A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some f...A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems.展开更多
The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The metho...The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A(αl),then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio,and use the minimum ratio among the group of ratios to measure the multi collinearity of A.According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix,the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm.The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit,the size of the measure reflects the multi collinearity of column vectors objectively.It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.展开更多
In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the co...In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the continuity of vector space operations is discussed and it is proved that the vector space with I-topology τ‖.,.‖ is not I-topological vector space but with τ*‖.,.‖ is I-topological vector space.Next we study the relationship between this two I-topologies and it is proved that τ*‖.,.‖■τ‖.,.‖.展开更多
This paper an cited instances in illustration of the incorrectness of the criteria of asymptotic stability of a class of nonlinear large seale system that L_j·T·Grujie gave in paper [1] by the comparison the...This paper an cited instances in illustration of the incorrectness of the criteria of asymptotic stability of a class of nonlinear large seale system that L_j·T·Grujie gave in paper [1] by the comparison theory and then corrected it,and has given the sufficient conditions of the asymptotic stability.展开更多
【目的】克服Lee-Carter模型中时间因子预测方法在处理人口死亡率数据的非线性和长记忆性方面存在的局限性。【方法】以最小Lp范数误差法作为差分移动平均自回归模型(autoregressive integrated moving average model,ARIMA),基于遗传...【目的】克服Lee-Carter模型中时间因子预测方法在处理人口死亡率数据的非线性和长记忆性方面存在的局限性。【方法】以最小Lp范数误差法作为差分移动平均自回归模型(autoregressive integrated moving average model,ARIMA),基于遗传算法优化的最小二乘支持向量机(least squares support vector machine,LSSVM)和长短期记忆网络(long-short term memory,LSTM)模块权重优化准则,以及结合串联和并联的组合方式,构建了串联模型(series model,SM)和并联模型(parallel model,PM);选取澳大利亚、英国、美国和中国(不包括中国香港、中国澳门和中国台湾地区)4个国家的男性人口死亡率数据进行实证分析,验证组合模型的预测优越性及适用的广泛性。【结果】组合模型的预测效果无论是在时间因子预测方面还是人口死亡率预测方面均优于ARIMA模型,且PM的预测效果优于SM的预测效果。【结论】本研究结果为人口死亡率预测提供新的研究思路与建模方法,也为应对长寿风险提供一定的理论依据。展开更多
文摘A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems.
基金Project(40144018)supported by the National Natural Science Foundation of China
文摘The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not.For its shortcoming,a method to measure multi collinearity of a matrix was put forward.The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A(αl),then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio,and use the minimum ratio among the group of ratios to measure the multi collinearity of A.According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix,the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm.The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit,the size of the measure reflects the multi collinearity of column vectors objectively.It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.
文摘In this paper using the concept of Felbin-type fuzzy 2-norm ‖.,.‖ on a vector space,two I-topologies τ‖.,.‖ and τ*‖.,.‖ is constructed.After making our elementary observations on this fuzzy I-topologies,the continuity of vector space operations is discussed and it is proved that the vector space with I-topology τ‖.,.‖ is not I-topological vector space but with τ*‖.,.‖ is I-topological vector space.Next we study the relationship between this two I-topologies and it is proved that τ*‖.,.‖■τ‖.,.‖.
文摘This paper an cited instances in illustration of the incorrectness of the criteria of asymptotic stability of a class of nonlinear large seale system that L_j·T·Grujie gave in paper [1] by the comparison theory and then corrected it,and has given the sufficient conditions of the asymptotic stability.
文摘【目的】克服Lee-Carter模型中时间因子预测方法在处理人口死亡率数据的非线性和长记忆性方面存在的局限性。【方法】以最小Lp范数误差法作为差分移动平均自回归模型(autoregressive integrated moving average model,ARIMA),基于遗传算法优化的最小二乘支持向量机(least squares support vector machine,LSSVM)和长短期记忆网络(long-short term memory,LSTM)模块权重优化准则,以及结合串联和并联的组合方式,构建了串联模型(series model,SM)和并联模型(parallel model,PM);选取澳大利亚、英国、美国和中国(不包括中国香港、中国澳门和中国台湾地区)4个国家的男性人口死亡率数据进行实证分析,验证组合模型的预测优越性及适用的广泛性。【结果】组合模型的预测效果无论是在时间因子预测方面还是人口死亡率预测方面均优于ARIMA模型,且PM的预测效果优于SM的预测效果。【结论】本研究结果为人口死亡率预测提供新的研究思路与建模方法,也为应对长寿风险提供一定的理论依据。
