where all buckets have the same capacities.In this work,we provide a combinatorial analysis of these trees where the generating function of the total weights satisfes an autonomous frst order diferential equation.We study the depth of the largest label（i.e.,the number of edges from the root node to the node containing label n）and give a closed formula for the probability distribution.Also we prove a limit law for this quantity which is a direct application of quasi power theorem and compute its mean and variance.Our results for b=1 reduce to the previous results for random recursive trees.     

Time to most recent common ancestor for stationary continuous state branching processes with immigration

Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random variables： the time to the most recent common ancestor （MRCA）, the size of the current population, and the size of the population just before MRCA. We obtain the bottleneck effect as well. The distribution of the number of the oldest families is also established. These generalize the results obtained by Y. T. Chen and J. F. Delmas.     

关于一些图类的L(1,2)-边标号

For a graph G and two positive integers j and k, an m-L(j, k)-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which are distance two apart receive labels differing by at least k. The λ′j,k-number of G is the minimum m of an m-L(j, k)-edge-labeling admitted by G.In this article, we study the L(1, 2)-edge-labeling for paths, cycles, complete graphs, complete multipartite graphs, infinite ?-regular trees and wheels.     

Limitations of the hyperplane separation technique for bounding the extension complexity of polytopes

The hyperplane separation bound is a lower bound on the extension complexity of a polytope. It is the main tool in Rothvoß's proof of an exponential bound for the matching polytope (Rothvoß, 2017). We show that the technique is sensitive to the choice of slack matrix and does not improve upon the best known lower bounds for spanning tree and completion time polytopes when applied to their canonical slack matrices. Stronger bounds may be obtained by appropriate rescalings and redundancy.     

GWLS-SVR模型的红枣树叶片叶绿素含量估算

叶绿素含量是红枣树光合作用能力、生长状况、营养状况的指示剂,不同地理位置种植的红枣树受到自然、人为等因素的影响,叶绿素含量分布有所不同,该研究实地测定了若羌县枣树叶片高光谱反射率及表征叶绿素含量的枣树叶片SPAD（soil plant analysis development)值。为了高效无损地估算红枣树叶片SPAD值,计算了红枣树叶片SPAD值全局莫兰指数,以SPAD值和高光谱波段之间的相关性为基础,通过C_P统计量计算重要程度高的特征波段,运用地理加权最小二乘支持向量回归GWLS-SVR（geographically weighted least squares-support vector regression）模型对红枣树叶片SPAD值进行预测,与多元线性回归（MLR）、支持向量机回归（SVR）模型比较并探讨GWLS-SVR模型估算红枣树叶片SPAD值的能力。结果表明：（1）光谱一阶导数可以有效去除噪声并突出光谱信息尤其是492~510,542~543,642~652,657~670和682~692 nm区间内显著的提高了与SPAD值的相关性。（2）C_P统计量方法能够有效的选择敏感区间的特征波段,进而提高模型估算精度,由统计量方法计算出原始光谱重要程度最高的两个变量为595与696 nm,光谱一阶导数的特征波段为688 nm。其中对于同一个敏感波段区间的波段组合总有单个波段的统计量低于多个波段组合的统计量,这可能是相近波段间的较强共线性导致的。（3）若羌县红枣树叶片SPAD值存在显著的空间聚集性,全局莫兰指数为0.125 8（p<0.1）,适合建立考虑空间位置的GWLS-SVR模型。（4）结合Bootstrap再抽样与t检验模型检验得到结合地理位置信息的GWLS-SVR模型总体上估算能力优于SVR和MLR模型,且结果高度显著（p<0.001）,其中基于光谱一阶导数的GWLS-SVR模型为最优的红枣树叶片SPAD值估算模型（R2为0.975,MSE为1.082）,能够为高光谱定量反演红枣树SPAD值进而快速无损的监测红枣生长状况提供一定参考。