曹操的用将锦囊 人才的能量来自组合

公元215年,曹操发兵西征张鲁,这时东吴孙权见有机可乘,率军攻打合肥。大兵压阵,合肥城内一片惶恐。镇守合肥的三员大将张辽、乐进、李典也是意见不一,有的主战,有的主守。这三员大将,无论资历还是能力,都各有千秋,不相上下。也正因如此,三人互不服气。

Conditional Similarity Reductions of Jimbo—Miwa Equation via the Classical Lie Group Approach

Recently, the Clarkson and Kruskal direct method has been modified to find new similarity reductions (conditional similarity reductions) of nonlinear systems and the results obtained by the modified direct method cannot be obtained by the current classical and/or non-classical Lie group approach. In this paper, we show that the conditional similarity reductions of the Jimbo-Miwa equation can be reobtained by adding an additional constraint equation to the original model to form a conditional equation system first and then solving the model system by means of the classical Lie group approach.

Generalized Toda Mechanics Associated with Classical Lie Algebras and Their Reductions

For any classical Lie algebra , we construct a family of integrable generalizations of Toda mechanics labeled a pair of ordered integers . The universal form of the Lax pair, equations of motion, Hamiltonian as well as Poisson brackets are provided, and explicit examples for with are also given. For all , it is shown that the dynamics of the - and the -Toda chains are natural reductions of that of the -chain, and for , there is also a family of symmetrically reduced Toda systems, the -Toda systems, which are also integrable. In the quantum case, all -Toda systems with 1$' SRC='http://ej.iop.org/images/0253-6102/41/3/339/ctp_41_3_339_12.gif'/> or 1$' SRC='http://ej.iop.org/images/0253-6102/41/3/339/ctp_41_3_339_13.gif'/> describe the dynamics of standard Toda variables coupled to noncommutative variables. Except for the symmetrically reduced cases, the integrability for all -Toda systems survive after quantization.

Symmetry Analysis and Exact Solutions of (2+1)-Dimensional Sawada-Kotera Equation

Based on the symbolic computation system Maple, the infinite-dimensional symmetry group of the （2＋1）- dimensional Sawada-Kotera equation is found by the classical Lie group method and the characterization of the group properties is given. The symmetry groups are used to perform the symmetry reduction. Moreover, with Lou＇s direct method that is based on Lax pairs, we obtain the symmetry transformations of the Sawada-Kotera and Konopelchenko Dubrovsky equations, respectively.

Integrable Couplings of Classical-Boussinesq Hierarchy and Its Hamiltonian Structure

By using a Lie algebra, an integrable couplings of the classicai-Boussinesq hierarchy is obtained. Then, the Hamiltonian structure of the integrable couplings of the classical-Boussinesq is obtained by the quadratic-form identity.

Symmetries and Exact Solutions of the Breaking Soliton Equation

With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)equation.Usingthe symmetries,we find six classical similarity reductions and two nonclassical similarity reductions of the BS equation.Varieties of exact solutions of the BS equation are obtained by solving the reduced equations.

Similarity Reduction Analysis for a Coupled KdV System

Using the direct method for a coupled KdV system, six types of the similarity reductions are obtained. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations.

Symmetry and Similarity Solutions of a （2＋1）-Dimensional Generalized Broer-Kaup System

We study the symmetries of a （2＋1）-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of similarity solutions are obtained.

Lie Point Symmetries of Differential-Difference Equations

In this paper, the classical Lie group approach is extended to find some Lie point symmetries of differentialdifference equations. It reveals that the obtained Lie point symmetries can constitute a Kac-Moody-Virasoro algebra.

A Classical Toda Family with a Common Virasoro Symmetry Algebra

By means of a simple ideal, which is firstly proposed for the continuous system, we present an arbitrary order classical Toda family invariant under common Virasoro-type symmetry algebra.

Symmetry Reductions of Two-Dimensional Variable Coefficient Burgers Equation

By use of a direct method, we discuss symmetries and reductions of the two-dimensional Burgers equation with variable coefficient (VCBurgers). Five types of symmetry-reducing VCBurgers to (1+1)-dimensional partial differential equation and three types of symmetry reducing VCBurgers to ordinary differential equation are obtained.

Noether-Lie Symmetry of Generalized Classical Mechanical Systems

In this paper, the Noether Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether Lie symmetry are obtained. An example is given to illustrate the application of the results.

巧取证据

李典借给一个商人5000元钱,可是不小心将借据丢失了,怎么找也找不到。借据丢了,就失去了商人借钱的有力证据;万一商人不认账,李典也没有办法。

A Note on Restricted Representations of the Witt Superalgebras

Let F be an algebraically closed field of prime characteristic p>3,and W(n)the Witt superalgebra over F,which is the Lie superalgebra of superderivations of the Grassmann algebra in n indeterminates.The dimensions of simple atypical modules in the restricted supermodule category for W(n)are precisely calculated in this paper,and thereby the dimensions of all simple modules can be precisely given.Moreover,the restricted supermodule category for W(n)is proved to have one block.