We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations withmixed partial derivatives.As an application,we classify equations u_(xt)=A(u,u_x)u_(xxx)+B(u,u_x) that admits de...We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations withmixed partial derivatives.As an application,we classify equations u_(xt)=A(u,u_x)u_(xxx)+B(u,u_x) that admits derivative-dependent functional separable solutions (DDFSSs) and illustrate how to construct those DDFSSs with some examples.展开更多
Based on the Global Color Symmetry Model, the non-perturbative Q, CD vacuum is investigated in the parameterized fully dressed quark propagator. Our theoretical predictions for various quantities characterized the QCD...Based on the Global Color Symmetry Model, the non-perturbative Q, CD vacuum is investigated in the parameterized fully dressed quark propagator. Our theoretical predictions for various quantities characterized the QCD vacuum are in agreement with those predicted by many other phenomenologieal QCD inspired models. The successful predictions clearly indicate the extensive validity of our parameterized quark propagator used here. A detailed discussion on the arbitrariness in determining the integration cut-off parameter ofμ in calculating QCD vacuum condensates and a good method, which avoided the dependence of calculating results on the cut-off parameter is also strongly recommended to readers.展开更多
We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two...We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two special cases in [D.K.Ludlow,P.A.Clarkson,and A.P.Bassom,Stud.Appl.Math.103 (1999) 183] and a theoremin [S.Y.Lou,M.Jia,X.Y.Tang,and F.Huang,Phys.Rev.E 75 (2007) 056318] are retrieved.展开更多
This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigati...This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.展开更多
We combine the tanh function method with the symmetry group method to construct new type of solutions of Davey-Stewartson equation and implemente it in a computer algebraic system. As a result, some new types of solut...We combine the tanh function method with the symmetry group method to construct new type of solutions of Davey-Stewartson equation and implemente it in a computer algebraic system. As a result, some new types of solutions are obtained. This method is also applied to other differential equations if the nonlinear evolution equations admit nontrivial one-parameter group of transformation.展开更多
Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis m...Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis method, the vector fields and symmetry reductions of the equation are derived, respectively. Moreover, based on the power series theory, a kind of explicit power series solutions for the equation are well constructed with a detailed derivation. Finally, by using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation.展开更多
Suppose that q is not a root of unity, it is proved in this paper that the center of the quantum group Uq(sl4) is isomorphic to a quotient algebra of polynomial algebra with four variables and one relation.
We prove some analogs inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies. As applications of one of those inequalities, the p-affine isoperimetric inequality and some other ine...We prove some analogs inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies. As applications of one of those inequalities, the p-affine isoperimetric inequality and some other inequalities are obtained.展开更多
Let f be a holomorphic Hecke eigenform of weight k for the modular groupΓ = SL2(Z) and let λf(n) be the n-th normalized Fourier coefficient. In this paper, by a new estimate of the second integral moment of the symm...Let f be a holomorphic Hecke eigenform of weight k for the modular groupΓ = SL2(Z) and let λf(n) be the n-th normalized Fourier coefficient. In this paper, by a new estimate of the second integral moment of the symmetric square L-function related to f, the estimate 1λf(n21) x2 k2(log(x + k))6n≤x is established, which improves the previous result.展开更多
The Nagumo equation ut = △u+ bu(u-a)(1-u), t>0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and...The Nagumo equation ut = △u+ bu(u-a)(1-u), t>0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the 'pathological' property of the fractal. However, it is shown that a global Holder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl's formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.展开更多
This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs(T) initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s + 1,3s + 1}, the differenc...This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs(T) initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s + 1,3s + 1}, the difference of the evolution with the linear evolution is in Hs1 (T) for all times, with at most polynomial growing HS1 norm. Unlike Korteweg-de Vries (KdV) equation, there are less symmetries of the Benjamin system, especially for the resonant function. The new ingredient is that we need to deal with some new difficulties that are caused by the lack of symmetries.展开更多
