In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with...In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.展开更多
In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix eleme...In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.展开更多
A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided differenc...A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.展开更多
AIMTo characterize temporal pattern of resolution and recurrence of naive choroidal neovascularization (CNV) secondary to wet age-related macular degeneration (AMD) treated with intravitreal bevacizumab on as needed r...AIMTo characterize temporal pattern of resolution and recurrence of naive choroidal neovascularization (CNV) secondary to wet age-related macular degeneration (AMD) treated with intravitreal bevacizumab on as needed regimen, and to analyze baseline risk factors for CNV resolution or recurrence.展开更多
In this paper, the 231 earthquake data of magnitude 5 and higher, between north (39.00o-42.00o) and east (26.00o-45.00o) coordinates in Turkey from July 12, 1900 to October 23, 2011 are statistically analyzed. The pro...In this paper, the 231 earthquake data of magnitude 5 and higher, between north (39.00o-42.00o) and east (26.00o-45.00o) coordinates in Turkey from July 12, 1900 to October 23, 2011 are statistically analyzed. The probability density function and cumulative function of the magnitude are derived. It is shown that magnitude random variable is distrib-uted as the exponential distribution. The recurrence periods is also calculated. Recurrence period is estimatedapproxi-matelytwo times a year for an earthquake having magnitude 5.2. Using the Gutenberg-Richter function, the relation between magnitude and frequency is represented.展开更多
Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,f...Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.展开更多
水质指标具有多元相关性、时序性和非线性的特点,为有效预测河流水质变化,针对水质数据存在缺失和异常的问题,提出基于灰色关联分析-门控循环单元(Grey Relational Analysis-Gated Recurrent Unit, GRA-GRU)的水质预测模型。以淮河流域...水质指标具有多元相关性、时序性和非线性的特点,为有效预测河流水质变化,针对水质数据存在缺失和异常的问题,提出基于灰色关联分析-门控循环单元(Grey Relational Analysis-Gated Recurrent Unit, GRA-GRU)的水质预测模型。以淮河流域水质数据为样本,使用线性插值修补缺失数据和剔除的异常数据。使用灰色关联分析计算不同水质指标间的相关性,选择高相关性的水质指标以确定输入变量,并使用门控循环单元(Gated Recurrent Unit, GRU)预测不同的水质指标。将GRA-GRU的预测结果与反向传播神经网络(Back Propagation Neural Network, BPNN)、循环神经网络(Recurrent Neural Network, RNN)、长短期记忆神经网络(Long Short Term Memory, LSTM)、GRU及灰色关联分析-长短期记忆神经网络(Grey Relational Analysis-Long Short Term Memory, GRA-LSTM)进行对比分析,结果显示GRA-GRU在不同水质指标预测上具有较好的适应性,可以有效降低预测误差。其中,与其他模型相比,GRA-GRU预测的化学需氧量在均方根误差上分别降低了3.617%、0.681%、0.478%、1.505%和0.471%。展开更多
文摘In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.
文摘In this paper, the general calculation formulas of radial matrix elements for relativistic n-dimensional hydrogen atom of spin S=0 are obtained, and the recurrence relation of different power order radial matrix elements are also derived.
基金Supported by the National Natural Science Foundation of China (10871178)the Natural Science Foundation of Zhejiang Province of China (Y606154)Foundation of the Education Department of Zhejiang Province of China (20071362)
文摘A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.
基金NIH grants R01EY007366 and R01EY018589(WRF),R01EY020617(LC)"RPB incorporated and unrestricted funds from Jacobs Retina Center"
文摘AIMTo characterize temporal pattern of resolution and recurrence of naive choroidal neovascularization (CNV) secondary to wet age-related macular degeneration (AMD) treated with intravitreal bevacizumab on as needed regimen, and to analyze baseline risk factors for CNV resolution or recurrence.
文摘In this paper, the 231 earthquake data of magnitude 5 and higher, between north (39.00o-42.00o) and east (26.00o-45.00o) coordinates in Turkey from July 12, 1900 to October 23, 2011 are statistically analyzed. The probability density function and cumulative function of the magnitude are derived. It is shown that magnitude random variable is distrib-uted as the exponential distribution. The recurrence periods is also calculated. Recurrence period is estimatedapproxi-matelytwo times a year for an earthquake having magnitude 5.2. Using the Gutenberg-Richter function, the relation between magnitude and frequency is represented.
基金The work was funded by the University of Jeddah,Saudi Arabia under Grant Number UJ–02–093–DR.The authors,therefore,acknowledge with thanks the University for technical and financial support.
文摘Moments of generalized order statistics appear in several areas of science and engineering.These moments are useful in studying properties of the random variables which are arranged in increasing order of importance,for example,time to failure of a computer system.The computation of these moments is sometimes very tedious and hence some algorithms are required.One algorithm is to use a recursive method of computation of these moments and is very useful as it provides the basis to compute higher moments of generalized order statistics from the corresponding lower-order moments.Generalized order statistics pro-vides several models of ordered data as a special case.The moments of general-ized order statistics also provide moments of order statistics and record values as a special case.In this research,the recurrence relations for single,product,inverse and ratio moments of generalized order statistics will be obtained for Lindley–Weibull distribution.These relations will be helpful for obtained moments of gen-eralized order statistics from Lindley–Weibull distribution recursively.Special cases of the recurrence relations will also be obtained.Some characterizations of the distribution will also be obtained by using moments of generalized order statistics.These relations for moments and characterizations can be used in differ-ent areas of computer sciences where data is arranged in increasing order.
文摘水质指标具有多元相关性、时序性和非线性的特点,为有效预测河流水质变化,针对水质数据存在缺失和异常的问题,提出基于灰色关联分析-门控循环单元(Grey Relational Analysis-Gated Recurrent Unit, GRA-GRU)的水质预测模型。以淮河流域水质数据为样本,使用线性插值修补缺失数据和剔除的异常数据。使用灰色关联分析计算不同水质指标间的相关性,选择高相关性的水质指标以确定输入变量,并使用门控循环单元(Gated Recurrent Unit, GRU)预测不同的水质指标。将GRA-GRU的预测结果与反向传播神经网络(Back Propagation Neural Network, BPNN)、循环神经网络(Recurrent Neural Network, RNN)、长短期记忆神经网络(Long Short Term Memory, LSTM)、GRU及灰色关联分析-长短期记忆神经网络(Grey Relational Analysis-Long Short Term Memory, GRA-LSTM)进行对比分析,结果显示GRA-GRU在不同水质指标预测上具有较好的适应性,可以有效降低预测误差。其中,与其他模型相比,GRA-GRU预测的化学需氧量在均方根误差上分别降低了3.617%、0.681%、0.478%、1.505%和0.471%。
