This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class...This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class, or some periodic functions. We prove that the EulerΓ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions Ø with ρ(Ø) < 1.展开更多
We propose a novel flow measurement method for gas–liquid two-phase slug flow by using the blind source separation technique. The flow measurement model is established based on the fluctuation characteristics of diff...We propose a novel flow measurement method for gas–liquid two-phase slug flow by using the blind source separation technique. The flow measurement model is established based on the fluctuation characteristics of differential pressure(DP) signals measured from a Venturi meter. It is demonstrated that DP signals of two-phase flow are a linear mixture of DP signals of single phase fluids. The measurement model is a combination of throttle relationship and blind source separation model. In addition, we estimate the mixture matrix using the independent component analysis(ICA) technique. The mixture matrix could be described using the variances of two DP signals acquired from two Venturi meters. The validity of the proposed model was tested in the gas–liquid twophase flow loop facility. Experimental results showed that for most slug flow the relative error is within 10%.We also find that the mixture matrix is beneficial to investigate the flow mechanism of gas–liquid two-phase flow.展开更多
基金by Basic and Advanced Research Project of CQCSTC(cstc2019jcyj-msxmX0107)Fundamental Research Funds of Chongqing University of Posts and Telecommunications(CQUPT:A2018-125).
文摘This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class F which contains Dirichlet L-functions,L-functions in the extended Selberg class, or some periodic functions. We prove that the EulerΓ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions Ø with ρ(Ø) < 1.
基金Supported by the National Natural Science Foundation of China(51304231)the Natural Science Foundation of Shandong Province(ZR2010EQ015)
文摘We propose a novel flow measurement method for gas–liquid two-phase slug flow by using the blind source separation technique. The flow measurement model is established based on the fluctuation characteristics of differential pressure(DP) signals measured from a Venturi meter. It is demonstrated that DP signals of two-phase flow are a linear mixture of DP signals of single phase fluids. The measurement model is a combination of throttle relationship and blind source separation model. In addition, we estimate the mixture matrix using the independent component analysis(ICA) technique. The mixture matrix could be described using the variances of two DP signals acquired from two Venturi meters. The validity of the proposed model was tested in the gas–liquid twophase flow loop facility. Experimental results showed that for most slug flow the relative error is within 10%.We also find that the mixture matrix is beneficial to investigate the flow mechanism of gas–liquid two-phase flow.
