Using the technique of integration within an ordered product （IWOP） of operators we construct intermediate coordinate-momentum representation, with which we build a type of operator Fredholm integration equation tha...Using the technique of integration within an ordered product （IWOP） of operators we construct intermediate coordinate-momentum representation, with which we build a type of operator Fredholm integration equation that is an operator generalization of the solution of thermo conduction equation. Then we seach for the solution of operator Fredholm integration equations, which provides us with a new approach for deriving some operator identities.展开更多
By introducing an image plane, the inverse heat conduction problem with free boundary is transformed into one with completely known boundaryt which is much simpler to handle.As a by-product, the classical Kirchhoff’s...By introducing an image plane, the inverse heat conduction problem with free boundary is transformed into one with completely known boundaryt which is much simpler to handle.As a by-product, the classical Kirchhoff’s transformation for accounting for variable conductivity is rederived and an invariance property of the inverse problem solution with respect to variable conductivity is indicated. Then a pair of complementary extremum principles are established on the image plane, providing a sound theoretical foundation for the Ritz’s method and finite element method (FEM).An example solved by FEM is also given.展开更多
基金The project supported by the President Foundation of the Chinese Academy of Sciences
文摘Using the technique of integration within an ordered product （IWOP） of operators we construct intermediate coordinate-momentum representation, with which we build a type of operator Fredholm integration equation that is an operator generalization of the solution of thermo conduction equation. Then we seach for the solution of operator Fredholm integration equations, which provides us with a new approach for deriving some operator identities.
文摘By introducing an image plane, the inverse heat conduction problem with free boundary is transformed into one with completely known boundaryt which is much simpler to handle.As a by-product, the classical Kirchhoff’s transformation for accounting for variable conductivity is rederived and an invariance property of the inverse problem solution with respect to variable conductivity is indicated. Then a pair of complementary extremum principles are established on the image plane, providing a sound theoretical foundation for the Ritz’s method and finite element method (FEM).An example solved by FEM is also given.
