Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are...Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.展开更多
In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovest...In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.展开更多
This paper presents some recent works on the control of dynamic systems,which have certain complex properties caused by singularity of the nonlinear structures,structure^varyings, or evolution process etc. First, we c...This paper presents some recent works on the control of dynamic systems,which have certain complex properties caused by singularity of the nonlinear structures,structure^varyings, or evolution process etc. First, we consider the structure singularity of nonlinear control systems. It was revealed that the focus of researches on nonlinear control theory is shifting from regular systems to singular systems. The singularity of nonlinear systems causes certain complexity. Secondly, the switched systems are considered. For such systems the complexity is caused by the structure varying. We show that the switched systems have significant characteristics of complex systems. Finally, we investigate the evolution systems. The evolution structure makes complexity, and itself is a proper model for complex systems.展开更多
We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group.Precisely,we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded...We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group.Precisely,we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded.Moreover,we show that a class of H-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.展开更多
This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kern...This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.展开更多
Two revised regional importance measures(RIMs),that is,revised contribution to variance of sample mean(RCVSM)and revised contribution to variance of sample variance(RCVSV),are defined herein by using the revised means...Two revised regional importance measures(RIMs),that is,revised contribution to variance of sample mean(RCVSM)and revised contribution to variance of sample variance(RCVSV),are defined herein by using the revised means of sample mean and sample variance,which vary with the reduced range of the epistemic parameter.The RCVSM and RCVSV can be computed by the same set of samples,thus no extra computational cost is introduced with respect to the computations of CVSM and CVSV.From the plots of RCVSM and RCVSV,accurate quantitative information on variance reductions of sample mean and sample variance can be read because of reduced upper bound of the range of the epistemic parameter.For general form of quadratic polynomial output,the analytical solutions of the original and the revised RIMs are given.Numerical example is employed and results demonstrate that the analytical results are consistent and accurate.An engineering example is applied to testify the validity and rationality of the revised RIMs,which can give instructions to the engineers about how to reduce variance of sample mean and sample variance by reducing the range of epistemic parameters.展开更多
The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an appl...The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an application of the above results, the authors give the Lp-boundedness for a class of the hyper singular integrals and the fractional integrals with variable kernel. Moreover, as another application of the above results, the authors prove the dimension free estimate for the hyper Riesz transform. This is an extension of the related result obtained by Stein.展开更多
文摘Necessary and sufficient conditions for equalities between a 2 y′(I-P Xx)y and minimum norm quadratic unbiased estimator of variance under the general linear model, where a 2 is a known positive number, are derived. Further, when the Gauss? Markov estimators and the ordinary least squares estimator are identical, a relative simply equivalent condition is obtained. At last, this condition is applied to an interesting example.
基金Supported by China Mathematics Tian Yuan Youth Foundation (10226024) and China Postdoctoral Science Foundation.
文摘In this paper, necessary and sufficient conditions for equalities betweenα~2y^1(I-P_X)y and under the general linear model, whereand α~2 is a known positive number, are derived. Furthermore, when the Gauss-Markovestimators and the ordinary least squares estimators are identical, we obtain a simpleequivalent condition.
基金This research is supported partly by key project of China G1998020308.
文摘This paper presents some recent works on the control of dynamic systems,which have certain complex properties caused by singularity of the nonlinear structures,structure^varyings, or evolution process etc. First, we consider the structure singularity of nonlinear control systems. It was revealed that the focus of researches on nonlinear control theory is shifting from regular systems to singular systems. The singularity of nonlinear systems causes certain complexity. Secondly, the switched systems are considered. For such systems the complexity is caused by the structure varying. We show that the switched systems have significant characteristics of complex systems. Finally, we investigate the evolution systems. The evolution structure makes complexity, and itself is a proper model for complex systems.
基金supported by National Natural Science Foundation of China(Grant No.11071119)
文摘We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group.Precisely,we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded.Moreover,we show that a class of H-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.
基金Project supported by the National Natural Science Foundation of China (No. 10001027).
文摘This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied.
基金supported by the National Natural Science Foundation of China(Grant No.51175425)the Special Research Fund for the Doctoral Program of Higher Education of China(Grant No.20116102110003)
文摘Two revised regional importance measures(RIMs),that is,revised contribution to variance of sample mean(RCVSM)and revised contribution to variance of sample variance(RCVSV),are defined herein by using the revised means of sample mean and sample variance,which vary with the reduced range of the epistemic parameter.The RCVSM and RCVSV can be computed by the same set of samples,thus no extra computational cost is introduced with respect to the computations of CVSM and CVSV.From the plots of RCVSM and RCVSV,accurate quantitative information on variance reductions of sample mean and sample variance can be read because of reduced upper bound of the range of the epistemic parameter.For general form of quadratic polynomial output,the analytical solutions of the original and the revised RIMs are given.Numerical example is employed and results demonstrate that the analytical results are consistent and accurate.An engineering example is applied to testify the validity and rationality of the revised RIMs,which can give instructions to the engineers about how to reduce variance of sample mean and sample variance by reducing the range of epistemic parameters.
基金the 973 Project of China(No.G1999075105)the National Natural ScienceFoundation of China(No.19631080,No.10271016)the Zhejiang Provincial Natural ScienceFoundation of China(No.RC97017,No.197042).
文摘The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an application of the above results, the authors give the Lp-boundedness for a class of the hyper singular integrals and the fractional integrals with variable kernel. Moreover, as another application of the above results, the authors prove the dimension free estimate for the hyper Riesz transform. This is an extension of the related result obtained by Stein.
