Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. ...Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. This simulation study considered the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration revealed that the BVAR models are excellent for time series length of T=8 for all levels of collinearity while the classical VAR is effective for time series length of T=16 for all collinearity levels except when ρ = -0.9 and ρ = -0.95. We therefore recommended that for effective short term forecasting, the time series length, forecasting horizon and the collinearity level should be considered.展开更多
In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3（n）. The aim of this paper is to generalize Tong＇s method to a class o...In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3（n）. The aim of this paper is to generalize Tong＇s method to a class of Dirichlet series L（s） which satisfies a functional equation. Let a（n） be an arithmetical function related f t to a Dirichlet series L（s）, and let E（x） be the error term of ∑＇n≤x a（n）. In this paper, after introducing a class of Diriclet series with a general functional equation （which contains the well-known Selberg class）, we establish a Tong-type identity and a Tong-type truncated formula for the error term of the Riesz mean of the coefficients of this Dirichlet series L（s）. This kind of Tong-type truncated formula could be used to study the mean square of E（x） under a certain assumption. In other words, we reduce the mean square of E（x） to the problem of finding a suitable constant σ＊ which is related to the mean square estimate of L（s）. We shall represent some results of functions in the Selberg class of degrees 2 -4.展开更多
Let Zm be the additive group of residue classes modulo m.Let s(m,n)denote the number of subgroups of the group Z_(m)×Z_(n),where m and n are arbitrary positive integers.For any x≥1,we consider the asymptotic beh...Let Zm be the additive group of residue classes modulo m.Let s(m,n)denote the number of subgroups of the group Z_(m)×Z_(n),where m and n are arbitrary positive integers.For any x≥1,we consider the asymptotic behavior of D_(s)(x):=∑m^(2)+n^(2)≤xS(M,n)and obtain an asymptotic formula by using the elementary method.展开更多
An upper bound is given for the error termS(r, |a j |,f) in Nevanlinna’s inequality. For given positive increasing functions p and $ with ∫ 1 ∞ dr/p(r) = ∫ 1 ∞ dr/r ?(r) = ∞, setP(r) = ∫ 1 r dt/p,Ψ(r) = ∫ 1 r...An upper bound is given for the error termS(r, |a j |,f) in Nevanlinna’s inequality. For given positive increasing functions p and $ with ∫ 1 ∞ dr/p(r) = ∫ 1 ∞ dr/r ?(r) = ∞, setP(r) = ∫ 1 r dt/p,Ψ(r) = ∫ 1 r dt/t ?(t) We prove that $$S(r, \left\{ {a_j } \right\}, f) \leqslant \log \frac{{T(r, f)\phi (T(r, f))}}{{p(r)}} + O(1)$$ holds, with a small exceptional set of r, for any finite set of points |a j | in the extended plane and any meromorphic function f such thatΨ(T(r, f)) =O(P(r)). This improves the known results of A. Hinkkanen and Y. F. Wang. The sharpness of the estimate is also considered.展开更多
In this paper we study the mean square of the error term in the Weyl's law of an irrational (2l + 1)-dimensional Heisenberg manifold. An asymptotic formula is established.