The objective of this paper is to discuss the issue of the projection uniformity of asymmetric fractional factorials.On the basis of Lee discrepancy,the authors define the projection Lee discrepancy to measure the uni...The objective of this paper is to discuss the issue of the projection uniformity of asymmetric fractional factorials.On the basis of Lee discrepancy,the authors define the projection Lee discrepancy to measure the uniformity for low-dimensional projection designs.Moreover,the concepts of uniformity pattern and minimum projection uniformity criterion are proposed,which can be used to assess and compare two and three mixed levels factorials.Statistical justification of uniformity pattern is also investigated.展开更多
According to the Ringel-Green theorem,the generic composition algebra of the Hall algebra provides a realization of the positive part of the quantum group.Furthermore,its Drinfeld double can be identified with the who...According to the Ringel-Green theorem,the generic composition algebra of the Hall algebra provides a realization of the positive part of the quantum group.Furthermore,its Drinfeld double can be identified with the whole quantum group,in which the BGP-reflection functors coincide with Lusztig's symmetries.It is first asserted that the elements corresponding to exceptional modules lie in the integral generic composition algebra,hence in the integral form of the quantum group.Then it is proved that these elements lie in the crystal basis up to a sign.Eventually,it is shown that the sign can be removed by the geometric method.The results hold for any type of Cartan datum.展开更多
基金National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘We present basic theory of variable separation for (1 + 1)-dimensional nonlinear evolution equations withmixed partial derivatives.As an application,we classify equations u_(xt)=A(u,u_x)u_(xxx)+B(u,u_x) that admits derivative-dependent functional separable solutions (DDFSSs) and illustrate how to construct those DDFSSs with some examples.
基金The project supported in part by National Natural Science Foundation of China under Grant Nos.10647002 and 10565001Natural Science Foundation of Guangxi Province under Grant Nos.0542042,0481030,and 0575020Guangxi University of Technology under Grant No.05006
文摘Based on the Global Color Symmetry Model, the non-perturbative Q, CD vacuum is investigated in the parameterized fully dressed quark propagator. Our theoretical predictions for various quantities characterized the QCD vacuum are in agreement with those predicted by many other phenomenologieal QCD inspired models. The successful predictions clearly indicate the extensive validity of our parameterized quark propagator used here. A detailed discussion on the arbitrariness in determining the integration cut-off parameter ofμ in calculating QCD vacuum condensates and a good method, which avoided the dependence of calculating results on the cut-off parameter is also strongly recommended to readers.
基金Supported by National Natural Science Foundations of China under Grant Nos.10735030,10475055,10675065,and 90503006National Basic Research Program of China (973 Program) under Grant No.2007CB814800+2 种基金PCSIRT (IRT0734)the Research Fund of Postdoctoral of China under Grant No.20070410727Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20070248120
文摘We investigate the symmetry reduction for the two-dimensional incompressible Navier-Stokes equationin conventional stream function form through Lie symmetry method and construct some similarity reduction solutions.Two special cases in [D.K.Ludlow,P.A.Clarkson,and A.P.Bassom,Stud.Appl.Math.103 (1999) 183] and a theoremin [S.Y.Lou,M.Jia,X.Y.Tang,and F.Huang,Phys.Rev.E 75 (2007) 056318] are retrieved.
基金Supported by National Natural Science Foundation of China under Grant No. 10972151the Natural Science Foundation of Higher Education Institution of Jiangsu Province under Grant No. 08KJB130002
文摘This paper focuses on studying a conformal invariance and a Noether symmetry, a Lie symmetry for a Birkhoffian system in event space. The definitions of the conformal invariance of the system are given. By investigation on the relations between the conformal invariance and the Noether symmetry, the conformal invariance and the Lie symmetry, the expressions of conformal factors of the system under these circumstances are obtained. The Noether conserved quantities and the Hojman conserved quantities directly derived from the conformal invariance are given. Two examples are given to illustrate the application of the results.
