The polynomial algebra is a deformed su（2） algebra. Here, we use polynomial algebra az a method to solve a series of deformed oscillators. Thus, we find a series of physics systems corresponding with polynomial alge...The polynomial algebra is a deformed su（2） algebra. Here, we use polynomial algebra az a method to solve a series of deformed oscillators. Thus, we find a series of physics systems corresponding with polynomial algebra with different highest orders.展开更多
An accurate determination of intedaminar transversal stresses in composite multilayered plates, especially near free-edge, is of great importance in the study of inter-ply damage modes, mainly in the initiation and gr...An accurate determination of intedaminar transversal stresses in composite multilayered plates, especially near free-edge, is of great importance in the study of inter-ply damage modes, mainly in the initiation and growth of delamination. In this paper, interlaminar stresses are determined by layer-wise mixed finite element model. Each layer is analyzed as an isolated one where the displacement continuity is ensured by means of Lagrange multipliers （which represent the statics variables）. This procedure allows the authors to work with any single plate model, obtaining the interlaminar stresses directly without loss of precision. The FSDT （first shear deformation theory） with transverse normal strain effects included is assumed in each layer, but Lagrange polynomials are used to describe the kinematic instead of Taylor＇s polynomial functions of the thickness coordinates, as is common. This expansion allows the authors to pose the interlaminar displacements compatibility simpler than the second one. The in-plane domain of the plate is discretized by four-node quadrilateral elements, both to the field of displacement and to the Lagrange multipliers. The mixed interpolation of tensorial components technique is applied to avoid the shear-locking in the finite element model. Several examples were carried out and the results have been satisfactorily compared with those available in the literature.展开更多
In this paper, we study(n-1)-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a ...In this paper, we study(n-1)-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a Nijenhuis operator is still a Nijenhuis operator. Finally, we give various constructions of Nijenhuis operators and some examples.展开更多
The integrable properties of the spheroidal equations are investigated. The shape-invariance property is proved to be retained for the spheroidal equations, for which the recurrence relations are obtained. This is the...The integrable properties of the spheroidal equations are investigated. The shape-invariance property is proved to be retained for the spheroidal equations, for which the recurrence relations are obtained. This is the extension of the recurrence relation of the Legendre polynomials.展开更多
Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried ...Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10975075Program for New Century Excellent Talents in University,and the Project-sponsored 5 by SRF for ROCS,SEM
文摘The polynomial algebra is a deformed su（2） algebra. Here, we use polynomial algebra az a method to solve a series of deformed oscillators. Thus, we find a series of physics systems corresponding with polynomial algebra with different highest orders.
文摘An accurate determination of intedaminar transversal stresses in composite multilayered plates, especially near free-edge, is of great importance in the study of inter-ply damage modes, mainly in the initiation and growth of delamination. In this paper, interlaminar stresses are determined by layer-wise mixed finite element model. Each layer is analyzed as an isolated one where the displacement continuity is ensured by means of Lagrange multipliers （which represent the statics variables）. This procedure allows the authors to work with any single plate model, obtaining the interlaminar stresses directly without loss of precision. The FSDT （first shear deformation theory） with transverse normal strain effects included is assumed in each layer, but Lagrange polynomials are used to describe the kinematic instead of Taylor＇s polynomial functions of the thickness coordinates, as is common. This expansion allows the authors to pose the interlaminar displacements compatibility simpler than the second one. The in-plane domain of the plate is discretized by four-node quadrilateral elements, both to the field of displacement and to the Lagrange multipliers. The mixed interpolation of tensorial components technique is applied to avoid the shear-locking in the finite element model. Several examples were carried out and the results have been satisfactorily compared with those available in the literature.
基金Supported by National Natural Science Foundation of China under Grant Nos.11471139,11271202,11221091,11425104Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20120031110022National Natural Science Foundation of Jilin Province under Grant No.20140520054JH
文摘In this paper, we study(n-1)-order deformations of an n-Lie algebra and introduce the notion of a Nijenhuis operator on an n-Lie algebra, which could give rise to trivial deformations. We prove that a polynomial of a Nijenhuis operator is still a Nijenhuis operator. Finally, we give various constructions of Nijenhuis operators and some examples.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002)
文摘The integrable properties of the spheroidal equations are investigated. The shape-invariance property is proved to be retained for the spheroidal equations, for which the recurrence relations are obtained. This is the extension of the recurrence relation of the Legendre polynomials.
文摘Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.
