There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works conc...There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.展开更多
With homotopy methods, this paper discusses the existence and the number of zeroes of nonlinear mappings on bounded regions and extends some classical theorems.
In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
Traditional variation analysis methods are not applicable to non-rigid assemblies due to possible part deformation during the assembly process. This paper presents the use of finite element methods to simulate assembl...Traditional variation analysis methods are not applicable to non-rigid assemblies due to possible part deformation during the assembly process. This paper presents the use of finite element methods to simulate assembly deformation. The relationship between the parts’ variation and the variation of the key points in final assembly for quality control is set up by calculating the spring back deformation after assembly. Moreover, the optimization method for non-rigid assembly variations based on finite element analysis is presented. The optimal objective is to reduce the manufacturing cost. The approach is implemented by using ANSYS and MATLAB. The test example shows that the proposed method is effective and applicable.展开更多
We propose two schemes for preparing four-photon cluster state through cross-Kerr nonlinearity. Two coherent fields interact when they enter a nonlinear Kerr medium. If the interaction time is chosen appropriately in ...We propose two schemes for preparing four-photon cluster state through cross-Kerr nonlinearity. Two coherent fields interact when they enter a nonlinear Kerr medium. If the interaction time is chosen appropriately in each Kerr medium, four-photon cluster state can be generated based on the results of two homodyne detectors in the first scheme. These schemes only use Kerr medium and homodyne measurements on coherent light fields, which can be effciently made in quantum optical laboratories. In addition, weak cross-Kerr nonlinearity is sufficient. All of the properties make these schemes feasible in experiments.展开更多
In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.
In this paper, we study the nonlinear discrete systems and obtain several lyapunov inequalities for them. Then we give the application for lyapunov inequality.
A judgment criterion to guarantee a point to be a Chen' s approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the d...A judgment criterion to guarantee a point to be a Chen' s approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen' s approximate zero may not be a Smale' s approximate zero. The error estimate obtained indicated the convergent order when we use |f(x) | < ε to stop computation in software.The result can also be applied for solving partial derivative and integration equations.展开更多
In this paper,a general scheme in digital self-interference cancellation at baseband for zero-IF full-duplex transceivers is presented. We model the self-interference signals specifically with only the nonlinear disto...In this paper,a general scheme in digital self-interference cancellation at baseband for zero-IF full-duplex transceivers is presented. We model the self-interference signals specifically with only the nonlinear distortion signals falling in receiving band considered. A joint estimation algorithm is proposed for compensating the time delay and frequency offset taking into account the IQ amplitude and phase imbalances from mixers. The memory effect and nonlinear distortion are adaptively estimated by the de-correlated normalized least mean square(DNLMS) algorithm. Numerical simulation results demonstrate that the proposed self-interference cancellation scheme can efficiently compensate the self-interference and outperform the existing traditional solutions.展开更多
This paper first elaborates the research situation and progress of Laplace characteristics and the eigenvalues value of graphs. The second is given an upper bound of characteristic value of a kind of special graph usi...This paper first elaborates the research situation and progress of Laplace characteristics and the eigenvalues value of graphs. The second is given an upper bound of characteristic value of a kind of special graph using the properties of similar matrices. At the same time, a new upper bound of Laplace characteristic values are given using properties of Laplace matrix and the similarity matrix, to improve the existing results. Then, we use the example of the upper bound of our results are more precise than some previous results. Finally the use Laplace non- zero eigenvalues of graph properties to give a bound expressions using the degree of square with a number of edges and the graph of the number, number of connected component expression map, it reflected the relationship between eigenvalues and the amount of Laplace.展开更多
This paper constructs a polyconvex stored energy function, satisfying the null condition, for isotropic compressible elastic materials with given Lame constants. The difference between this stored energy function and ...This paper constructs a polyconvex stored energy function, satisfying the null condition, for isotropic compressible elastic materials with given Lame constants. The difference between this stored energy function and St Venant-Kirchhoff's is a three order term.展开更多
This paper presents a trust region algorithm with null space technique fornonlinear equality constrained optimization. Considering in the null space methods that,the convergent rate of range space step is faster than ...This paper presents a trust region algorithm with null space technique fornonlinear equality constrained optimization. Considering in the null space methods that,the convergent rate of range space step is faster than the null space step for the most cases,the proposed algorithm computes null steps more often than range space step. Moreover,the new algorithm is based on the reduced Hessian SQP method. Global convergence ofthe proposed algorithm is proved. The effectiveness of the method is demonstrated bysome numerical examples.展开更多
The authors generalize the works in [5] and [6] to prove a Hopf index theorem associated to a smooth section of a real vector bundle with non-isolated zero points.
In this paper, we consider the solution of the following rational systems of difference equations：xn＋1=zn-1xn-2/xn-2±yn,yn＋1=xn-1yn-2/yn-2±zn,zn＋1=yn-1zn-2/zn-1±xn,where initial conditions are nonze...In this paper, we consider the solution of the following rational systems of difference equations：xn＋1=zn-1xn-2/xn-2±yn,yn＋1=xn-1yn-2/yn-2±zn,zn＋1=yn-1zn-2/zn-1±xn,where initial conditions are nonzero real numbers.展开更多
文摘There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.
