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一种计算Tchebyscheff映射高阶关联函数的数论方法 被引量:1
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作者 周兴旺 《四川大学学报(自然科学版)》 CAS CSCD 北大核心 2022年第5期33-38,共6页
关联函数是混沌映射的统计理论的核心.本文主要研究Tchebyscheff映射的高阶关联函数的计算问题.对此问题,已有Beck于1991年提出的一种图论方法.然而,当映射和关联函数的阶都比较大时该方法非常低效.本文基于Tchebyscheff映射关联函数的... 关联函数是混沌映射的统计理论的核心.本文主要研究Tchebyscheff映射的高阶关联函数的计算问题.对此问题,已有Beck于1991年提出的一种图论方法.然而,当映射和关联函数的阶都比较大时该方法非常低效.本文基于Tchebyscheff映射关联函数的定义提出了一种数论方法.该方法将关联函数的计算问题转化为一类具有严格单调递增指数的指数型丢番图方程的求解问题,进而逐级地求得方程的解.然后,本文研究了当映射的阶不小于关联函数的阶时非零关联函数的计算问题.计算结果显示,此时关联函数的值不依赖于映射的阶,且非零关联函数的个数与第二类斯特林数密切相关.作为应用本文最后计算了满足条件的所有12阶非零关联函数的值. 展开更多
关键词 关联函数 tchebyscheff映射 指数型丢番图方程
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切比雪夫映射族关联函数的指数型丢番图方程
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作者 周兴旺 《四川大学学报(自然科学版)》 CAS CSCD 北大核心 2023年第6期66-71,共6页
切比雪夫映射族是一类典型的混沌映射,关联函数是研究其统计性质的关键.本文所研究的指数型丢番图方程源于该映射族的关联函数的计算问题.为求得该方程的解,本文首先对该方程进行简化,使简化后的方程具有严格单调递增的指数及非零系数.... 切比雪夫映射族是一类典型的混沌映射,关联函数是研究其统计性质的关键.本文所研究的指数型丢番图方程源于该映射族的关联函数的计算问题.为求得该方程的解,本文首先对该方程进行简化,使简化后的方程具有严格单调递增的指数及非零系数.然后本文引入了“块”的概念,根据简化方程所含块的个数对其进行了分类,进而将原丢番图方程求解问题转化为由块所构成的丢番图方程的求解问题.本文最后研究了一个和两个块的情形,并举例说明了本文结果的应用. 展开更多
关键词 指数型丢番图方程 关联函数 切比雪夫映射
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Two Models of Optical Pulse Self-Compressor Combined the Nonlinear Coupler with Backward Raman Fiber Amplifier
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作者 Quang Quy Ho Van Bien Chu 《Journal of Electromagnetic Analysis and Applications》 2012年第9期379-385,共7页
Based on the nonlinearity of the nonlinear optical coupler (NOC) and the amplifying capacity of the backward Raman fiber amplifier (PBRFA), two new optical systems to compress the optical pulse (Optical Pulse Self-Com... Based on the nonlinearity of the nonlinear optical coupler (NOC) and the amplifying capacity of the backward Raman fiber amplifier (PBRFA), two new optical systems to compress the optical pulse (Optical Pulse Self-Compressor: OPSC) are proposed. Using the expressions describing relationship between input and output intensities from ports of the NOC and the derived expression describing the amplification of the PBRFA, the compressing process of the optical pulse propagating through the OPSC is simulated. The results show that the peak of the optical pulse will be enhanced and the duration of the optical pulse will be reduced significantly. Consequently, the shape of input pulse is completely compressed with the certain efficiency. It means the optical pulse is self-compressed without the external pump pulse by proposing the OPSC. 展开更多
关键词 Intelligent Transportation System MICROSTRIP Phased Array Antenna tchebyscheff POLYNOMIAL Electromagnetic Interference
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Vehicular Radio Scanner Using Phased Array Antenna for Dedicated Short Range Communication Service
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作者 Tapas Mondal Priyanka Shishodiya +1 位作者 Rowdra Ghatak Sekhar Ranjan Bhadra Chaudhuri 《Journal of Electromagnetic Analysis and Applications》 2012年第9期362-366,共5页
Now a day’s accidents are very common due to increased population of vehicle. In order to ensure safety measures in the vehicle this paper has proposed some methodologies regarding careful driving by automatically sc... Now a day’s accidents are very common due to increased population of vehicle. In order to ensure safety measures in the vehicle this paper has proposed some methodologies regarding careful driving by automatically scanning and analyzing the blind spot area of an intelligent mobile vehicle. A vehicular antenna with minimum perturbation is proposed to be fitted on the vehicle and collect information of the concern area which would ensure visibility of the operator i.e. masked or integrated within the car body. This paper has dealt with the design of Tchebyscheff polynomial based prototype planar microstrip phased array antenna and also redesigned the same when implemented in the body of the car being considered as an electromagnetically large element. Both the design has been experimentally verified with the measurement. The simulated and the measured results in both the cases are found to be in good agreement. More than 11 dB gain was observed at perfectly 30° angles from its broad side direction as desired for blind spot detection with minimum amount of electromagnetic interference inside the car. 展开更多
关键词 ntelligent TRANSPORTATION System MICROSTRIP Phased Array Antenna tchebyscheff POLYNOMIAL ELECTROMAGNETIC INTERFERENCE
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正交多项式逼近去白噪 被引量:8
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作者 杨云飞 王华忠 曹景忠 《石油地球物理勘探》 EI CSCD 北大核心 2001年第6期704-706,共3页
杨云飞 ,王华忠 ,曹景忠 .正交多项式逼近去白噪 .石油地球物理勘探 ,2 0 0 1,36 (6 ) :70 4~ 70 6  本文介绍一种多项式拟合去白噪方法 ,它利用切比雪夫多项式或勒让德多项式拟合逼近数据列去除白噪。使用该方法对测井数据和野外地... 杨云飞 ,王华忠 ,曹景忠 .正交多项式逼近去白噪 .石油地球物理勘探 ,2 0 0 1,36 (6 ) :70 4~ 70 6  本文介绍一种多项式拟合去白噪方法 ,它利用切比雪夫多项式或勒让德多项式拟合逼近数据列去除白噪。使用该方法对测井数据和野外地震数据进行处理 ,应用效果良好。 展开更多
关键词 地震数据处理 去噪 切比雪夫多项式 勒让德多项式 拟合去白噪方法
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