There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment （BCDSTRE）, i.e., the coupling of branching chain and random walk. In Section...There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment （BCDSTRE）, i.e., the coupling of branching chain and random walk. In Section 2, we prove that any BCDSTRE must be a Markov chain in time random environment when we consider the distribution of the particles in space as a random element. In Section 3, we calculate the first-order moments and the second-order moments of BCDSTRE.展开更多
Influenced by globalization,rural transition in developed Western countries has experienced processes of productivism,post-productivism,and multifunctional development.By contrast,rural transition in most developing c...Influenced by globalization,rural transition in developed Western countries has experienced processes of productivism,post-productivism,and multifunctional development.By contrast,rural transition in most developing countries has been accompanied by rapid urbanization,which has become a core topic in geography research.As the world’s largest developing country,China has undergone profound development since the reform and opening-up.Moreover,rural spaces in some eastern coastal areas have entered the stage of reconstruction after decades of industrialization and urbanization.This paper takes Suzhou as the case area and measures the process of rural transition from 1990 to 2015 by constructing an index system.It then analyzes the characteristics of space-time evolution using exploratory spatial data analysis(ESDA)methods to reveal the influence of economic and social development on rural transition.The results show that rural transition,which generally entails the weakening of rurality and enhancing of urbanity on a macro scale,tends to be heterogeneous across different regions on a micro scale.This paper argues that multifunctionality will be the main future trend of rural transition in rapidly urbanizing areas.The experience in Suzhou could provide an example for establishing policies on sustainable development in rural spaces and achieving urban-rural co-governance.展开更多
The quantum electrodynamics(QED)in a spatially flat(1+3)-dimensional Friedmann-Lema?tre-Robertson-Walker(FLRW)space-time with a Milne-type scale factor is outlined focusing on the amplitudes of the allowed processes i...The quantum electrodynamics(QED)in a spatially flat(1+3)-dimensional Friedmann-Lema?tre-Robertson-Walker(FLRW)space-time with a Milne-type scale factor is outlined focusing on the amplitudes of the allowed processes in the first order perturbations.The definition of the transition rates is reconsidered such that an appropriate angular behavior of the probability for creation of an electron-positron pair from a photon is obtained,which has a similar rate as the creation of a photon and an electron-positron pair from vacuum.It is shown that these processes are allowed only in the first order perturbations,since the photon emission or absorption by an electron or positron are forbidden.展开更多
Quantum theory according to the Copenhagen interpretation holds that, when a quantum interaction is observed (i.e., “measured”), the observer’s measuring devices temporarily become a part of the quantum system. Rel...Quantum theory according to the Copenhagen interpretation holds that, when a quantum interaction is observed (i.e., “measured”), the observer’s measuring devices temporarily become a part of the quantum system. Relativity theory holds that the event clock of the absorbed or emitted photon or graviton is frozen in time relative to all clocks outside the observed system. If we harmonize both theories, this would appear to imply that time continuity must be interrupted at each instant of observed photon or graviton interaction with matter. It is as if a segment of space-time is clipped out during each such observed interaction. If so, we must dispense with the notion of an absolutely smooth and continuous space-time and replace it with an observation-dependent, discontinuous, relativistic/quantum space-time. Mathematical physicists should be able to model this hypothesis (call it a “time-jump hypothesis”) and its inherent discontinuous space-time in their further efforts at unification.展开更多
基金Supported by the NSFC(10371092,11771185,10871200)
文摘There are three parts in this article. In Section 1, we establish the model of branching chain with drift in space-time random environment （BCDSTRE）, i.e., the coupling of branching chain and random walk. In Section 2, we prove that any BCDSTRE must be a Markov chain in time random environment when we consider the distribution of the particles in space as a random element. In Section 3, we calculate the first-order moments and the second-order moments of BCDSTRE.
基金National Social Science Foundation of China,No.21FSHB014National Natural Science Foundation of China,No.42001196。
文摘Influenced by globalization,rural transition in developed Western countries has experienced processes of productivism,post-productivism,and multifunctional development.By contrast,rural transition in most developing countries has been accompanied by rapid urbanization,which has become a core topic in geography research.As the world’s largest developing country,China has undergone profound development since the reform and opening-up.Moreover,rural spaces in some eastern coastal areas have entered the stage of reconstruction after decades of industrialization and urbanization.This paper takes Suzhou as the case area and measures the process of rural transition from 1990 to 2015 by constructing an index system.It then analyzes the characteristics of space-time evolution using exploratory spatial data analysis(ESDA)methods to reveal the influence of economic and social development on rural transition.The results show that rural transition,which generally entails the weakening of rurality and enhancing of urbanity on a macro scale,tends to be heterogeneous across different regions on a micro scale.This paper argues that multifunctionality will be the main future trend of rural transition in rapidly urbanizing areas.The experience in Suzhou could provide an example for establishing policies on sustainable development in rural spaces and achieving urban-rural co-governance.
文摘The quantum electrodynamics(QED)in a spatially flat(1+3)-dimensional Friedmann-Lema?tre-Robertson-Walker(FLRW)space-time with a Milne-type scale factor is outlined focusing on the amplitudes of the allowed processes in the first order perturbations.The definition of the transition rates is reconsidered such that an appropriate angular behavior of the probability for creation of an electron-positron pair from a photon is obtained,which has a similar rate as the creation of a photon and an electron-positron pair from vacuum.It is shown that these processes are allowed only in the first order perturbations,since the photon emission or absorption by an electron or positron are forbidden.
文摘Quantum theory according to the Copenhagen interpretation holds that, when a quantum interaction is observed (i.e., “measured”), the observer’s measuring devices temporarily become a part of the quantum system. Relativity theory holds that the event clock of the absorbed or emitted photon or graviton is frozen in time relative to all clocks outside the observed system. If we harmonize both theories, this would appear to imply that time continuity must be interrupted at each instant of observed photon or graviton interaction with matter. It is as if a segment of space-time is clipped out during each such observed interaction. If so, we must dispense with the notion of an absolutely smooth and continuous space-time and replace it with an observation-dependent, discontinuous, relativistic/quantum space-time. Mathematical physicists should be able to model this hypothesis (call it a “time-jump hypothesis”) and its inherent discontinuous space-time in their further efforts at unification.
