The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine ...The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.展开更多
Standard generalised method of moments(GMM)estimation was developed for nonsingular system of moment conditions.However,many important economic models are characterised by singular system of moment conditions.This pap...Standard generalised method of moments(GMM)estimation was developed for nonsingular system of moment conditions.However,many important economic models are characterised by singular system of moment conditions.This paper shows that efficient GMM estimation of such models can be achieved by using the reflexive generalised inverses,in particular the Moore–Penrose generalised inverse,of the variance matrix of the sample moment conditions as the weighting matrix.We provide a consistent estimator of the optimal weighting matrix and establish its consistency.Potential issues of using generalised inverse and some remedies are also discussed.展开更多
A reined global-local approach based on the scaled boundary inite element method（SBFEM） is proposed to improve the accuracy of predicted singular stress ield. The proposed approach is carried out in conjunction with...A reined global-local approach based on the scaled boundary inite element method（SBFEM） is proposed to improve the accuracy of predicted singular stress ield. The proposed approach is carried out in conjunction with two steps. First, the entire structure is analyzed by employing an arbitrary numerical method. Then, the interested region, which contains stress singularity, is re-solved using the SBFEM by placing the scaling center right at the singular stress point with the boundary conditions evaluated from the irst step imposed along the whole boundary including the side-faces. Beneiting from the semi-analytical nature of the SBFEM, the singular stress ield can be predicted accurately without highly reined meshes. It provides the FEM or other numerical methods with a rather simple and convenient way to improve the accuracy of stress analysis. Numerical examples validate the effectiveness of the proposed approach in dealing with various kinds of problems.展开更多
基金Supported by Science Fund of the Education Departmentof Guangxi province( 2 0 0 3) and the NationalNatural Science Foundation of China( 1 0 361 0 0 3)
文摘The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.
基金supported by the National Natural Science Foundation of China(NSFC grant:71661137005,71473040 and 11571081).
文摘Standard generalised method of moments(GMM)estimation was developed for nonsingular system of moment conditions.However,many important economic models are characterised by singular system of moment conditions.This paper shows that efficient GMM estimation of such models can be achieved by using the reflexive generalised inverses,in particular the Moore–Penrose generalised inverse,of the variance matrix of the sample moment conditions as the weighting matrix.We provide a consistent estimator of the optimal weighting matrix and establish its consistency.Potential issues of using generalised inverse and some remedies are also discussed.
基金supported by the National Key Research and Development plan (Grant No. 2016YFB0201001)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51421064)the National Natural Science Foundation of China (Grant No. 51138001)
文摘A reined global-local approach based on the scaled boundary inite element method（SBFEM） is proposed to improve the accuracy of predicted singular stress ield. The proposed approach is carried out in conjunction with two steps. First, the entire structure is analyzed by employing an arbitrary numerical method. Then, the interested region, which contains stress singularity, is re-solved using the SBFEM by placing the scaling center right at the singular stress point with the boundary conditions evaluated from the irst step imposed along the whole boundary including the side-faces. Beneiting from the semi-analytical nature of the SBFEM, the singular stress ield can be predicted accurately without highly reined meshes. It provides the FEM or other numerical methods with a rather simple and convenient way to improve the accuracy of stress analysis. Numerical examples validate the effectiveness of the proposed approach in dealing with various kinds of problems.
