In this article,the Moore-Gibson-Thompson heat equation in three-dimensional cylindrical domain are studied.Using a second order differential inequality,we obtain that the solution can decay exponentially as the dista...In this article,the Moore-Gibson-Thompson heat equation in three-dimensional cylindrical domain are studied.Using a second order differential inequality,we obtain that the solution can decay exponentially as the distance from the entry section tends to infinity.Our result can be seen as a version of Saint-Venant principle.展开更多
The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the ...The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.展开更多
In a test of the weak equivalence principle （WEP） with a rotating torsion pendulum, it is important to estimate the amplitude of the modulation signal with high precision. We use a torsional filter to remove the fre...In a test of the weak equivalence principle （WEP） with a rotating torsion pendulum, it is important to estimate the amplitude of the modulation signal with high precision. We use a torsional filter to remove the free oscillation signal and employ the correlation method to estimate the amplitude of the modulation signal. The data analysis of an experiment shows that the uncertainties of amplitude components of the modulation signal obtained by the correlation method are in agreement with those due to white noise. The power spectral density of the modulation signal obtained by the correlation method is about one order higher than the thermal noise limit. It indicates that the correlation method is an effective way to estimate the amplitude of the modulation signal and it is instructive to conduct a high-accuracy WEP test.展开更多
In this short note,we are concerned with the global existence and stability of solutions to the river flow system.We introduce a new technique to set up a relation between the Riemann invariants and the finite mass to...In this short note,we are concerned with the global existence and stability of solutions to the river flow system.We introduce a new technique to set up a relation between the Riemann invariants and the finite mass to obtain a time-independent,bounded solution for any adiabatic exponent.The global existence of solutions was known long ago[Klingenberg and Lu in Commun.Math.Phys.187:327-340,1997].However,since the uncertainty of the function b(x),which corresponds physically to the slope of the topography,the L∞estimates growed larger with respect to the time variable.As a result,it does not guarantee the stability of solutions.By employing a suitable mathematical transformation to control the slope of the topography by the friction and the finite mass,we prove the uniformly bounded estimate with respect to the time variable.This means that our solutions are stable.展开更多
When multicollinearity is present in a set of the regression variables,the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper,generalized ridg...When multicollinearity is present in a set of the regression variables,the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper,generalized ridge estimate(K)of the regression coefficient=vec(B)is considered in multivaiale linear regression model.The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter matrix K.Moreover,it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several weaknesses.In order to overcome these weaknesses,a new family of criteria Q(c)is adpoted which includes the criterion MSE and criterion LS as its special case.The good properties of the criteria Q(c)are proved and discussed from theoretical point of view.The statistical meaning of the scale c is explained and the methods of determining c are also given.展开更多
基金Supported by the National Natural Science Foundation of China (11371175)the Research Team of Guangzhou Huashang College(2021HSKT01)Guangzhou Huashang College Mentorship Program(2020HSDS16)。
文摘In this article,the Moore-Gibson-Thompson heat equation in three-dimensional cylindrical domain are studied.Using a second order differential inequality,we obtain that the solution can decay exponentially as the distance from the entry section tends to infinity.Our result can be seen as a version of Saint-Venant principle.
基金supported by the National Natural Science Foundation of China,Grant Nos.42174011,41874001 and 41664001Innovation Found Designated for Graduate Students of ECUT,Grant No.DHYC-202020。
文摘The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575160,91636221,and 11605065)
文摘In a test of the weak equivalence principle （WEP） with a rotating torsion pendulum, it is important to estimate the amplitude of the modulation signal with high precision. We use a torsional filter to remove the free oscillation signal and employ the correlation method to estimate the amplitude of the modulation signal. The data analysis of an experiment shows that the uncertainties of amplitude components of the modulation signal obtained by the correlation method are in agreement with those due to white noise. The power spectral density of the modulation signal obtained by the correlation method is about one order higher than the thermal noise limit. It indicates that the correlation method is an effective way to estimate the amplitude of the modulation signal and it is instructive to conduct a high-accuracy WEP test.
基金supported by the Zhejiang Natural Science Foundation of China(Grant No.LY17A010019)the second author is supported by the Zhejiang Natural Science Foundation of China(Grant No.LY20A010023)+1 种基金the National Natural Science Foundation of China(Grant No.12071106)the third author is supported by the Grant-in-Aid for Scientific Research(C)17K05315,Japan.
文摘In this short note,we are concerned with the global existence and stability of solutions to the river flow system.We introduce a new technique to set up a relation between the Riemann invariants and the finite mass to obtain a time-independent,bounded solution for any adiabatic exponent.The global existence of solutions was known long ago[Klingenberg and Lu in Commun.Math.Phys.187:327-340,1997].However,since the uncertainty of the function b(x),which corresponds physically to the slope of the topography,the L∞estimates growed larger with respect to the time variable.As a result,it does not guarantee the stability of solutions.By employing a suitable mathematical transformation to control the slope of the topography by the friction and the finite mass,we prove the uniformly bounded estimate with respect to the time variable.This means that our solutions are stable.
基金The projects Supported by Natural Science Foundation of Fujian Province
文摘When multicollinearity is present in a set of the regression variables,the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper,generalized ridge estimate(K)of the regression coefficient=vec(B)is considered in multivaiale linear regression model.The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter matrix K.Moreover,it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several weaknesses.In order to overcome these weaknesses,a new family of criteria Q(c)is adpoted which includes the criterion MSE and criterion LS as its special case.The good properties of the criteria Q(c)are proved and discussed from theoretical point of view.The statistical meaning of the scale c is explained and the methods of determining c are also given.
