In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-...In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-momentum tensor. We then generalise to construct a fourth rank stress energy-momentum tensor and apply it to Dirac field of quantum particles. Furthermore, since the established fourth rank energy-momentum tensors have mathematical properties of the Riemann curvature tensor, thus it is reasonable to suggest that quantum fields should also possess geometric structures of a Riemannian manifold.展开更多
Compared with the rank reduction estimator(RARE) based on second-order statistics(called SOS-RARE), the RARE based on fourth-order cumulants(referred to as FOC-RARE) can handle more sources and restrain the negative i...Compared with the rank reduction estimator(RARE) based on second-order statistics(called SOS-RARE), the RARE based on fourth-order cumulants(referred to as FOC-RARE) can handle more sources and restrain the negative impacts of the Gaussian colored noise. However, the unexpected modeling errors appearing in practice are known to significantly degrade the performance of the RARE. Therefore, the direction-of-arrival(DOA) estimation performance of the FOC-RARE is quantitatively derived. The explicit expression for direction-finding(DF) error is derived via the first-order perturbation analysis, and then the theoretical formula for the mean square error(MSE) is given. Simulation results demonstrate the validation of the theoretical analysis and reveal that the FOC-RARE is more robust to the unexpected modeling errors than the SOS-RARE.展开更多
Compared to the rank reduction estimator(RARE)based on second-order statistics(called SOS-RARE),the RARE employing fourth-order cumulants(referred to as FOC-RARE)is capable of dealing with more sources and mitigating ...Compared to the rank reduction estimator(RARE)based on second-order statistics(called SOS-RARE),the RARE employing fourth-order cumulants(referred to as FOC-RARE)is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise.However,in the presence of unexpected modeling errors,the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE,even for a known array covariance matrix.For this reason,the angle resolution capability of the FOC-RARE was theoretically analyzed.Firstly,the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method.Then,with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution,the theoretical formulas for the angle resolution probability of the FOC-RARE were presented.Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling errors than that of the SOS-RARE from the resolution point of view.展开更多
In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international sp...In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international spread of the infectious diseases. The relationship between epidemiology, mathematical modeling and computational tools lets us to build and test theories on the development and fighting with a disease. This study is motivated by the study of epidemiological models applied to infectious diseases in an optimal control perspective. We use the numerical methods to display the solutions of the optimal control problems to find the effect of vaccination on these models. Finally, global sensitivity analysis LHS Monte Carlo method using Partial Rank Correlation Coefficient (PRCC) has been performed to investigate the key parameters in model equations. This present work will advance the understanding about the spread of infectious diseases and lead to novel conceptual understanding for spread of them.展开更多
IntroductionBeing of great value to railway transport and hence to nationaleconomy,electrification of railways has been carried out very rapidlyin China in the past 30 years.By the end of 1990,some 6941 km ofelectrifi...IntroductionBeing of great value to railway transport and hence to nationaleconomy,electrification of railways has been carried out very rapidlyin China in the past 30 years.By the end of 1990,some 6941 km ofelectrified railways have been opened to traffic and about 16,000 kmor one fourth of the total railway length are expected to be electrified,accounting for 45% of the total railway freight volume.At present,Shaanxi Province ranks first with respect to展开更多
Zhejiang,an eastern coastal province of China,ranks the fourth place in the country for its GDP contribution of 430 million yuan in 2015with an increase of 8 percent.The province has formed the economic structure feat...Zhejiang,an eastern coastal province of China,ranks the fourth place in the country for its GDP contribution of 430 million yuan in 2015with an increase of 8 percent.The province has formed the economic structure featured with a large number of SMEs since the reform and opening up policy implemented in the 1980s.As of the end of June 2015,the registered enterprises in Zhejiang reach nearly 500,000,of which SMEs,accounting for 95%,contribute to over 60%of the province’s GDP.展开更多
Shanghai GM has been again elected one of the most respected companies of 2002 in China Shanghai GM has again been elected one of the most respected companies in China, jointly by Management Case Research Center of Be...Shanghai GM has been again elected one of the most respected companies of 2002 in China Shanghai GM has again been elected one of the most respected companies in China, jointly by Management Case Research Center of Beijing University and the Economy Observer. As the only auto company in the list, its position in the list rose to fourth, from tenth in 2001. It ranks No. 1 in foreign invested companies.展开更多
文摘In this work, we introduce the new concept of fourth rank energy-momentum tensor. We first show that a fourth rank electromagnetic energy-momentum tensor can be constructed from the second rank electromagnetic energy-momentum tensor. We then generalise to construct a fourth rank stress energy-momentum tensor and apply it to Dirac field of quantum particles. Furthermore, since the established fourth rank energy-momentum tensors have mathematical properties of the Riemann curvature tensor, thus it is reasonable to suggest that quantum fields should also possess geometric structures of a Riemannian manifold.
