In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly va...In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly valid asymptotic solution of arbitrary order for these types of problems.展开更多
In this paper,the authors obtain two kinds of Kastler-Kalau-Walze type theorems for conformal perturbations of twisted Dirac operators and conformal perturbations of signature operators by a vector bundle with a non-u...In this paper,the authors obtain two kinds of Kastler-Kalau-Walze type theorems for conformal perturbations of twisted Dirac operators and conformal perturbations of signature operators by a vector bundle with a non-unitary connection on six-dimensional manifolds with(respectively without)boundary.展开更多
In this paper,we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary.Furthermore,we provide the proof of the Dabrowski–Sitarz–Zalecki type theorems associated w...In this paper,we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary.Furthermore,we provide the proof of the Dabrowski–Sitarz–Zalecki type theorems associated with the spectral Einstein functionals for perturbations of Dirac operators,particularly in the cases of on 4-dimensional manifolds with boundary.展开更多
A solvable model of lateral line of a fish based on a wave equation with additional boundary conditions on a set of isolated points is proposed.Within the framework of this model it is shown that the ratio of pressure...A solvable model of lateral line of a fish based on a wave equation with additional boundary conditions on a set of isolated points is proposed.Within the framework of this model it is shown that the ratio of pressures on lateral lines on different fish flanks,as well as the cross section of sound scattering on both the lines,strongly depends on angles of incidence of incoming sound waves.The strong angular dependence of the pressure ratio seems to be sufficient for the fish to determine the directions from which the sound is coming.展开更多
文摘In this paper, we reveal the multiple boundary layer phenomena of the solution of nonlinear higher order elliptic equations with perturbation both in boundary and in operator, and provide a method to find uniformly valid asymptotic solution of arbitrary order for these types of problems.
基金supported by the National Natural Science Foundation of China(No.11771070)the School-Level Project of Dongbei University of Finance and Economics(No.DUFE202159).
文摘In this paper,the authors obtain two kinds of Kastler-Kalau-Walze type theorems for conformal perturbations of twisted Dirac operators and conformal perturbations of signature operators by a vector bundle with a non-unitary connection on six-dimensional manifolds with(respectively without)boundary.
基金Supported by NSFC(Grant Nos.12301063 and 11771070)2024 Liaoning Provincial Natural Science Foundation Program(Ph.D.Research Start-up Project)(Grant No.2024-BS-205)。
文摘In this paper,we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary.Furthermore,we provide the proof of the Dabrowski–Sitarz–Zalecki type theorems associated with the spectral Einstein functionals for perturbations of Dirac operators,particularly in the cases of on 4-dimensional manifolds with boundary.
基金supported by the Ministry of Education and Science of Ukraine(Grant No.0115U003208)。
文摘A solvable model of lateral line of a fish based on a wave equation with additional boundary conditions on a set of isolated points is proposed.Within the framework of this model it is shown that the ratio of pressures on lateral lines on different fish flanks,as well as the cross section of sound scattering on both the lines,strongly depends on angles of incidence of incoming sound waves.The strong angular dependence of the pressure ratio seems to be sufficient for the fish to determine the directions from which the sound is coming.
