Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the nu...Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the numbers of eigen vance of A∈PD_0(R)\DD_0(R)are equal to the numbers of a_(ii),i∈N in positive and negative real part respectively.Some couter examples are given which present the condnions can not be omitted.展开更多
As it is well known,it is difficult to identify a nonlinear time varying system using traditional identification approaches,especially under unknown nonlinear function.Neural networks have recently emerged as a succes...As it is well known,it is difficult to identify a nonlinear time varying system using traditional identification approaches,especially under unknown nonlinear function.Neural networks have recently emerged as a successful tool in the area of identification and control of time invariant nonlinear systems.However,it is still difficult to apply them to complicated time varying system identification.In this paper we present a learning algorithm for identification of the nonlinear time varying system using feedforward neural networks.The main idea of this approach is that we regard the weights of the network as a state of a time varying system,then use a Kalman filter to estimate the state.Thus the network implements nonlinear and time varying mapping.We derived both the global and local learning algorithms.Simulation results demonstrate the effectiveness of this approach.展开更多
Abstract In this work, ionization potentials and quantum effects of ls^2 np^2 P Rydberg states of lithium are calculated based on the calibrated quantum defect function. Energy levels and quantum defects for ls^2np^2P...Abstract In this work, ionization potentials and quantum effects of ls^2 np^2 P Rydberg states of lithium are calculated based on the calibrated quantum defect function. Energy levels and quantum defects for ls^2np^2P bound states and their adjacent continuum states are calculated with the R-matrix theory, and then the quantum defect function of the ls^2np （n ≥ 7） channel is obtained, which varies smoothly with the energy based on the quantum defect theory. The accurate quantum defect of the ls^2 7p^2P state derived from the experimental data is used to calibrate the original quantum defect function. The new function is used to calculate ionization potentials and quantum effects of ls^2np ^2P （n ≥ 7） Rydberg states. Present calculations are in agreement with recent experimental data in whole.展开更多
Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases wi...Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, when R-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regular R-matrices which appear in weak Hopf algebras are considered.展开更多
This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary...This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary calculation. It is shown that the Lax representation enjoys a dynamical r-matrix formula instead of a classical one in the Poisson bracket on R2N. Consequently the resulting system is proved to be completely integrable in view of its r-matrix structure.展开更多
A class of generalization of Toda mechanics with long range interactions isconstructed in this paper. These systems are associated with the loop algebras L(B_r) in the sensethat their Lax matrices can be realized in t...A class of generalization of Toda mechanics with long range interactions isconstructed in this paper. These systems are associated with the loop algebras L(B_r) in the sensethat their Lax matrices can be realized in terms of the c = 0 representations of the affine Liealgebras B_r~((1)) . We adopt a pair of ordered integers (m, n) to describe the Toda mechanicssystem when we present the equations of motion and the Hamiltonian structure. We also extract theclassical r matrix which satisfy the classical Yang-Baxter relation. Such generalizations willbecome systems with noncommutative variables in the quantum case.展开更多
This paper constructs a dual bialgebra for a multi-parameter FRT-bialgebra related to a Hayashi's R-matrix by using the skew-derivation method and proves that the pairing between them is non-degenerate.
We establish Berry-Esseen bounds and Cramér type large deviations for the eigenvalues of Wigner Hermitian matrices in the bulk and at the edge cases. Similar results are also obtained for covariance matrices.
We study the concept of module twistor for a module over an algebra. This concept provides a unifying framework for various deformed constructions of modules over algebras, such as module R-matrices,(n-factor iterated...We study the concept of module twistor for a module over an algebra. This concept provides a unifying framework for various deformed constructions of modules over algebras, such as module R-matrices,(n-factor iterated) twisted tensor products and L-R-twisted tensor products of algebras. Among the main results,we find the relations among these constructions. Furthermore, we study some properties of module twistors.展开更多
Let R be a left and right Noetherian ring and n, k be any non-negative integers. R is said to satisfy the Auslander-type condition Gn（k） if the right fiat dimension of the （i ＋ 1）-th term in a minimal injective r...Let R be a left and right Noetherian ring and n, k be any non-negative integers. R is said to satisfy the Auslander-type condition Gn（k） if the right fiat dimension of the （i ＋ 1）-th term in a minimal injective resolution of RR is at most i ＋ k for any 0 ≤ i ≤ n - 1. In this paper, we prove that R is Gn（k） if and only if so is a lower triangular matrix ring of any degree t over R.展开更多
文摘Let DD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(jj)|≥A_iA_j,i≠j,i,j∈N}.PD_0(R)={A∈C^(n×#)||Rea_(ii)Rea_(kk)|≥A_iA_jA_k,i≠j≠k,i,j,k∈N}. In this paper,we show DD_0(R)PD_0(R),and the conditions under which the numbers of eigen vance of A∈PD_0(R)\DD_0(R)are equal to the numbers of a_(ii),i∈N in positive and negative real part respectively.Some couter examples are given which present the condnions can not be omitted.
