The nonlinear Riemann problems were converted into nonlinear singular integral equ ations and the existence of the solution for the problem was proved by means of contract principle.
We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary i...We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.展开更多
We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representat...We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.展开更多
In order to achieve the goal of “carbon peak” in 2030 and “carbon neutralization” in 2060, the task of energy conservation has risen to the national strategic level, and its work is urgent. It focuses on energy sa...In order to achieve the goal of “carbon peak” in 2030 and “carbon neutralization” in 2060, the task of energy conservation has risen to the national strategic level, and its work is urgent. It focuses on energy saving and energy consumption in data center, 5G network and other fields. The gravity heat pipe double cycle air conditioning is a kind of room air conditioning which uses natural cooling source with high efficiency. According to the outdoor meteorological parameters of ten typical cities in China, the calculation model of unit hybrid refrigeration mode is established by using integral method. A simplified algorithm for statistical summation is proposed. Then it compares with the same type of refrigerant pump air conditioner, water-cooled chiller and natural cooling plate. The results show that the annual operation time of gravity heat pipe double cycle air conditioner is 50.8% longer than that of refrigerant pump air conditioner. Then the calculation model is verified by the annual actual operation data of a data center in Changsha. The results show that the double cycle air conditioner with gravity heat pipe can save about 34% energy compared with the chiller. The accuracy of the calculation model is 17.5%, which meets the engineering accuracy requirements. The application of gravity heat pipe double cycle air conditioning in hot summer and cold winter area is a scheme worthy of popularization and application.展开更多
文摘The nonlinear Riemann problems were converted into nonlinear singular integral equ ations and the existence of the solution for the problem was proved by means of contract principle.
文摘We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.
文摘We reduce the initial value problem for the generalized Schroedinger equation with piecewise-constant leading coefficient to the system of Volterra type integral equations and construct new useful integral representations for the fundamental solutions of the Schroedinger equation. We also investigate some significant properties of the kernels of these integral representations. The integral representations of fundamental solutions enable to obtain the basic integral equations, which are a powerful tool for solving inverse spectral problems.
文摘In order to achieve the goal of “carbon peak” in 2030 and “carbon neutralization” in 2060, the task of energy conservation has risen to the national strategic level, and its work is urgent. It focuses on energy saving and energy consumption in data center, 5G network and other fields. The gravity heat pipe double cycle air conditioning is a kind of room air conditioning which uses natural cooling source with high efficiency. According to the outdoor meteorological parameters of ten typical cities in China, the calculation model of unit hybrid refrigeration mode is established by using integral method. A simplified algorithm for statistical summation is proposed. Then it compares with the same type of refrigerant pump air conditioner, water-cooled chiller and natural cooling plate. The results show that the annual operation time of gravity heat pipe double cycle air conditioner is 50.8% longer than that of refrigerant pump air conditioner. Then the calculation model is verified by the annual actual operation data of a data center in Changsha. The results show that the double cycle air conditioner with gravity heat pipe can save about 34% energy compared with the chiller. The accuracy of the calculation model is 17.5%, which meets the engineering accuracy requirements. The application of gravity heat pipe double cycle air conditioning in hot summer and cold winter area is a scheme worthy of popularization and application.