基金Project(61201381) supported by the National Natural Science Foundation of ChinaProject(YP12JJ202057) supported by the Future Development Foundation of Zhengzhou Information Science and Technology College,China
文摘Compared with the rank reduction estimator(RARE) based on second-order statistics(called SOS-RARE), the RARE based on fourth-order cumulants(referred to as FOC-RARE) can handle more sources and restrain the negative impacts of the Gaussian colored noise. However, the unexpected modeling errors appearing in practice are known to significantly degrade the performance of the RARE. Therefore, the direction-of-arrival(DOA) estimation performance of the FOC-RARE is quantitatively derived. The explicit expression for direction-finding(DF) error is derived via the first-order perturbation analysis, and then the theoretical formula for the mean square error(MSE) is given. Simulation results demonstrate the validation of the theoretical analysis and reveal that the FOC-RARE is more robust to the unexpected modeling errors than the SOS-RARE.
基金Project(61201381)supported by the National Nature Science Foundation of ChinaProject(YP12JJ202057)supported by the Future Development Foundation of Zhengzhou Information Science and Technology College,China
文摘Compared to the rank reduction estimator(RARE)based on second-order statistics(called SOS-RARE),the RARE employing fourth-order cumulants(referred to as FOC-RARE)is capable of dealing with more sources and mitigating the negative influences of the Gaussian colored noise.However,in the presence of unexpected modeling errors,the resolution behavior of the FOC-RARE also deteriorate significantly as SOS-RARE,even for a known array covariance matrix.For this reason,the angle resolution capability of the FOC-RARE was theoretically analyzed.Firstly,the explicit formula for the mathematical expectation of the FOC-RARE spatial spectrum was derived through the second-order perturbation analysis method.Then,with the assumption that the unexpected modeling errors were drawn from complex circular Gaussian distribution,the theoretical formulas for the angle resolution probability of the FOC-RARE were presented.Numerical experiments validate our analytical results and demonstrate that the FOC-RARE has higher robustness to the unexpected modeling errors than that of the SOS-RARE from the resolution point of view.
文摘In the current work, we study two infectious disease models and we use nonlinear optimization and optimal control theory which helps to find strategies towards transmission control and to forecast the international spread of the infectious diseases. The relationship between epidemiology, mathematical modeling and computational tools lets us to build and test theories on the development and fighting with a disease. This study is motivated by the study of epidemiological models applied to infectious diseases in an optimal control perspective. We use the numerical methods to display the solutions of the optimal control problems to find the effect of vaccination on these models. Finally, global sensitivity analysis LHS Monte Carlo method using Partial Rank Correlation Coefficient (PRCC) has been performed to investigate the key parameters in model equations. This present work will advance the understanding about the spread of infectious diseases and lead to novel conceptual understanding for spread of them.
文摘IntroductionBeing of great value to railway transport and hence to nationaleconomy,electrification of railways has been carried out very rapidlyin China in the past 30 years.By the end of 1990,some 6941 km ofelectrified railways have been opened to traffic and about 16,000 kmor one fourth of the total railway length are expected to be electrified,accounting for 45% of the total railway freight volume.At present,Shaanxi Province ranks first with respect to
文摘Zhejiang,an eastern coastal province of China,ranks the fourth place in the country for its GDP contribution of 430 million yuan in 2015with an increase of 8 percent.The province has formed the economic structure featured with a large number of SMEs since the reform and opening up policy implemented in the 1980s.As of the end of June 2015,the registered enterprises in Zhejiang reach nearly 500,000,of which SMEs,accounting for 95%,contribute to over 60%of the province’s GDP.
文摘Shanghai GM has been again elected one of the most respected companies of 2002 in China Shanghai GM has again been elected one of the most respected companies in China, jointly by Management Case Research Center of Beijing University and the Economy Observer. As the only auto company in the list, its position in the list rose to fourth, from tenth in 2001. It ranks No. 1 in foreign invested companies.
