The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi...The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.展开更多
To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second ki...To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type.展开更多
To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are pr...To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.展开更多
By the function transformation and the first integral of the ordinary differential equations, the problem of solving the solutions of the double sine-Gordon equation and the treble sine-Gordon equation is researched, ...By the function transformation and the first integral of the ordinary differential equations, the problem of solving the solutions of the double sine-Gordon equation and the treble sine-Gordon equation is researched, and the new solutions are obtained. First, the problem of solving the solutions of the double sine-Gordon equation and the treble sine-Gordon equation is changed to the problem of solving the solutions of the nonlinear ordinary differential equation. Second, with the help of the B?cklund transformation and the nonlinear superposition formula of solutions of the first kind of elliptic equation and the Riccati equation, the new infinite sequence soliton-like solutions of two kinds of sine-Gordon equations are constructed.展开更多
On March 6,2010,an earthquake of M L4. 5 took place in Luanxian,Hebei Province,with plenty of foreshocks and aftershocks. From December 2009 to March 2010,a series of M L≥ 2. 5 earthquakes were recorded by the digita...On March 6,2010,an earthquake of M L4. 5 took place in Luanxian,Hebei Province,with plenty of foreshocks and aftershocks. From December 2009 to March 2010,a series of M L≥ 2. 5 earthquakes were recorded by the digital seismic network of the capital region,which were selected to calculate the apparent stress in this region. The results show that,firstly,a high value anomaly of apparent stress appeared before the M L4. 5 and peak value appeared on the main shock, which then decreased after the ML4. 5 earthquake. The apparent stress of the main shock is much greater than that of most aftershocks,the sequence type is considered as a main shock-aftershock. Secondly,the size of apparent stress perfectly reflects the state of the stress field in the hypocenter region,and we can discuss seismic sequence properties through the changing process of apparent stress,in combination with the traditional methods to identify a sequence more accurately. Finally,in the case of magnitude less than or equal to M L3. 3,correlation between magnitude and apparent stress is positive.展开更多
In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are...In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given.展开更多
In this paper, the asymptotic attractor of the 2-D damped and driven Navier-Stokes equation is studied by constructing a finite-dimensional solution sequence, and it is proved that this solution sequence approximates ...In this paper, the asymptotic attractor of the 2-D damped and driven Navier-Stokes equation is studied by constructing a finite-dimensional solution sequence, and it is proved that this solution sequence approximates the global attractor infinitely after a long time. The dimension estimate of the asymptotic attractor is obtained in the end.展开更多
文摘The boundary value problem of plate bending problem on two_parameter foundation was discussed.Using two series of the high_order fundamental solution sequences, namely, the fundamental solution sequences for the multi_harmonic operator and Laplace operator, applying the multiple reciprocity method(MRM), the MRM boundary integral equation for plate bending problem was constructed. It proves that the boundary integral equation derived from MRM is essentially identical to the conventional boundary integral equation. Hence the convergence analysis of MRM for plate bending problem can be obtained by the error estimation for the conventional boundary integral equation. In addition, this method can extend to the case of more series of the high_order fundamental solution sequences.
基金Supported by the Natural Natural Science Foundation of China under Grant No.10461006the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China under Grant No.NJZZ07031the Natural Science Foundation of Inner Mongolia Autonomous Region,China under Grant No.2010MS0111
文摘To seek new infinite sequence soliton-like exact solutions to nonlinear evolution equations （NEE（s））, by developing two characteristics of construction and mechanization on auxiliary equation method, the second kind of elliptie equation is highly studied and new type solutions and Backlund transformation are obtained. Then （2＋ l ）-dimensional breaking soliton equation is chosen as an example and its infinite sequence soliton-like exact solutions are constructed with the help of symbolic computation system Mathematica, which include infinite sequence smooth soliton-like solutions of Jacobi elliptic type, infinite sequence compact soliton solutions of Jacobi elliptic type and infinite sequence peak soliton solutions of exponential function type and triangular function type.
基金supported by the National Natural Science Foundation of China(Grant No.10862003)the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China(Grant No.NJZZ07031)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2010MS0111)
文摘To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.
文摘By the function transformation and the first integral of the ordinary differential equations, the problem of solving the solutions of the double sine-Gordon equation and the treble sine-Gordon equation is researched, and the new solutions are obtained. First, the problem of solving the solutions of the double sine-Gordon equation and the treble sine-Gordon equation is changed to the problem of solving the solutions of the nonlinear ordinary differential equation. Second, with the help of the B?cklund transformation and the nonlinear superposition formula of solutions of the first kind of elliptic equation and the Riccati equation, the new infinite sequence soliton-like solutions of two kinds of sine-Gordon equations are constructed.
基金funded by the Spark Program of the Earthquake Sciences(XH14005Y)Seismic Situation Tracing Youth Task in 2015(2015010307)Subjects of "Earthquake Monitoring,Prediction and Scieatific Research of 2015",Earthquake Administration of Tianjin Municipality,China(150201)
文摘On March 6,2010,an earthquake of M L4. 5 took place in Luanxian,Hebei Province,with plenty of foreshocks and aftershocks. From December 2009 to March 2010,a series of M L≥ 2. 5 earthquakes were recorded by the digital seismic network of the capital region,which were selected to calculate the apparent stress in this region. The results show that,firstly,a high value anomaly of apparent stress appeared before the M L4. 5 and peak value appeared on the main shock, which then decreased after the ML4. 5 earthquake. The apparent stress of the main shock is much greater than that of most aftershocks,the sequence type is considered as a main shock-aftershock. Secondly,the size of apparent stress perfectly reflects the state of the stress field in the hypocenter region,and we can discuss seismic sequence properties through the changing process of apparent stress,in combination with the traditional methods to identify a sequence more accurately. Finally,in the case of magnitude less than or equal to M L3. 3,correlation between magnitude and apparent stress is positive.
基金supported by the National Science Foundation of China and Shanghai Pujian Program
文摘In this article, we study Levitin-Polyak type well-posedness for generalized vector equilibrium problems with abstract and functional constraints. Criteria and characterizations for these types of well-posednesses are given.
基金the National Natural Science Foundation of China(Grant No.11701399).
文摘In this paper, the asymptotic attractor of the 2-D damped and driven Navier-Stokes equation is studied by constructing a finite-dimensional solution sequence, and it is proved that this solution sequence approximates the global attractor infinitely after a long time. The dimension estimate of the asymptotic attractor is obtained in the end.