基金National Natural Science Foundation of China!(No.6 97740 33)
文摘As it is well known,it is difficult to identify a nonlinear time varying system using traditional identification approaches,especially under unknown nonlinear function.Neural networks have recently emerged as a successful tool in the area of identification and control of time invariant nonlinear systems.However,it is still difficult to apply them to complicated time varying system identification.In this paper we present a learning algorithm for identification of the nonlinear time varying system using feedforward neural networks.The main idea of this approach is that we regard the weights of the network as a state of a time varying system,then use a Kalman filter to estimate the state.Thus the network implements nonlinear and time varying mapping.We derived both the global and local learning algorithms.Simulation results demonstrate the effectiveness of this approach.
基金National Natural Science Foundation of China under Grant No.10404017the Basic Research Foundation of Beijing Institute of Technology
文摘Abstract In this work, ionization potentials and quantum effects of ls^2 np^2 P Rydberg states of lithium are calculated based on the calibrated quantum defect function. Energy levels and quantum defects for ls^2np^2P bound states and their adjacent continuum states are calculated with the R-matrix theory, and then the quantum defect function of the ls^2np （n ≥ 7） channel is obtained, which varies smoothly with the energy based on the quantum defect theory. The accurate quantum defect of the ls^2 7p^2P state derived from the experimental data is used to calibrate the original quantum defect function. The new function is used to calculate ionization potentials and quantum effects of ls^2np ^2P （n ≥ 7） Rydberg states. Present calculations are in agreement with recent experimental data in whole.
文摘Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, when R-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regular R-matrices which appear in weak Hopf algebras are considered.
文摘This paper deals with the integrability of a finite-dimensional Hamiltonian system linked with the generalized coupled KdV hierarchy. For this purpose the associated Lax representation is presented after an elementary calculation. It is shown that the Lax representation enjoys a dynamical r-matrix formula instead of a classical one in the Poisson bracket on R2N. Consequently the resulting system is proved to be completely integrable in view of its r-matrix structure.
文摘A class of generalization of Toda mechanics with long range interactions isconstructed in this paper. These systems are associated with the loop algebras L(B_r) in the sensethat their Lax matrices can be realized in terms of the c = 0 representations of the affine Liealgebras B_r~((1)) . We adopt a pair of ordered integers (m, n) to describe the Toda mechanicssystem when we present the equations of motion and the Hamiltonian structure. We also extract theclassical r matrix which satisfy the classical Yang-Baxter relation. Such generalizations willbecome systems with noncommutative variables in the quantum case.
文摘This paper constructs a dual bialgebra for a multi-parameter FRT-bialgebra related to a Hayashi's R-matrix by using the skew-derivation method and proves that the pairing between them is non-degenerate.
基金supported by National Natural Science Foundation of China(Grant No.11171262)the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20130141110076)
文摘We establish Berry-Esseen bounds and Cramér type large deviations for the eigenvalues of Wigner Hermitian matrices in the bulk and at the edge cases. Similar results are also obtained for covariance matrices.
基金supported by National Natural Science Foundation of China (Grant Nos. 11201285 and 11371238)the First-class Discipline of Universities in Shanghai
文摘We study the concept of module twistor for a module over an algebra. This concept provides a unifying framework for various deformed constructions of modules over algebras, such as module R-matrices,(n-factor iterated) twisted tensor products and L-R-twisted tensor products of algebras. Among the main results,we find the relations among these constructions. Furthermore, we study some properties of module twistors.
基金supported by the Specialized Research Fund for the Doctoral Pro-gram of Higher Education(Grant No.20100091110034)National Natural Science Foundation of China(Grant Nos.11171142,11126169,11101217)+2 种基金Natural Science Foundation of Jiangsu Province of China(Grant Nos.BK2010047,BK2010007)the Scientific Research Fund of Hunan Provincial Education Department(Grant No.10C1143)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Let R be a left and right Noetherian ring and n, k be any non-negative integers. R is said to satisfy the Auslander-type condition Gn（k） if the right fiat dimension of the （i ＋ 1）-th term in a minimal injective resolution of RR is at most i ＋ k for any 0 ≤ i ≤ n - 1. In this paper, we prove that R is Gn（k） if and only if so is a lower triangular matrix ring of any degree t over R.