基金This work is supported in part by the National Natural Sciece Foundation of China.
文摘With homotopy methods, this paper discusses the existence and the number of zeroes of nonlinear mappings on bounded regions and extends some classical theorems.
基金Foundation item： Supported by the Sichuan Educational Comittee Science Foundation for Youths（08ZB002） Supported by the National Secience Foundation of Yibin University（2008Z02）
文摘In this paper, the author has given an existence theorem for the resonant equation,-△pu=λ1｜u｜p-2u＋f（u）＋h（x）,without any Landesman-Lazer conditions on h（x）.
基金Supported by the Natural Science Foundation of China (No. 50205028) and the Natural Science Foundation of Chongqing City (No. 2005BB2022 ).
文摘Traditional variation analysis methods are not applicable to non-rigid assemblies due to possible part deformation during the assembly process. This paper presents the use of finite element methods to simulate assembly deformation. The relationship between the parts’ variation and the variation of the key points in final assembly for quality control is set up by calculating the spring back deformation after assembly. Moreover, the optimization method for non-rigid assembly variations based on finite element analysis is presented. The optimal objective is to reduce the manufacturing cost. The approach is implemented by using ANSYS and MATLAB. The test example shows that the proposed method is effective and applicable.
基金National Natural Science Foundation of China under Grant No.10574022the Natural Science Foundation of Fujian Province of China under Grant Nos.2007J0002 and 2007J0197the Foundation for Universities in Fujian Province under Grant No.2007F5041
文摘We propose two schemes for preparing four-photon cluster state through cross-Kerr nonlinearity. Two coherent fields interact when they enter a nonlinear Kerr medium. If the interaction time is chosen appropriately in each Kerr medium, four-photon cluster state can be generated based on the results of two homodyne detectors in the first scheme. These schemes only use Kerr medium and homodyne measurements on coherent light fields, which can be effciently made in quantum optical laboratories. In addition, weak cross-Kerr nonlinearity is sufficient. All of the properties make these schemes feasible in experiments.
文摘In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.
基金Supported by NSF of Zhejiang Province(2006A05192)
文摘In this paper, we study the nonlinear discrete systems and obtain several lyapunov inequalities for them. Then we give the application for lyapunov inequality.
文摘A judgment criterion to guarantee a point to be a Chen' s approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen' s approximate zero may not be a Smale' s approximate zero. The error estimate obtained indicated the convergent order when we use |f(x) | < ε to stop computation in software.The result can also be applied for solving partial derivative and integration equations.
基金supported in part by the National Natural Science Foundation of China(No.61601027)
文摘In this paper,a general scheme in digital self-interference cancellation at baseband for zero-IF full-duplex transceivers is presented. We model the self-interference signals specifically with only the nonlinear distortion signals falling in receiving band considered. A joint estimation algorithm is proposed for compensating the time delay and frequency offset taking into account the IQ amplitude and phase imbalances from mixers. The memory effect and nonlinear distortion are adaptively estimated by the de-correlated normalized least mean square(DNLMS) algorithm. Numerical simulation results demonstrate that the proposed self-interference cancellation scheme can efficiently compensate the self-interference and outperform the existing traditional solutions.
文摘This paper first elaborates the research situation and progress of Laplace characteristics and the eigenvalues value of graphs. The second is given an upper bound of characteristic value of a kind of special graph using the properties of similar matrices. At the same time, a new upper bound of Laplace characteristic values are given using properties of Laplace matrix and the similarity matrix, to improve the existing results. Then, we use the example of the upper bound of our results are more precise than some previous results. Finally the use Laplace non- zero eigenvalues of graph properties to give a bound expressions using the degree of square with a number of edges and the graph of the number, number of connected component expression map, it reflected the relationship between eigenvalues and the amount of Laplace.
基金Project supported by the National Natural Science of Foundation of China (No. 19871015)
文摘This paper constructs a polyconvex stored energy function, satisfying the null condition, for isotropic compressible elastic materials with given Lame constants. The difference between this stored energy function and St Venant-Kirchhoff's is a three order term.
基金This research is partly supported by the Hunan Provincial Natural Science Foundtion of China and Hunan Provincial Education Foundation of China 02B021
文摘This paper presents a trust region algorithm with null space technique fornonlinear equality constrained optimization. Considering in the null space methods that,the convergent rate of range space step is faster than the null space step for the most cases,the proposed algorithm computes null steps more often than range space step. Moreover,the new algorithm is based on the reduced Hessian SQP method. Global convergence ofthe proposed algorithm is proved. The effectiveness of the method is demonstrated bysome numerical examples.
文摘The authors generalize the works in [5] and [6] to prove a Hopf index theorem associated to a smooth section of a real vector bundle with non-isolated zero points.
文摘In this paper, we consider the solution of the following rational systems of difference equations：xn＋1=zn-1xn-2/xn-2±yn,yn＋1=xn-1yn-2/yn-2±zn,zn＋1=yn-1zn-2/zn-1±xn,where initial conditions are nonzero real numbers.
