In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and d...In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fok- ker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dy- namic entropy density and dynamic information density and the nonlinear evolution equa- tions of Boltzmann dynamic entropy density and dynamic information density, that de- scribe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic infor- mation densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and in- formation have been combined with the state and its law of motion of the systems. Fur- thermore we presented the formulas of two kinds of entropy production rates and infor- mation dissipation rates, the expressions of two kinds of drift information flows and diffu- sion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy produc- tion rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel capacities reflecting the dynam展开更多
Under the background of new infrastructure,the Yellow River Basin’s superior growth cannot be separated originating with the synergistic effect of scientific and technological inventiveness and ecological civilizatio...Under the background of new infrastructure,the Yellow River Basin’s superior growth cannot be separated originating with the synergistic effect of scientific and technological inventiveness and ecological civilization construction.In light of the coupling coordination analysis of the coordination effect of provincial high-tech industry agglomeration and resource carrying capacity in the Yellow River Basin from 2009 to 2021,The evolution of the geographical and temporal pattern of development was investigated using the Moran index and kernel density estimation.The results show that the agglomeration of high-tech industries in the Yellow River Basin presents a development trend of seek improvement in stability,and there is a good coupling and coordination throughout the progression of scientific and technological innovation and the loading capacity of the resource,from the viewpoint of a time series.From the perspective of spatial pattern distribution,the whole basin aims at the lower reaches,accelerates the optimization of digital industry and promotes Yellow River Basin development of superior quality through innovation support and increase of input,and based on policy guidance.展开更多
文摘In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fok- ker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dy- namic entropy density and dynamic information density and the nonlinear evolution equa- tions of Boltzmann dynamic entropy density and dynamic information density, that de- scribe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic infor- mation densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and in- formation have been combined with the state and its law of motion of the systems. Fur- thermore we presented the formulas of two kinds of entropy production rates and infor- mation dissipation rates, the expressions of two kinds of drift information flows and diffu- sion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy produc- tion rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel capacities reflecting the dynam
基金supported by the 2021 Research and Practice Project of Higher Education Teaching Reform in Henan Province(Grant No.2021SJGLX072Y).
文摘Under the background of new infrastructure,the Yellow River Basin’s superior growth cannot be separated originating with the synergistic effect of scientific and technological inventiveness and ecological civilization construction.In light of the coupling coordination analysis of the coordination effect of provincial high-tech industry agglomeration and resource carrying capacity in the Yellow River Basin from 2009 to 2021,The evolution of the geographical and temporal pattern of development was investigated using the Moran index and kernel density estimation.The results show that the agglomeration of high-tech industries in the Yellow River Basin presents a development trend of seek improvement in stability,and there is a good coupling and coordination throughout the progression of scientific and technological innovation and the loading capacity of the resource,from the viewpoint of a time series.From the perspective of spatial pattern distribution,the whole basin aims at the lower reaches,accelerates the optimization of digital industry and promotes Yellow River Basin development of superior quality through innovation support and increase of input,and based on policy guidance.
