In this paper,a■-invariant Lorentz metric on the Dirac-Lu space is given,and then the geodesic equationis investigated.Finally,we discuss the field equations and find their solutions by the method of separating varia...In this paper,a■-invariant Lorentz metric on the Dirac-Lu space is given,and then the geodesic equationis investigated.Finally,we discuss the field equations and find their solutions by the method of separating variables.展开更多
Special solution of the （2＋1）-dimensional Sawada Kotera equation is decomposed into three （0＋1）- dimensional Bargmann flows. They are straightened out on the Jacobi variety of the associated hyperelliptic curve....Special solution of the （2＋1）-dimensional Sawada Kotera equation is decomposed into three （0＋1）- dimensional Bargmann flows. They are straightened out on the Jacobi variety of the associated hyperelliptic curve. Explicit algebraic-geometric solution is obtained on the basis of a deeper understanding of the KdV hierarchy.展开更多
In this paper,the modern geometrical structure of analytical mechanics,the exterior differential forms and the geometrical meaning of dynamic equations are briefly discussed.
In this paper,by using the basic properties of arithmetic functionσ(n),the existence of amicable pairs is discussed.We prove that all prime cubes are anti-sociable numbers.
A wave equation with variable coefficients and nonlinear boundary feedback is studied. The results of energy decay of the solution are obtained by multiplier method and Riemann geometry method. Previous results obtain...A wave equation with variable coefficients and nonlinear boundary feedback is studied. The results of energy decay of the solution are obtained by multiplier method and Riemann geometry method. Previous results obtained in the literatures are generalized in this paper.展开更多
This paper considers the energy decay of the wave equation with variable coefficients in an exterior domain.The damping is put on partly the boundary and partly on the interior of the domain.The energy decay results a...This paper considers the energy decay of the wave equation with variable coefficients in an exterior domain.The damping is put on partly the boundary and partly on the interior of the domain.The energy decay results are established by Riemannian geometry method.展开更多
In this paper, by using the factorization equation of the N= 2 supersymmetric gauge theory, we study N= 1 theory in Argyres–Douglas points. We suppose that all monopoles become massive. We derive general Picard–Fuch...In this paper, by using the factorization equation of the N= 2 supersymmetric gauge theory, we study N= 1 theory in Argyres–Douglas points. We suppose that all monopoles become massive. We derive general Picard–Fuchs equations for glueball superfields. These equations are hypergeometric equations and have regular singular points corresponding to Argyres–Douglas points. Furthermore, we obtain the solution of these differential equations.展开更多
We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a...We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.展开更多
A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability an...A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson＇s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.展开更多
This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the...This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the Bcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry.Then,all of the symmetry reductions are provided in terms of the optimal system method,and the exact explicit solutions are investigated by the symmetry reductions and Bcklund transformations.展开更多
基金supported by National Key Basic Research Project of China under Grant Nos.2004CB31800 and 2006CB805905National Natural Science Foundation of China under Grant No.10731080 and CUMT
文摘In this paper,a■-invariant Lorentz metric on the Dirac-Lu space is given,and then the geodesic equationis investigated.Finally,we discuss the field equations and find their solutions by the method of separating variables.
基金The project supported by the Special Funds for Major State Basic Research Project under Grant No.G2000077301
文摘Special solution of the （2＋1）-dimensional Sawada Kotera equation is decomposed into three （0＋1）- dimensional Bargmann flows. They are straightened out on the Jacobi variety of the associated hyperelliptic curve. Explicit algebraic-geometric solution is obtained on the basis of a deeper understanding of the KdV hierarchy.
基金Work supported by NSF of Henan Education Commission
文摘In this paper,the modern geometrical structure of analytical mechanics,the exterior differential forms and the geometrical meaning of dynamic equations are briefly discussed.
基金the National Natural Science Foundation of China （No. 10771186） the Natural Science Foundation of Guangdong Province （No. 06029035） the Science Foundation of Maoming University （No. 201076）.
文摘In this paper,by using the basic properties of arithmetic functionσ(n),the existence of amicable pairs is discussed.We prove that all prime cubes are anti-sociable numbers.
基金This research is supported by the National Science Foundation of China under Grant No. 60774014 and the Science Foundation of Shanxi Province under Grant No. 2007011002. The authors would like to express their sincere thanks to Shugen CHAI for his valuable comments and useful suggestions on the manuscript of this work.
文摘A wave equation with variable coefficients and nonlinear boundary feedback is studied. The results of energy decay of the solution are obtained by multiplier method and Riemann geometry method. Previous results obtained in the literatures are generalized in this paper.
基金supported by the National Science Foundation China under Grant Nos.61174083,61403239,61473126,and 11171195the National Natural Science Foundation of China for the Youth under Grant No.11401351
文摘This paper considers the energy decay of the wave equation with variable coefficients in an exterior domain.The damping is put on partly the boundary and partly on the interior of the domain.The energy decay results are established by Riemannian geometry method.
文摘In this paper, by using the factorization equation of the N= 2 supersymmetric gauge theory, we study N= 1 theory in Argyres–Douglas points. We suppose that all monopoles become massive. We derive general Picard–Fuchs equations for glueball superfields. These equations are hypergeometric equations and have regular singular points corresponding to Argyres–Douglas points. Furthermore, we obtain the solution of these differential equations.
基金supported by National Natural Science Foundation of China(Grant Nos.11371125,11171307 and 61374086)Natural Science Foundation of Zhejiang Province(Grant No.LY13A010004)+1 种基金Natural Science Foundation of Hunan Province(Grant No.12C0577)PhD Students Innovation Foundation of Hunan Province(Grant No.CX2012B153)
文摘We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.
文摘A modified mathematical model of hepatitis C viral dynamics has been presented in this paper, which is described by four coupled ordinary differential equations. The aim of this paper is to perform global stability analysis using geometric approach to stability, based on the higher-order generalization of Bendixson＇s criterion. The result is also supported numerically. An important epidemiological issue of eradicating hepatitis C virus has been addressed through the global stability analysis.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 10971018the Natural Science Foundation of Shandong Province under Grant No.ZR2010AM029+1 种基金the Promotive Research Fund for Young and Middle-Aged Scientists of Shandong Province under Grant No.BS2010SF001the Doctoral Foundation of Binzhou University under Grant No.2009Y01
文摘This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the Bcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry.Then,all of the symmetry reductions are provided in terms of the optimal system method,and the exact explicit solutions are investigated by the symmetry reductions and Bcklund transformations.
