This paper aims to determine the geodesic precession in Yu's (Ω, Aab)-field the- ory[1], and to compare the result with that of the Schwarzschild orbit.
Further exploration of the fteld theory as first proposed by Yu (1989) is here presented to cover the equation of motion of a test particle which induces gravitational radiation. The same theory is shown to contain an...Further exploration of the fteld theory as first proposed by Yu (1989) is here presented to cover the equation of motion of a test particle which induces gravitational radiation. The same theory is shown to contain an exact gravitational radiation equation derived as a logical consequence of field equations without extra postulates. In this general dynamic context the theory is renamed 'The field Theory'.展开更多
Some analytic and probabilistic properties of the weak Poincaré inequality are obtained. In particular, for strong Feller Markov processes the existence of this inequality is equivalent to each of the following: ...Some analytic and probabilistic properties of the weak Poincaré inequality are obtained. In particular, for strong Feller Markov processes the existence of this inequality is equivalent to each of the following: (i)the Liouville property (or the irreducibility); (ii) the existence of successful couplings (or shift-couplings); (iii)the convergence of the Markov process in total variation norm; (iv) the triviality of the tail (or the invariant)σ-field; (v) the convergence of the density. Estimates of the convergence rate in total variation norm of Markov processes are obtained using the weak Poincaré inequality.展开更多
文摘This paper aims to determine the geodesic precession in Yu's (Ω, Aab)-field the- ory[1], and to compare the result with that of the Schwarzschild orbit.
文摘Further exploration of the fteld theory as first proposed by Yu (1989) is here presented to cover the equation of motion of a test particle which induces gravitational radiation. The same theory is shown to contain an exact gravitational radiation equation derived as a logical consequence of field equations without extra postulates. In this general dynamic context the theory is renamed 'The field Theory'.
基金This work was partially supported by the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 10025105) the National Natural Science Foundation of China (Grant No. 10121101) Core Teachers Project and Teaching and R
文摘Some analytic and probabilistic properties of the weak Poincaré inequality are obtained. In particular, for strong Feller Markov processes the existence of this inequality is equivalent to each of the following: (i)the Liouville property (or the irreducibility); (ii) the existence of successful couplings (or shift-couplings); (iii)the convergence of the Markov process in total variation norm; (iv) the triviality of the tail (or the invariant)σ-field; (v) the convergence of the density. Estimates of the convergence rate in total variation norm of Markov processes are obtained using the weak Poincaré inequality.
