Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence o...Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.展开更多
In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained ...In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.展开更多
Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and su...Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and sufficient conditions for the existence of and the expressions for the msc solutions and the ssd solutions are obtained for the system.展开更多
A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
Dense arrays of Fe-Cr alloy clusters with different Cr ratios were fabricated by gas-phase cluster beam deposition. The complex multiphase structure and various coupling effects in the cluster arrays were studied. A l...Dense arrays of Fe-Cr alloy clusters with different Cr ratios were fabricated by gas-phase cluster beam deposition. The complex multiphase structure and various coupling effects in the cluster arrays were studied. A lattice mismatched tetragonal-like morphology of the Fe-Cr alloy cluster was observed at large Cr ratio. An exchange bias effect was observed and was shown to be dependent on the proportion of the Cr components in the alloy. With the increase of the Cr composition, the exchange bias field became smaller and stronger dipolar interactions between the clusters developed. Residual coercivity and magnetization, which were more remarkable in the tetragonal-like clusters, were observed above the ferromagnetic-superparamagnetic transition temperature. The experimental results of the coercive field and the bias field at different temperatures demonstrated that the tetragonal-like clusters had better thermal stability and greater anisotropy.展开更多
An array extension method in a noisy environment was proposed to improve angular resolution and array gain. The proposed method combines the FOC （fourth-order cumulants） technique with the ETAM （extended towed arra...An array extension method in a noisy environment was proposed to improve angular resolution and array gain. The proposed method combines the FOC （fourth-order cumulants） technique with the ETAM （extended towed array measurements） method to extend array aperture and suppress Gaussian noise, First, successive measurements of a virtual uniform linear array were constructed by applying lburth-order cumulants to measurements of uniform linear array; Gaussian noise in these measurements was also eliminated. Then, the array was extended by compensating phase differences using the ETAM method, Finally, the synthetic aperture was extended further by the fourth-order cumulants technique. The proposed FOC-ETAM-FOC method not only improves angular resolution and array gain, but also effectively suppresses Gaussian noise. Furthermore, it inherits the advantages of the ETAM method. Simulation results showed that the FOC-ETAM-FOC method achieved better angular resolution and array gain than the ETAM method. Furthermore this method outperforms the ETAM method in Gaussian noise environment.展开更多
We demonstrate experimentally the population inversion between 7S1/2 and 6P3/2 levels of cesium in thermal cesium cell with a 455.5 nm pumping laser.We calculate the relative population probabilities at each level the...We demonstrate experimentally the population inversion between 7S1/2 and 6P3/2 levels of cesium in thermal cesium cell with a 455.5 nm pumping laser.We calculate the relative population probabilities at each level theoretically with the density matrix method.In a steady state,5.8% atoms are at 7S1/2 level and 2.9% at 6P3/2 level,which builds up the population inversion between the two levels.We obtain the fluorescence spectra produced in thermal cesium cell in our experiment.The measured relative intensity of each available fluorescence spectral line in the experiment agrees very well with the theoretical result.The demonstrated population inversion between 7S1/2 and 6P3/2 levels can be used to construct an active optical clock of four-level system with a wavelength of 1469.9 nm.展开更多
文摘Generally unitary solution to the system of martix equations over the quaternion field [X mA ns =B ns ,X nn C nt =D nt ] is considered. A necessary and sufficient condition for the existence of and the expression for the generally unitary solution of the system are derived.
文摘In this paper, by using the matrix representation of the generalized quaternion algebra, we discussed solution problem for two classes of the first_degree algebraic equation of the generalized quaternion and obtained critical conditions on existence of a unique solution, infinitely many solutions or nonexistence any solution for the two classes algebraic equation.
文摘Minor self conjugate (msc) and skewpositive semidefinite (ssd) solutions to the system of matrix equations over skew fields [A mn X nn =A mn ,B sn X nn =O sn ] are considered. Necessary and sufficient conditions for the existence of and the expressions for the msc solutions and the ssd solutions are obtained for the system.
文摘A norm of a quaternion matrix is defined. The expressions of the least square solutions of the quaternion matrix equation AX = B and the equation with the constraint condition DX = E are given.
基金supported by the National Natural Science Foundation of China(No.11627806 and No.61301015)the Priority Academic Programme Development of Jiangsu Higher Education Institutions
文摘Dense arrays of Fe-Cr alloy clusters with different Cr ratios were fabricated by gas-phase cluster beam deposition. The complex multiphase structure and various coupling effects in the cluster arrays were studied. A lattice mismatched tetragonal-like morphology of the Fe-Cr alloy cluster was observed at large Cr ratio. An exchange bias effect was observed and was shown to be dependent on the proportion of the Cr components in the alloy. With the increase of the Cr composition, the exchange bias field became smaller and stronger dipolar interactions between the clusters developed. Residual coercivity and magnetization, which were more remarkable in the tetragonal-like clusters, were observed above the ferromagnetic-superparamagnetic transition temperature. The experimental results of the coercive field and the bias field at different temperatures demonstrated that the tetragonal-like clusters had better thermal stability and greater anisotropy.
基金Supported by the National Science Foundation of China (No.60872146)
文摘An array extension method in a noisy environment was proposed to improve angular resolution and array gain. The proposed method combines the FOC （fourth-order cumulants） technique with the ETAM （extended towed array measurements） method to extend array aperture and suppress Gaussian noise, First, successive measurements of a virtual uniform linear array were constructed by applying lburth-order cumulants to measurements of uniform linear array; Gaussian noise in these measurements was also eliminated. Then, the array was extended by compensating phase differences using the ETAM method, Finally, the synthetic aperture was extended further by the fourth-order cumulants technique. The proposed FOC-ETAM-FOC method not only improves angular resolution and array gain, but also effectively suppresses Gaussian noise. Furthermore, it inherits the advantages of the ETAM method. Simulation results showed that the FOC-ETAM-FOC method achieved better angular resolution and array gain than the ETAM method. Furthermore this method outperforms the ETAM method in Gaussian noise environment.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10874009 and 11074011)
文摘We demonstrate experimentally the population inversion between 7S1/2 and 6P3/2 levels of cesium in thermal cesium cell with a 455.5 nm pumping laser.We calculate the relative population probabilities at each level theoretically with the density matrix method.In a steady state,5.8% atoms are at 7S1/2 level and 2.9% at 6P3/2 level,which builds up the population inversion between the two levels.We obtain the fluorescence spectra produced in thermal cesium cell in our experiment.The measured relative intensity of each available fluorescence spectral line in the experiment agrees very well with the theoretical result.The demonstrated population inversion between 7S1/2 and 6P3/2 levels can be used to construct an active optical clock of four-level system with a wavelength of 1469.9 nm.
