We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and the...We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.展开更多
To solve the problem of the spatial correlation for adjacent areas in traditional spectral unmixing methods, we propose an area-correlated spectral unmixing method based on Bayesian nonnegative matrix factorization. I...To solve the problem of the spatial correlation for adjacent areas in traditional spectral unmixing methods, we propose an area-correlated spectral unmixing method based on Bayesian nonnegative matrix factorization. In the proposed me-thod, the spatial correlation property between two adjacent areas is expressed by a priori probability density function, and the endmembers extracted from one of the adjacent areas are used to estimate the priori probability density func-tions of the endmembers in the current area, which works as a type of constraint in the iterative spectral unmixing process. Experimental results demonstrate the effectivity and efficiency of the proposed method both for synthetic and real hyperspectral images, and it can provide a useful tool for spatial correlation and comparation analysis between ad-jacent or similar areas.展开更多
Let A=M-N be a regular splitting of an M-matrix. We study the spectral properties of the ineration matrix M-1N. Under a mild assumption on M-1 N. some necessary and sufficent conditions such that p(M-1N)=1 are obtaine...Let A=M-N be a regular splitting of an M-matrix. We study the spectral properties of the ineration matrix M-1N. Under a mild assumption on M-1 N. some necessary and sufficent conditions such that p(M-1N)=1 are obtained and the algebraic multiplicity and the index associated with eigenvalue 1 in M-1N are considered.展开更多
If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses cons...If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.展开更多
以NACA 65(12)–10独立基准叶片为对象,使用线性传声器阵列和SODIX(SOurce DIrectivity modeling in the cross-spectral matriX)方法对基准叶片前缘噪声指向性分布特征及波浪前缘对叶片前缘噪声的影响进行了实验研究。开发了SODIX数据...以NACA 65(12)–10独立基准叶片为对象,使用线性传声器阵列和SODIX(SOurce DIrectivity modeling in the cross-spectral matriX)方法对基准叶片前缘噪声指向性分布特征及波浪前缘对叶片前缘噪声的影响进行了实验研究。开发了SODIX数据处理程序并进行了数值仿真验证,结果表明:不同指向角下计算结果的最大误差不超过0.26 dB。在半消声室内,利用由31个传声器组成的非均匀分布优化阵列,对NACA 65(12)–10独立基准叶片和仿生学叶片的前缘噪声开展了参数化声学实验。结果表明:在40°~142°指向角测量范围内,基准叶片前缘噪声指向性符合典型偶极子声源特征,峰值在130°指向角附近;随着频率升高,基准叶片前缘噪声指向性产生了显著的“波瓣”现象,频率越高,“波瓣”越多。进一步研究表明:不同波长和幅值的前缘构型都可以有效降低指向角测量范围内的前缘噪声;与波浪前缘的波长相比,波浪前缘的幅值对前缘噪声的影响更为显著,特别是在90°~120°指向角范围内,A30W20叶型的降噪量可达7.71 dB。展开更多
文摘We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.
文摘To solve the problem of the spatial correlation for adjacent areas in traditional spectral unmixing methods, we propose an area-correlated spectral unmixing method based on Bayesian nonnegative matrix factorization. In the proposed me-thod, the spatial correlation property between two adjacent areas is expressed by a priori probability density function, and the endmembers extracted from one of the adjacent areas are used to estimate the priori probability density func-tions of the endmembers in the current area, which works as a type of constraint in the iterative spectral unmixing process. Experimental results demonstrate the effectivity and efficiency of the proposed method both for synthetic and real hyperspectral images, and it can provide a useful tool for spatial correlation and comparation analysis between ad-jacent or similar areas.
基金Supported by National Natural Science Foundation of China
文摘Let A=M-N be a regular splitting of an M-matrix. We study the spectral properties of the ineration matrix M-1N. Under a mild assumption on M-1 N. some necessary and sufficent conditions such that p(M-1N)=1 are obtained and the algebraic multiplicity and the index associated with eigenvalue 1 in M-1N are considered.
文摘If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.