Standard automatic dependent surveillance broadcast (ADS-B) reception algorithms offer considerable performance at high signal-to-noise ratios (SNRs). However, the performance of ADS-B algorithms in applications can b...Standard automatic dependent surveillance broadcast (ADS-B) reception algorithms offer considerable performance at high signal-to-noise ratios (SNRs). However, the performance of ADS-B algorithms in applications can be problematic at low SNRs and in high interference situations, as detecting and decoding techniques may not perform correctly in such circumstances. In addition, conventional error correction algorithms have limitations in their ability to correct errors in ADS-B messages, as the bit and confidence values may be declared inaccurately in the event of low SNRs and high interference. The principal goal of this paper is to deploy a Long Short-Term Memory (LSTM) recurrent neural network model for error correction in conjunction with a conventional algorithm. The data of various flights are collected and cleaned in an initial stage. The clean data is divided randomly into training and test sets. Next, the LSTM model is trained based on the training dataset, and then the model is evaluated based on the test dataset. The proposed model not only improves the ADS-B In packet error correction rate (PECR), but it also enhances the ADS-B In terms of sensitivity. The performance evaluation results reveal that the proposed scheme is achievable and efficient for the avionics industry. It is worth noting that the proposed algorithm is not dependent on conventional algorithms’ prerequisites.展开更多
A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are ...A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are given to confirm the theoretical analysis of the proposed method.展开更多
针对飞行器飞行试验中外测级间段数据缺失和精度不高的问题,提出了基于长短期记忆(long-short term memory,LSTM)网络的外测级间段数据预测方法。利用遥测视速度数据和外测融合数据建立LSTM网络回归模型,将外测级间段数据作为缺失数据...针对飞行器飞行试验中外测级间段数据缺失和精度不高的问题,提出了基于长短期记忆(long-short term memory,LSTM)网络的外测级间段数据预测方法。利用遥测视速度数据和外测融合数据建立LSTM网络回归模型,将外测级间段数据作为缺失数据进行预测插值,可将制导工具系统误差以及飞行器初始误差,包括遥外测时间对不准误差,一并利用回归网络表示,从而将遥测视速度数据作为网络输入,得到外测级间段的预测数据。试验数据处理结果证明,基于LSTM网络获得的外测级间段预测数据满足精度要求,所提方法具有实际应用价值。展开更多
大型龙门五轴机床的热变形是影响加工精度的重要因素之一。文章探讨了环境温度变化对机床热变形的影响规律。为提升大型龙门数控机床环境综合热误差预测精度,设计了一种基于带卷积的灰色长短期记忆神经网络(grey long short-term memory...大型龙门五轴机床的热变形是影响加工精度的重要因素之一。文章探讨了环境温度变化对机床热变形的影响规律。为提升大型龙门数控机床环境综合热误差预测精度,设计了一种基于带卷积的灰色长短期记忆神经网络(grey long short-term memory neural network, CNN-GreyLSTM)的热误差预测模型。以某大型龙门机床为研究对象,使用有限元仿真与试验相结合的方式分析了环境温度变化引起的刀尖点热漂移误差。分别采用CNN-Grey-LSTM、CNNLSTM和带卷积积分的灰色神经网络模型(GNNMCI(1,N))建立热误差模型并进行对比分析。结果表明,与常见的神经网络相比,CNN-Grey-LSTM模型能更好适应复杂多变的数据特征和时间序列预测问题,体现出更好的预测精度与鲁棒性。展开更多
文摘Forecasts can either be short term, medium term or long term. In this work we considered short term forecast because of the problem of limited data or time series data that is often encounter in time series analysis. This simulation study considered the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration revealed that the BVAR models are excellent for time series length of T=8 for all levels of collinearity while the classical VAR is effective for time series length of T=16 for all collinearity levels except when ρ = -0.9 and ρ = -0.95. We therefore recommended that for effective short term forecasting, the time series length, forecasting horizon and the collinearity level should be considered.
基金supported by National Key Basic Research Program of China (Grant No. 2013CB834201)National Natural Science Foundation of China (Grant No. 11171344)+1 种基金Natural Science Foundation of Beijing (Grant No. 1112010)the Fundamental Research Funds for the Central Universities in China (Grant No. 2012YS01)
文摘In 1956, Tong established an asymptotic formula for the mean square of the error term of the summatory function of the Piltz divisor function d3（n）. The aim of this paper is to generalize Tong＇s method to a class of Dirichlet series L（s） which satisfies a functional equation. Let a（n） be an arithmetical function related f t to a Dirichlet series L（s）, and let E（x） be the error term of ∑＇n≤x a（n）. In this paper, after introducing a class of Diriclet series with a general functional equation （which contains the well-known Selberg class）, we establish a Tong-type identity and a Tong-type truncated formula for the error term of the Riesz mean of the coefficients of this Dirichlet series L（s）. This kind of Tong-type truncated formula could be used to study the mean square of E（x） under a certain assumption. In other words, we reduce the mean square of E（x） to the problem of finding a suitable constant σ＊ which is related to the mean square estimate of L（s）. We shall represent some results of functions in the Selberg class of degrees 2 -4.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11971476)。
文摘Let Zm be the additive group of residue classes modulo m.Let s(m,n)denote the number of subgroups of the group Z_(m)×Z_(n),where m and n are arbitrary positive integers.For any x≥1,we consider the asymptotic behavior of D_(s)(x):=∑m^(2)+n^(2)≤xS(M,n)and obtain an asymptotic formula by using the elementary method.
