A natural extension of the Lorentz transformation to its complex version was constructed together with a parallel extension of the Minkowski M<sup>4</sup> model for special relativity (SR) to complex C<...A natural extension of the Lorentz transformation to its complex version was constructed together with a parallel extension of the Minkowski M<sup>4</sup> model for special relativity (SR) to complex C<sup>4</sup> space-time. As the [signed] absolute values of complex coordinates of the underlying motion’s characterization in C<sup>4</sup> one obtains a Newtonian-like type of motion whereas as the real parts of the complex motion’s description and of the complex Lorentz transformation, all the SR theory as modeled by M<sup>4</sup> real space-time can be recovered. This means all the SR theory is preserved in the real subspace M<sup>4</sup> of the space-time C<sup>4</sup> while becoming simpler and clearer in the new complex model’s framework. Since velocities in the complex model can be determined geometrically, with no primary use of time, time turns out to be definable within the equivalent theory of the reduced complex C<sup>4</sup> model to the C<sup>3</sup> “para-space” model. That procedure allows us to separate time from the (para)space and consider all the SR theory as a theory of C<sup>3</sup> alone. On the other hand, the complex time defined within the C<sup>3</sup> theory is interpreted and modeled by the single separate C<sup>1</sup> complex plane. The possibility for application of the C<sup>3</sup> model to quantum mechanics is suggested. As such, the model C<sup>3</sup> seems to have unifying abilities for application to different physical theories.展开更多
In this paper, a low-dimensional multiple-input and multiple-output （MIMO） model predictive control （MPC） configuration is presented for partial differential equation （PDE） unknown spatially-distributed systems ...In this paper, a low-dimensional multiple-input and multiple-output （MIMO） model predictive control （MPC） configuration is presented for partial differential equation （PDE） unknown spatially-distributed systems （SDSs）. First, the dimension reduction with principal component analysis （PCA） is used to transform the high-dimensional spatio-temporal data into a low-dimensional time domain. The MPC strategy is proposed based on the online correction low-dimensional models, where the state of the system at a previous time is used to correct the output of low-dimensional models. Sufficient conditions for closed-loop stability are presented and proven. Simulations demonstrate the accuracy and efficiency of the proposed methodologies.展开更多
The rate of vertical differential movement of the great Weihe fault (west segment) in different periods is analyzed by using the data of the historic evolution of the Zhouyuan plateau surface. Results show that the ra...The rate of vertical differential movement of the great Weihe fault (west segment) in different periods is analyzed by using the data of the historic evolution of the Zhouyuan plateau surface. Results show that the rate reached a maximum in the Ming Dynasty, about 6. 4 mm/a, which corresponded well to the period of strongearthquake on the Wei River fault in the 15-16th centuries. Based on such a correspondence, the time separation between active periods of Ms=8. 0 strong earthquakes in the Wei River fault depression is investigated.展开更多
We study jump-diffusion processes with two well-separated time scales. It is proved that the rate of strong convergence to the averaged effective dynamics is of order O（ε1/2）, where s 〈〈 1 is the parameter measur...We study jump-diffusion processes with two well-separated time scales. It is proved that the rate of strong convergence to the averaged effective dynamics is of order O（ε1/2）, where s 〈〈 1 is the parameter measuring the disparity of the time scales in the system. The convergence rate is shown to be optimal through examples. The result sheds light on the designing of efficient numerical methods for multiscale stochastic ,dynamics.展开更多
文摘A natural extension of the Lorentz transformation to its complex version was constructed together with a parallel extension of the Minkowski M<sup>4</sup> model for special relativity (SR) to complex C<sup>4</sup> space-time. As the [signed] absolute values of complex coordinates of the underlying motion’s characterization in C<sup>4</sup> one obtains a Newtonian-like type of motion whereas as the real parts of the complex motion’s description and of the complex Lorentz transformation, all the SR theory as modeled by M<sup>4</sup> real space-time can be recovered. This means all the SR theory is preserved in the real subspace M<sup>4</sup> of the space-time C<sup>4</sup> while becoming simpler and clearer in the new complex model’s framework. Since velocities in the complex model can be determined geometrically, with no primary use of time, time turns out to be definable within the equivalent theory of the reduced complex C<sup>4</sup> model to the C<sup>3</sup> “para-space” model. That procedure allows us to separate time from the (para)space and consider all the SR theory as a theory of C<sup>3</sup> alone. On the other hand, the complex time defined within the C<sup>3</sup> theory is interpreted and modeled by the single separate C<sup>1</sup> complex plane. The possibility for application of the C<sup>3</sup> model to quantum mechanics is suggested. As such, the model C<sup>3</sup> seems to have unifying abilities for application to different physical theories.
基金supported by National High Technology Research and Development Program of China (863 Program)(No. 2009AA04Z162)National Nature Science Foundation of China(No. 60825302, No. 60934007, No. 61074061)+1 种基金Program of Shanghai Subject Chief Scientist,"Shu Guang" project supported by Shang-hai Municipal Education Commission and Shanghai Education Development FoundationKey Project of Shanghai Science and Technology Commission, China (No. 10JC1403400)
文摘In this paper, a low-dimensional multiple-input and multiple-output （MIMO） model predictive control （MPC） configuration is presented for partial differential equation （PDE） unknown spatially-distributed systems （SDSs）. First, the dimension reduction with principal component analysis （PCA） is used to transform the high-dimensional spatio-temporal data into a low-dimensional time domain. The MPC strategy is proposed based on the online correction low-dimensional models, where the state of the system at a previous time is used to correct the output of low-dimensional models. Sufficient conditions for closed-loop stability are presented and proven. Simulations demonstrate the accuracy and efficiency of the proposed methodologies.
文摘The rate of vertical differential movement of the great Weihe fault (west segment) in different periods is analyzed by using the data of the historic evolution of the Zhouyuan plateau surface. Results show that the rate reached a maximum in the Ming Dynasty, about 6. 4 mm/a, which corresponded well to the period of strongearthquake on the Wei River fault in the 15-16th centuries. Based on such a correspondence, the time separation between active periods of Ms=8. 0 strong earthquakes in the Wei River fault depression is investigated.
文摘We study jump-diffusion processes with two well-separated time scales. It is proved that the rate of strong convergence to the averaged effective dynamics is of order O（ε1/2）, where s 〈〈 1 is the parameter measuring the disparity of the time scales in the system. The convergence rate is shown to be optimal through examples. The result sheds light on the designing of efficient numerical methods for multiscale stochastic ,dynamics.