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004CB318000
文摘We combine the tanh function method with the symmetry group method to construct new type of solutions of Davey-Stewartson equation and implemente it in a computer algebraic system. As a result, some new types of solutions are obtained. This method is also applied to other differential equations if the nonlinear evolution equations admit nontrivial one-parameter group of transformation.
基金Supported by the Fundamental Research Fund for Talents Cultivation Project of the China University of Mining and Technology under Grant No.YC150003
文摘Under investigation in this paper is the invariance properties of the time fractional Rosenau-Haynam equation, which can be used to describe the formation of patterns in liquid drops. By using the Lie group analysis method, the vector fields and symmetry reductions of the equation are derived, respectively. Moreover, based on the power series theory, a kind of explicit power series solutions for the equation are well constructed with a detailed derivation. Finally, by using the new conservation theorem, two kinds of conservation laws of the equation are well constructed with a detailed derivation.
基金supported by National Natural Science Foundation of China (Grant No.10771182)Doctorate Foundation Ministry of Education of China (Grant No. 200811170001)
文摘Suppose that q is not a root of unity, it is proved in this paper that the center of the quantum group Uq(sl4) is isomorphic to a quotient algebra of polynomial algebra with four variables and one relation.
基金supported by National Natural Science Foundation of China(Grant Nos.11671325 and 11401486)the Natural Science Foundation Project of CQ CSTC(Grant No.cstc2016jcyj A0465)
文摘We prove some analogs inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies. As applications of one of those inequalities, the p-affine isoperimetric inequality and some other inequalities are obtained.
基金supported by the National Natural Science Foundation of China(No.11301142)the Key Project of Colleges and Universities of Henan Province(No.15A110014)
文摘Let f be a holomorphic Hecke eigenform of weight k for the modular groupΓ = SL2(Z) and let λf(n) be the n-th normalized Fourier coefficient. In this paper, by a new estimate of the second integral moment of the symmetric square L-function related to f, the estimate 1λf(n21) x2 k2(log(x + k))6n≤x is established, which improves the previous result.
文摘The Nagumo equation ut = △u+ bu(u-a)(1-u), t>0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the 'pathological' property of the fractal. However, it is shown that a global Holder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl's formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.
基金supported by National Natural Science Foundation of China(Grant Nos.11171026 and 11271175)National Natural Science Foundation of Shandong Province(Grant No.ZR2012AQ026)
文摘This paper is intended as an attempt to set up the global smoothing for the periodic Benjamin equation. It is shown that for Hs(T) initial data with 8 〉 -1/2 and for any s 〈 s1〈 min{s + 1,3s + 1}, the difference of the evolution with the linear evolution is in Hs1 (T) for all times, with at most polynomial growing HS1 norm. Unlike Korteweg-de Vries (KdV) equation, there are less symmetries of the Benjamin system, especially for the resonant function. The new ingredient is that we need to deal with some new difficulties that are caused by the lack of symmetries.
基金supported by the National Natural Science Foundations of China under Grant Nos.11271147 and 11401596
文摘The objective of this paper is to discuss the issue of the projection uniformity of asymmetric fractional factorials.On the basis of Lee discrepancy,the authors define the projection Lee discrepancy to measure the uniformity for low-dimensional projection designs.Moreover,the concepts of uniformity pattern and minimum projection uniformity criterion are proposed,which can be used to assess and compare two and three mixed levels factorials.Statistical justification of uniformity pattern is also investigated.
基金supported by the National Natural Science Foundation of China (No. 10631010) the NationalKey Basic Research Programme of China (No. 2006CB805905)
文摘According to the Ringel-Green theorem,the generic composition algebra of the Hall algebra provides a realization of the positive part of the quantum group.Furthermore,its Drinfeld double can be identified with the whole quantum group,in which the BGP-reflection functors coincide with Lusztig's symmetries.It is first asserted that the elements corresponding to exceptional modules lie in the integral generic composition algebra,hence in the integral form of the quantum group.Then it is proved that these elements lie in the crystal basis up to a sign.Eventually,it is shown that the sign can be removed by the geometric method.The results hold for any type of Cartan datum.