We study the functional separation of variables to the nonlinear heat equation： ut = （A（x）D（u）ux^n）x＋ B（x）Q（u）, Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables...We study the functional separation of variables to the nonlinear heat equation： ut = （A（x）D（u）ux^n）x＋ B（x）Q（u）, Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained.展开更多
Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhom...Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero- Degasperis-Focas equation.展开更多
Using the (2+1)-dimensional Broer-Kaup equation as an simple example, a new direct method is developed to find symmetry groups and symmetry algebras and then exact solutions of nonlinear mathematical physical equations.
It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
Group-invariant solutions to certain plane curve motions in Euclidean and centro-affine geometries areobtained. The behavior of some solutions is also presented.
In foreign language teaching, the communicative approach has been a dominant method for decades. However, some misconceptions of the communicative approach affect the results of group interaction teaching. This articl...In foreign language teaching, the communicative approach has been a dominant method for decades. However, some misconceptions of the communicative approach affect the results of group interaction teaching. This article tries to explore some existing problems as well as some relevant solution in the application of group activities in colleges with the aid of observation, questionnaire and interview.展开更多
It is already known that there are several nonlinearity criteria such asalgebraic degree nonlinearity, distance to linear structures, correlation immune, propagationcriterion, differential uniformity, which are used t...It is already known that there are several nonlinearity criteria such asalgebraic degree nonlinearity, distance to linear structures, correlation immune, propagationcriterion, differential uniformity, which are used to check whether a cryptographic function is weakor not. In this paper we will discuss these criteria from a valuation point of view, and considerthe largest transformation group which leave a criterion invariant, which is named its symmetrygroup. It can serve as a way of comparing the stability of nonlinearity criteria under the action ofinvertible transformations.展开更多
The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dim...The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.展开更多
基金National Natural Science Foundation of China under Grant No.10671156the Program for New Century Excellent Talents in Universities under Grant No.NCET-04-0968
文摘We study the functional separation of variables to the nonlinear heat equation： ut = （A（x）D（u）ux^n）x＋ B（x）Q（u）, Ax≠0. Such equation arises from non-Newtonian fluids. Its functional separation of variables is studied by using the group foliation method. A classification of the equation which admits the functional separable solutions is performed. As a consequence, some solutions to the resulting equations are obtained.
基金The project supported by Scientific Research and of Education Department of Heilongjiang Province of China under Grant No. 11511008
文摘Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero- Degasperis-Focas equation.
文摘Using the (2+1)-dimensional Broer-Kaup equation as an simple example, a new direct method is developed to find symmetry groups and symmetry algebras and then exact solutions of nonlinear mathematical physical equations.
文摘It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
文摘Group-invariant solutions to certain plane curve motions in Euclidean and centro-affine geometries areobtained. The behavior of some solutions is also presented.
文摘In foreign language teaching, the communicative approach has been a dominant method for decades. However, some misconceptions of the communicative approach affect the results of group interaction teaching. This article tries to explore some existing problems as well as some relevant solution in the application of group activities in colleges with the aid of observation, questionnaire and interview.
基金This research is supported by the National Natural Science Foundation of China(19831070)
文摘It is already known that there are several nonlinearity criteria such asalgebraic degree nonlinearity, distance to linear structures, correlation immune, propagationcriterion, differential uniformity, which are used to check whether a cryptographic function is weakor not. In this paper we will discuss these criteria from a valuation point of view, and considerthe largest transformation group which leave a criterion invariant, which is named its symmetrygroup. It can serve as a way of comparing the stability of nonlinearity criteria under the action ofinvertible transformations.
基金Supported by Natural Science Foundation of Sichuan Education Committee under Grant No. 11ZA100
文摘The duality properties of string cosmology model with negative energy matter are investigated by means of renormalization group equation,the cosmological solutions with exotic matter coupling are obtained in D=d+1 dimensional space-time.These inflation-power solutions can describe accelerated and decelerated process in the early universe,and the duality solutions can be generated through O(d,d) transformations.
