The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the on...The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.展开更多
In this paper,we prove the global well-posedness of the 2 D Boussinesq equations with three kinds of partial dissipation;among these the initial data(u_(0),θ_(0))is required such that its own and the derivative of on...In this paper,we prove the global well-posedness of the 2 D Boussinesq equations with three kinds of partial dissipation;among these the initial data(u_(0),θ_(0))is required such that its own and the derivative of one of its directions(x,y)are assumed to be L^(2)(R^(2)).Our results only need the lower regularity of the initial data,which ensures the uniqueness of the solutions.展开更多
Helium is the second most abundant element in the universe, and together with silica, they are important components of giant planets. Exploring the reactivity and state of helium and silica under high pressure is cruc...Helium is the second most abundant element in the universe, and together with silica, they are important components of giant planets. Exploring the reactivity and state of helium and silica under high pressure is crucial for understanding of the evolution and internal structure of giant planets. Here, using first-principles calculations and crystal structure predictions, we identify four stable phases of a helium-silica compound with seven/eight-coordinated silicon atoms at pressure of 600–4000 GPa, corresponding to the interior condition of the outer planets in the solar system. The density of He Si O2 agrees with current structure models of the planets.This helium-silica compound exhibits a superionic-like helium diffusive state under the high-pressure and hightemperature conditions along the isentropes of Saturn, a metallic fluid state in Jupiter, and a solid state in the deep interiors of Uranus and Neptune. These results show that helium may affect the erosion of the rocky core in giant planets and may help to form a diluted core region, which not only highlight the reactivity of helium under high pressure but also provide evidence helpful for building more sophisticated interior models of giant planets.展开更多
This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational ...This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational formulation of the variation problem and the discrete solution to the time-fractional and space-fractional difference equation using separating variables method and two-side Z-transform method.展开更多
文摘The authors investigate the problem of impulse control of a partially observed diffusion process. The authors study the impulse control of Zakai type equations. The associated value function is characterized as the only viscosity solution of the corresponding quasi-variational inequality. The authors show the optimal cost function for the problem with incomplete information can be approximated by a sequence of value functions of the previous type.
基金partially supported by key research grant of the Academy for Multidisciplinary Studies,CNUsupported by NSFC(11901040)+1 种基金Beijing Municipal Commission of Education(KM202011232020)Beijing Natural Science Foundation(1204030)。
文摘In this paper,we prove the global well-posedness of the 2 D Boussinesq equations with three kinds of partial dissipation;among these the initial data(u_(0),θ_(0))is required such that its own and the derivative of one of its directions(x,y)are assumed to be L^(2)(R^(2)).Our results only need the lower regularity of the initial data,which ensures the uniqueness of the solutions.
基金the financial support from the National Natural Science Foundation of China (Grant Nos. 12125404, 11974162, and 11834006)the Fundamental Research Funds for the Central Universities。
文摘Helium is the second most abundant element in the universe, and together with silica, they are important components of giant planets. Exploring the reactivity and state of helium and silica under high pressure is crucial for understanding of the evolution and internal structure of giant planets. Here, using first-principles calculations and crystal structure predictions, we identify four stable phases of a helium-silica compound with seven/eight-coordinated silicon atoms at pressure of 600–4000 GPa, corresponding to the interior condition of the outer planets in the solar system. The density of He Si O2 agrees with current structure models of the planets.This helium-silica compound exhibits a superionic-like helium diffusive state under the high-pressure and hightemperature conditions along the isentropes of Saturn, a metallic fluid state in Jupiter, and a solid state in the deep interiors of Uranus and Neptune. These results show that helium may affect the erosion of the rocky core in giant planets and may help to form a diluted core region, which not only highlight the reactivity of helium under high pressure but also provide evidence helpful for building more sophisticated interior models of giant planets.
文摘This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational formulation of the variation problem and the discrete solution to the time-fractional and space-fractional difference equation using separating variables method and two-side Z-transform method.
