We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU...We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.展开更多
Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary m...Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.展开更多
In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order qua...In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.展开更多
The U1 matrix and extreme U1 matrix were successfully used to study quadratic doubly stochastic operators by R. Ganikhodzhaev and F. Shahidi [Linear Algebra Appl., 2010, 432： 24-35], where a necessary condition for a...The U1 matrix and extreme U1 matrix were successfully used to study quadratic doubly stochastic operators by R. Ganikhodzhaev and F. Shahidi [Linear Algebra Appl., 2010, 432： 24-35], where a necessary condition for a U1 matrix to be extreme was given. S. Yang and C. Xu [Linear Algebra Appl., 2013, 438： 3905-3912] gave a necessary and sufficient condition for a symmetric nonnegative matrix to be an extreme U1 matrix and investigated the structure of extreme U1 matrices. In this paper, we count the number of the permutation equivalence classes of the n × n extreme U1 matrices and characterize the structure of the quadratic stochastic operators and the quadratic doubly stochastic operators.展开更多
This paper deals with a discrete-time dynamical system generated by a modified susceptible-infected-recovered-dead model(SIRD model;nonlinear operator)in threedimensional simplex.We introduce a novel approach that inc...This paper deals with a discrete-time dynamical system generated by a modified susceptible-infected-recovered-dead model(SIRD model;nonlinear operator)in threedimensional simplex.We introduce a novel approach that incorporates the SIRD model with the quadratic stochastic operator(QSO)that allows for real-time forecasting.The basic reproductive number Ro is obtained.We describe the set of fixed points of the operator and demonstrate that all fixed points are non-hyperbolic.Further,we study the asymptotical behavior of the trajectories of this system and show that SIRD operators havea regularity property.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056.
文摘We show that the time-dependent two-mode Fresnel operator is just the time-evolutional unitary operator governed by the Hamiltonian composed of quadratic combination of canonical operators in the way of exhibiting SU（1,1） algebra. This is an approach for obtaining the time-dependent Hamiltonian from the preassigned time evolution in classical phase space, an approach which is in contrast to Lewis-Riesenfeld＇s invariant operator theory of treating timedependent harmonic oscillators.
基金The authors would like to thank Prof. Y.D. Zhang for selfless helps and valuable discussions.
文摘Making use of the transformation relation among usual, normal, and antinormal ordering for the multimode boson exponential quadratic polynomial operators （BEQPO＇s）I we present the analytic expression of arbitrary matrix elements for BEQPO＇s. As a preliminary application, we obtain the exact expressions of partition function about the boson quadratic polynomial system, matrix elements in particle-number, coordinate, and momentum representation, and P representation for the BEQPO＇s.
基金supported by the National Natural Science Foundation of China(Grant No.11371293)the Civil Military Integration Research Foundation of Shaanxi Province,China(Grant No.13JMR13)+2 种基金the Natural Science Foundation of Shaanxi Province,China(Grant No.14JK1246)the Mathematical Discipline Foundation of Shaanxi Province,China(Grant No.14SXZD015)the Basic Research Project Foundation of Weinan City,China(Grant No.2013JCYJ-4)
文摘In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators.
基金Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 61301296, 61377006, 61201396） and the National Natural Science Foundation of China-Guangdong Joint Found （No. U1201255）.
文摘The U1 matrix and extreme U1 matrix were successfully used to study quadratic doubly stochastic operators by R. Ganikhodzhaev and F. Shahidi [Linear Algebra Appl., 2010, 432： 24-35], where a necessary condition for a U1 matrix to be extreme was given. S. Yang and C. Xu [Linear Algebra Appl., 2013, 438： 3905-3912] gave a necessary and sufficient condition for a symmetric nonnegative matrix to be an extreme U1 matrix and investigated the structure of extreme U1 matrices. In this paper, we count the number of the permutation equivalence classes of the n × n extreme U1 matrices and characterize the structure of the quadratic stochastic operators and the quadratic doubly stochastic operators.
文摘This paper deals with a discrete-time dynamical system generated by a modified susceptible-infected-recovered-dead model(SIRD model;nonlinear operator)in threedimensional simplex.We introduce a novel approach that incorporates the SIRD model with the quadratic stochastic operator(QSO)that allows for real-time forecasting.The basic reproductive number Ro is obtained.We describe the set of fixed points of the operator and demonstrate that all fixed points are non-hyperbolic.Further,we study the asymptotical behavior of the trajectories of this system and show that SIRD operators havea regularity property.
