A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ ...A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ with the assumptions on reconstruction space. If the reconstruction space satisfies one-to-one relationship between the samples and the reconstruction model, then we propose a method, which achieves consistent signal reconstruction. At the same time, when the number of samples is more than the number of reconstruction functions, the minimal-norm reconstruction signal can be obtained. Finally, it is demonstrated that the minimal-norm reconstruction can outperform consistent signal reconstruction in both theory and simulations for the problem.展开更多
The connection between APOTP （asymptotic pseudo orbit tracing property） for a continuous map on a compact metric space and that for the shift map on the inverse limit space is investigated. As an application, it is ...The connection between APOTP （asymptotic pseudo orbit tracing property） for a continuous map on a compact metric space and that for the shift map on the inverse limit space is investigated. As an application, it is showed that the shift map on Henderson pseudoarc has APOTP.展开更多
In this paper, an algorithm based on a shifted inverse power iteration for computing generalized eigenvalues with corresponding eigenvectors of a large scale sparse symmetric positive definite matrix pencil is present...In this paper, an algorithm based on a shifted inverse power iteration for computing generalized eigenvalues with corresponding eigenvectors of a large scale sparse symmetric positive definite matrix pencil is presented. It converges globally with a cubic asymptotic convergence rate, preserves sparsity of the original matrices and is fully parallelizable. The algebraic multilevel itera-tion method (AMLI) is used to improve the efficiency when symmetric positive definite linear equa-tions need to be solved.展开更多
The inversion of TEM data, using the observed magnetic fields instead of that of apparent resistivities data in this paper, avoids the errors caused by the definition of the apparent resistivity. The inversed results...The inversion of TEM data, using the observed magnetic fields instead of that of apparent resistivities data in this paper, avoids the errors caused by the definition of the apparent resistivity. The inversed results by fitting the magnetic fields of the transmitter source's image with the observed magnetic fields are relatively less affected by the conductivity inhomogeneity. The MT apparent curve is calculated on the basis of the conductivity model constructed from the TEM inversion results. This curve is used as a reference curve for the correction of MT static shift, which makes the correction more reliable. Meanwhile, the domain transformation is also achieved from time to frequency between the two kinds of electromagnetic data. Therefore, the correction of the MT static shift is actualized using TEM inversion method. The corresponding application research shows that this method is very effective for the identification and correction of the MT static shift.展开更多
Many optical systems that deal with polarization rely on the adaptability of controlling light reflection in the lithography-free nanostructure. In this study, we explore the Goos–H?nchen(GH) shift and Imbert–Fedoro...Many optical systems that deal with polarization rely on the adaptability of controlling light reflection in the lithography-free nanostructure. In this study, we explore the Goos–H?nchen(GH) shift and Imbert–Fedorov(IF) shift in a biaxial hyperbolic film on a uniaxial hyperbolic substrate. This research statistically calculates and analyzes the GH shift and IF shift for the natural biaxial hyperbolic material(NBHM). We select the surface with the strongest anisotropy within the NBHM and obtain the complex beam-shift spectrum. By incorporating the NBHM film, the GH shift caused by a transversely magnetic incident-beam on the surface increases significantly compared with that on the uniaxial hyperbolic material. The maximum of GH shift can reach 86 λ0at about 841 cm-1when the thickness of NBHM is 90 nm, and the IF shift can approach 2.7 λ0for a circularly-polarized beam incident on a 1700-nm-thick NBHM. It is found that the spatialshift increases when a highly anisotropic hyperbolic polariton is excited in hyperbolic material, where the shift spectrum exhibits an oscillating behaviour accompanied with sharp shift peak(steep slope). This large spatial shift may provide an alternative strategy to develop novel sub-micrometric optical devices and biosensors.展开更多
In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160 are presented a...In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper.展开更多
It is difficult to obtain the asymmetrical factor along the observation direction parallel to the plasma mid-plane when the detected radiation is also in the mid-plane. This paper considers the magnetic surfaces and G...It is difficult to obtain the asymmetrical factor along the observation direction parallel to the plasma mid-plane when the detected radiation is also in the mid-plane. This paper considers the magnetic surfaces and Grad-Shafranov shift, and develops a new method for inverse asymmetric electron density information, during magnetic equilibrium configuration in a tokamak.展开更多
This paper provides a new approach to spatial spectral estimation, called eigenvalue shift superresolution algorithm. This method avoids the inverse covariance matrix. It can be applied to the processing of data recei...This paper provides a new approach to spatial spectral estimation, called eigenvalue shift superresolution algorithm. This method avoids the inverse covariance matrix. It can be applied to the processing of data received by spatially distributed array of sensors.展开更多
In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holde...In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.展开更多
文摘A method that attempts to recover signal using generalized inverse theory is presented to obtain a good approximation of the signal in reconstruction space from its generalized samples. The proposed approaches differ with the assumptions on reconstruction space. If the reconstruction space satisfies one-to-one relationship between the samples and the reconstruction model, then we propose a method, which achieves consistent signal reconstruction. At the same time, when the number of samples is more than the number of reconstruction functions, the minimal-norm reconstruction signal can be obtained. Finally, it is demonstrated that the minimal-norm reconstruction can outperform consistent signal reconstruction in both theory and simulations for the problem.