文摘An upper bound is given for the error termS(r, |a j |,f) in Nevanlinna’s inequality. For given positive increasing functions p and $ with ∫ 1 ∞ dr/p(r) = ∫ 1 ∞ dr/r ?(r) = ∞, setP(r) = ∫ 1 r dt/p,Ψ(r) = ∫ 1 r dt/t ?(t) We prove that $$S(r, \left\{ {a_j } \right\}, f) \leqslant \log \frac{{T(r, f)\phi (T(r, f))}}{{p(r)}} + O(1)$$ holds, with a small exceptional set of r, for any finite set of points |a j | in the extended plane and any meromorphic function f such thatΨ(T(r, f)) =O(P(r)). This improves the known results of A. Hinkkanen and Y. F. Wang. The sharpness of the estimate is also considered.
基金supported by National Natural Science Foundation of China (Grant No. 10771127)
文摘In this paper we study the mean square of the error term in the Weyl's law of an irrational (2l + 1)-dimensional Heisenberg manifold. An asymptotic formula is established.
文摘Standard automatic dependent surveillance broadcast (ADS-B) reception algorithms offer considerable performance at high signal-to-noise ratios (SNRs). However, the performance of ADS-B algorithms in applications can be problematic at low SNRs and in high interference situations, as detecting and decoding techniques may not perform correctly in such circumstances. In addition, conventional error correction algorithms have limitations in their ability to correct errors in ADS-B messages, as the bit and confidence values may be declared inaccurately in the event of low SNRs and high interference. The principal goal of this paper is to deploy a Long Short-Term Memory (LSTM) recurrent neural network model for error correction in conjunction with a conventional algorithm. The data of various flights are collected and cleaned in an initial stage. The clean data is divided randomly into training and test sets. Next, the LSTM model is trained based on the training dataset, and then the model is evaluated based on the test dataset. The proposed model not only improves the ADS-B In packet error correction rate (PECR), but it also enhances the ADS-B In terms of sensitivity. The performance evaluation results reveal that the proposed scheme is achievable and efficient for the avionics industry. It is worth noting that the proposed algorithm is not dependent on conventional algorithms’ prerequisites.
基金Supported by National Natural Science Fund of China (11061021)Key Project of Chinese Ministry of Education (12024)+2 种基金Natural Science Fund of Inner Mongolia Autonomous Region (2012MS0108,2012MS0106,2011BS0102)Scientific Research Projection of Higher Schools of Inner Mongolia (NJZZ12011,NJZY13199)Program of Higher-level talents of Inner Mongolia University (125119,Z200901004,30105-125132)
文摘A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are given to confirm the theoretical analysis of the proposed method.
文摘针对飞行器飞行试验中外测级间段数据缺失和精度不高的问题,提出了基于长短期记忆(long-short term memory,LSTM)网络的外测级间段数据预测方法。利用遥测视速度数据和外测融合数据建立LSTM网络回归模型,将外测级间段数据作为缺失数据进行预测插值,可将制导工具系统误差以及飞行器初始误差,包括遥外测时间对不准误差,一并利用回归网络表示,从而将遥测视速度数据作为网络输入,得到外测级间段的预测数据。试验数据处理结果证明,基于LSTM网络获得的外测级间段预测数据满足精度要求,所提方法具有实际应用价值。
