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例谈对称性在积分解题中的妙用
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作者 郑淑红 《和田师范专科学校学报》 2007年第4期190-191,共2页
利用对称性特点解积分题,能获得简捷解题途径,是对称法的一种妙用,能使复杂的问题简单化。
关键词 积分 对称 轮换对称 数式对称
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Variable Separation for(1+1)-Dimensional Nonlinear Evolution Equations with Mixed Partial Derivatives 被引量:1
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作者 WANG Peng-Zhou ZHANG Shun-Li 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第10期797-802,共6页
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
关键词 (1 1)-dimensional nonlinear evolution equations variable separation generalized conditional symmetry derivative-dependent functional separable solution
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Non-perturbative Aspects of QCD and Parameterized Quark Propagator 被引量:2
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作者 ZHOU Li-Juan GU Yun-Ting +2 位作者 MA Wei-Xing MENG Cheng-Ju PAN Ji-Huan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第1期181-188,共8页
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
关键词 global color symmetry model parameterized quark propagator non-perturbative QCD vacuumand vacuum condensate
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Some Similarity Reduction Solutions to Two-Dimensional Incompressible Navier-Stokes Equation 被引量:1
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作者 JIAO Xiao-Yu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第9期389-394,共6页
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
关键词 Lie symmetry method Navier Stokes equation similarity reduction
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Conformal Invariance and Noether Symmetry, Lie Symmetry of Birkhoffian Systems in Event Space 被引量:4
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作者 张毅 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第1期166-170,共5页
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
关键词 Birkhoffian system event space conformal invariance Noether symmetry Lie symmetry
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New Formal Solutions of Davey-Stewartson Equation via Combined tanh Function Method with Symmetry Method
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作者 ZHI Hong-Yan ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第4期587-593,共7页
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
关键词 tanh function method symmetry group method Davey-Stewartson equation exact solution
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Lie Symmetries,Conservation Laws and Explicit Solutions for Time Fractional Rosenau–Haynam Equation 被引量:2
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作者 Chun-Yan Qin Shou-Fu Tian +1 位作者 t Xiu-Bin Wang Tian-Tian Zhang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第2期157-165,共9页
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
关键词 time fractional Rosenau–Haynam equation Lie symmetry conservation laws
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Quantum Weyl symmetric polynomials and the center of quantum group U_q(sl_4) 被引量:1
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作者 WU JingYan WEI JunChao LI LiBin 《Science China Mathematics》 SCIE 2011年第1期55-64,共10页
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.
关键词 quantized enveloping algebra quantum group quantum symmetric polynomials CENTER
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Some logarithmic Minkowski inequalities for nonsymmetric convex bodies 被引量:3
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作者 WANG XingXing XU WenXue ZHOU JiaZu 《Science China Mathematics》 SCIE CSCD 2017年第10期1857-1872,共16页
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
关键词 log-Minkowski inequality Minkowski inequality p-affine isoperimetric inequality dual log-Minkowski inequality
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Estimates for Fourier Coefficients of Cusp Forms in Weight Aspect
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作者 Hengcai TANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2016年第5期793-802,共10页
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
关键词 Forms normalized symmetric modular absolute instead Mellin inequality sufficiently approximate
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THE NAGUMO EQUATION ON SELF-SIMILAR FRACTAL SETS
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作者 HU JIAXINDepartment of Mathematics, Tsinghua University, Beijing 100084, China. 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2002年第4期519-530,共12页
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
关键词 Fractal set Spectral dimension Sobolev-type inequality Strong (Weak) solution
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Global smoothing for the periodic Benjamin equation in low-regularity spaces 被引量:1
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作者 SHI ShaoGuang LI JunFeng 《Science China Mathematics》 SCIE 2013年第10期2051-2061,共11页
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
关键词 Benjamin equation WELL-POSEDNESS global smoothing
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Uniformity Pattern of Asymmetric Fractional Factorials
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作者 QIN Hong WANG Zhenghong CHATTERJEE Kashinath 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2016年第2期499-510,共12页
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
关键词 Lower bound minimum projection uniformity ORTHOGONALITY projection Lee discrepancy uniformity pattern.
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The Elements in Crystal Bases Corresponding to Exceptional Modules
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作者 Yong JIANG Jie SHENG Jie XIAO 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2010年第1期1-20,共20页
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
关键词 Crystal basis Hall algebra Exceptional module
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