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凸域内的平均随机弦长及其极值
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作者 赵江甫 《浙江大学学报(理学版)》 CAS CSCD 北大核心 2024年第3期299-307,共9页
为研究在不同随机意义下平面凸域内的平均随机弦长问题,以圆域、正三角形域、矩形域、正方形域为例,用定义法得到这些凸域内的各平均随机弦长。用弦幂积分及其不等式,讨论了任意凸域内5种平均随机弦长的极值问题,并建立了相应的不等式... 为研究在不同随机意义下平面凸域内的平均随机弦长问题,以圆域、正三角形域、矩形域、正方形域为例,用定义法得到这些凸域内的各平均随机弦长。用弦幂积分及其不等式,讨论了任意凸域内5种平均随机弦长的极值问题,并建立了相应的不等式。在此基础上,提出了2个猜想。 展开更多
关键词 平均随机弦 极值 凸域 平均距离 幂积分 积分几何
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关于圆上随机弦奇论问题的解析 被引量:1
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作者 郑长波 孟宪涛 《沈阳师范大学学报(自然科学版)》 CAS 2012年第2期164-167,共4页
介绍了圆上随机弦的贝特朗奇论问题,由于弦的做法具有任意性,构造出5种不同的随机弦,按照每一种随机弦的构造方法分别求解其奇论问题,得到了7种解法。然后进行奇论解析,分析其一个问题有无穷答案的原因之一是随机弦构造方法的不同并对... 介绍了圆上随机弦的贝特朗奇论问题,由于弦的做法具有任意性,构造出5种不同的随机弦,按照每一种随机弦的构造方法分别求解其奇论问题,得到了7种解法。然后进行奇论解析,分析其一个问题有无穷答案的原因之一是随机弦构造方法的不同并对其进行具体阐述,其二是计算概率P所确定随机试验有差异。通过分析,出现同一个问题多种答案的直接原因是各个解法在计算概率时所依据的随机试验是相异的,根本原因则是人们对构造随机弦任意性理解的不同,共同点是随机点在基本事件空间内都是均匀分布。得到对随机弦的"任意"性不同理解的7种解法的相应结果是正确的,奇论问题并不"奇",在三维球体中仍有相应的Bertrand奇论存在。 展开更多
关键词 随机弦 随机试验 几何概率 奇论
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Simulation of pavement roughness based on time domain model 被引量:2
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作者 钮凯健 李昶 《Journal of Southeast University(English Edition)》 EI CAS 2010年第3期475-479,共5页
In order to describe pavement roughness more intuitively and effectively, a method of pavement roughness simulation, i.e., the stochastic sinusoidal wave, is introduced. The method is based on the primary idea that pa... In order to describe pavement roughness more intuitively and effectively, a method of pavement roughness simulation, i.e., the stochastic sinusoidal wave, is introduced. The method is based on the primary idea that pavement roughness is denoted as the sum of numerous sines or cosines with stochastic phases, and uses the discrete spectrum to approach the target stochastic process. It is a discrete numerical method used to simulate pavement roughness. According to a given pavement power spectral density (PSD) coefficient, under the condition that the character of displacement frequency based on the time domain model is in accordance with the given pavement surface spectrum, the pavement roughness is optimized to stochastic equivalent vibrations by computer simulation, and the curves that describe pavement roughness under each grade are obtained. The results show that the stochastic sinusoidal wave is suitable for simulation of measured pavement surface spectra based on the time domain model. The method of the stochastic sinusoidal wave is important to the research on vehicle ride comfort due to its rigorous mathematical derivation, extensive application range and intuitive simulation curve. Finally, a roughness index defined as the nominal roughness index (NRI) is introduced, and it has correlation with the PSD coefficient. 展开更多
关键词 pavement roughness stochastic sinusoidal wave stochastic process power spectral density (PSD) coefficient time domain nominal roughness index (NRI)
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Efficient and Accurate Simulator for Rayleigh and Rician Fading 被引量:2
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作者 王俊峰 马秀荣 +1 位作者 滕建辅 崔玥 《Transactions of Tianjin University》 EI CAS 2012年第4期243-247,共5页
With an improved Rayleigh fading model and a zero-mean stochastic sinusoid as the scattering and specular components respectively,a stochastic simulation model is proposed for the generation of Rayleigh and Rician fad... With an improved Rayleigh fading model and a zero-mean stochastic sinusoid as the scattering and specular components respectively,a stochastic simulation model is proposed for the generation of Rayleigh and Rician fading waveforms.Compared with the existing stochastic models,the proposed simulator needs only one trial to obtain the desired statistical properties even if the number of samples is not large enough.Moreover,the proposed simulation model can directly generate multiple uncorrelated waveforms for different fading scenarios,such as single-input single-output frequency selective channels and multiple-input multiple-output channels.The performance evaluation and comparison show that the proposed simulator is efficient and accurate. 展开更多
关键词 fading channel simulator Rayleigh fading Rician fading statistical property
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