基金Supported by the NNSF of China (10361001) the NSF of the Education Committee of Jiangsu Province (05KJB110033)Young Teachers' Project of College of Anhui Province (2006jqll62).
文摘The connection between APOTP （asymptotic pseudo orbit tracing property） for a continuous map on a compact metric space and that for the shift map on the inverse limit space is investigated. As an application, it is showed that the shift map on Henderson pseudoarc has APOTP.
文摘In this paper, an algorithm based on a shifted inverse power iteration for computing generalized eigenvalues with corresponding eigenvectors of a large scale sparse symmetric positive definite matrix pencil is presented. It converges globally with a cubic asymptotic convergence rate, preserves sparsity of the original matrices and is fully parallelizable. The algebraic multilevel itera-tion method (AMLI) is used to improve the efficiency when symmetric positive definite linear equa-tions need to be solved.
文摘The inversion of TEM data, using the observed magnetic fields instead of that of apparent resistivities data in this paper, avoids the errors caused by the definition of the apparent resistivity. The inversed results by fitting the magnetic fields of the transmitter source's image with the observed magnetic fields are relatively less affected by the conductivity inhomogeneity. The MT apparent curve is calculated on the basis of the conductivity model constructed from the TEM inversion results. This curve is used as a reference curve for the correction of MT static shift, which makes the correction more reliable. Meanwhile, the domain transformation is also achieved from time to frequency between the two kinds of electromagnetic data. Therefore, the correction of the MT static shift is actualized using TEM inversion method. The corresponding application research shows that this method is very effective for the identification and correction of the MT static shift.
基金Project supported by the Natural Science Foundation of Heilongjiang Province, China (Grant No. LH2020A014)the Fund from the Education Commission of Heilongjiang Province, China (Grant No. 2020-KYYWF352)+1 种基金the Fund from the Key Laboratory of Engineering Dielectrics and Its Application (Harbin University of Science and Technology),Ministry of Education, China (Grant Nos. KFM202005 and KF20171110)the Harbin Normal University Postgraduate Innovative Research Project, Heilongjiang Province, China (Grant Nos. HSDSSCX2022-53 and HSDSSCX2022-49)。
文摘Many optical systems that deal with polarization rely on the adaptability of controlling light reflection in the lithography-free nanostructure. In this study, we explore the Goos–H?nchen(GH) shift and Imbert–Fedorov(IF) shift in a biaxial hyperbolic film on a uniaxial hyperbolic substrate. This research statistically calculates and analyzes the GH shift and IF shift for the natural biaxial hyperbolic material(NBHM). We select the surface with the strongest anisotropy within the NBHM and obtain the complex beam-shift spectrum. By incorporating the NBHM film, the GH shift caused by a transversely magnetic incident-beam on the surface increases significantly compared with that on the uniaxial hyperbolic material. The maximum of GH shift can reach 86 λ0at about 841 cm-1when the thickness of NBHM is 90 nm, and the IF shift can approach 2.7 λ0for a circularly-polarized beam incident on a 1700-nm-thick NBHM. It is found that the spatialshift increases when a highly anisotropic hyperbolic polariton is excited in hyperbolic material, where the shift spectrum exhibits an oscillating behaviour accompanied with sharp shift peak(steep slope). This large spatial shift may provide an alternative strategy to develop novel sub-micrometric optical devices and biosensors.
基金supported by the National Natural Science Foundation of the People’s Republic of China“The research of finite element methods for eigenvalue problems in inverse scattering”(12261024)。
文摘In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper.
文摘It is difficult to obtain the asymmetrical factor along the observation direction parallel to the plasma mid-plane when the detected radiation is also in the mid-plane. This paper considers the magnetic surfaces and Grad-Shafranov shift, and develops a new method for inverse asymmetric electron density information, during magnetic equilibrium configuration in a tokamak.
文摘This paper provides a new approach to spatial spectral estimation, called eigenvalue shift superresolution algorithm. This method avoids the inverse covariance matrix. It can be applied to the processing of data received by spatially distributed array of sensors.
文摘In this paper, we consider operators arising in the modeling of renewable systems with elements that can be in different states. These operators are functional operators with non-Carlemann shifts and they act in Holder spaces with weight. The main attention was paid to non-linear equations relating coefficients to operators with a shift. The solutions of these equations were used to reduce the operators under consideration to operators with shift, the invertibility conditions for which were found in previous articles of the authors. To construct the solution of the non-linear equation, we consider the coefficient factorization problem (the homogeneous equation with a zero right-hand side) and the jump problem (the non-homogeneous equation with a unit coefficient). The solution of the general equation is represented as a composition of the solutions to these two problems.
