1-似空间的可数积是D-空间(英文)

不知道是否每个Lindelf空间都是D-空间,因此很有必要考虑什么样的Lindelf空间是D-空间的问题.1-似空间的可数积是Lindelf空间,但不知道它是否是D-空间。为了研究笛卡尔积是D-空间的空间,证明了1-似空间的可数积是D-空间,作为此结论与其他结论的推论得到Lindelf散布空间的可数积是D-空间。

严格p空间的可数积

本文证明具有p序列、严格p序列的空间都是可数可积性,肯定地回答了严格p空间的可数积保持问题.

Lanev空间的可数积

Nogura讨论了Frechet空间的乘积,并且问两个Lasnev空间乘积的强Frechet子空间是否是可度量化空间。本文应用Foged中关于Lasnev空间的特征肯定地回答Nogura的问题。 本文中所论空间均指满足正则且T_1分离性公理的拓扑空间。空间X的子集族称为闭包保持的。

W-Like空间可数积的Lindelof性质

（１）Ｘ是Ｗ┐Ｌｉｋｅ空间，则ｂＸ是Ｌｉｎｄｅｌｏｆ空间；（２）若Ｘｎ，ｎ∈Ｎ是Ｗ┐Ｌｉｋｅ空间，则∏ｎ∈ＮＸｎ是Ｌｉｎｄｅｌｏｆ空间．

某些广义度量空间的可数乘积

证明了具有点可数性质、似G_δ性质及似度量空间性质这3种拓扑空间类中的一些空间具有可数可积性.

Matrix Lie Algebras and Integrable Couplings

Three kinds of higher-dimensional Lie algebras are given which can be used to directly construct integrable couplings of the soliton integrable systems. The relations between the Lie algebras are discussed. Finally, the integrable couplings and the Hamiltonian structure of Giachetti-Johnson hierarchy and a new integrable system are obtained, respectively.

A New Integrable Lattice Hierarchy and Its Two Discrete Integrable Couplings

A new and efficient way is presented for discrete integrable couplings with the help of two semi-direct sum Lie algebras. As its applications, two discrete integrable couplings associated with the lattice equation are worked out. The approach can be used to study other discrete integrable couplings of the discrete hierarchies of solition equations.

Higher-Dimensional Integrable Systems Arising from Motions of Curves on S^2(R)and S^3(R)

We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).

Integrability and Gauge Fixing for Bosonic String on AdS_3×S^3

The integrability and the TST transformation of the bosonic string on AdS3× S^3 are studied. The Lax connection for gauge fixed theory is constructed and proved to be fiat.

Expansion of Lie Algebra and Its Application

Firstly we expand a finite-dimensional Lie algebra into a higher-dimenslonal one. By making use of the later and its corresponding loop algebra, the expanding integrable model of the multi-component NLS-mKdV hierarchy is worked out.

Generalized Multi-component TC Hierarchy and Its Multi-component Integrable Coupling System

A new 3M-dimensional Lie algebra X is constructed firstly. Then, the corresponding loop algebra X is produced, whose commutation operation defined by us is as simple and straightforward as that in the loop algebra A1.It follows that a generalscheme for generating multi-component integrable hierarchy is proposed. By taking advantage of X, a new isospectral problem is established, and then well-known multi-component TC hierarchy is obtained. Finally,an expanding loop algebra FM of the loop algebra X is presented. Based on the FM, the multi-component integrable coupling system of the generalized multi-component TC hierarchy has been worked out. The method in this paper can be applied to other nonlinear evolution equations hierarchies. It is easy to find that we can construct any finite-dimensional Lie algebra by this approach.

High—Dimensional Integrable Models with Infinitely Dimensional Virasoro—Type Symmetry Algebra

Using every realization of the Virasoro-type symmetry algebra , we can obtain various high-dimensional integrable models under the meaning that they possess infinitely many symmetries. By means of a concrete realization, many -dimensional equations which possess Kac–Moody–Virasoro-type infinite dimensional symmetry algebras are obtained.

Characteristic Numbers of Matrix Lie Algebras

A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.

A Finite-dimensional Integrable System with Time Parameter

In this paper a finite dimensional Liouville completely integrable system With timedependent coefficients: H=1/2(P,P) +1/2 t-3 (q,Aq) -1/8 t-9/2 (q,q)2, is obtained. It is proved that when (p,q) satisfies two noninvolutive systems (H) and (F1), the constraint u =1 /2t-9/2 (q,q) - 7x/(12t) gives a solution of generalized CKdV equation.

Similarity Solutions for Generalized Variable Coefficients Zakharov-Kuznetsov Equation under Some Integrability Conditions

In this paper, the symmetry method has been carried over to the generalized variable coefficients Zakharov- Kuznetsov equation. The infinitesimal symmetries and the optimal system are deduced and from this optimal system seven basic fields are determined, and for every vector field in the optimal system the admissible forms of the coefficients are found and this also leads us to transform the given equation into partial differential equations in two variables. After using some referenced transformations the mentioned partial differential equations eventually reduce to ordinary differential equations. The search for solutions to those equations has yielded many exact solutions in most cases.

Symmetries and Algebras of a (2+1)-Dimensional MKdV-Type System

In this paper, a （2＋1）-dimensional MKdV-type system is considered. By applying the formal series symmetry approach, a set of infinitely many generalized symmetries is obtained. These symmetries constitute a closed infinite-dimensional Lie algebra which is a generalization of w∞ type algebra. Thus the complete integrability of this system is confirmed.

A Type of New Loop Algebra and a Generalized Tu Formula

A new Lie algebra, which is far different form the known An-1, is established, for which the corresponding loop algebra is given. From this, two isospectral problems are revealed, whose compatibility condition reads a kind of zero curvature equation, which permits Lax integrable hierarchies of soliton equations. To aim at generating Hamiltonian structures of such soliton-equation hierarchies, a beautiful Killing-Cartan form, a generalized trace functional of matrices, is given, for which a generalized Tu formula （GTF） is obtained, while the trace identity proposed by Tu Guizhang [J. Math. Phys. 30 （1989） 330] is a special case of the GTF. The computing formula on the constant γ to be determined appearing in the GTF is worked out, which ensures the exact and simple computation on it. Finally, we take two examples to reveal the applications of the theory presented in the article. In details, the first example reveals a new Liouville-integrable hierarchy of soliton equations along with two potential functions and Hamiltonian structure. To obtain the second integrable hierarchy of soliton equations, a higher-dimensional loop algebra is first constructed. Thus, the second example shows another new Liouville integrable hierarchy with 5-potential component functions and bi- Hamiltonian structure. The approach presented in the paper may be extensively used to generate other new integrable soliton-equation hierarchies with multi-Hamiltonian structures.

New Matrix Loop Algebra and Its Application

A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly,as its application,the multi-component TC equation hierarchy is obtained,then by use of trace identity the Hamiltonian structure of the above system is presented.Finally,the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra.

Two New Expanding Lie Algebras and Their Integrable Models

A new Lax integrable hierarchy is obtained by constructing an isospectraJ problem with constrained conditions. Two kinds of integrable couplings are obtained by constructing two new expanding Lie algebras of the Lie algebra Be, respectively.

Two types of new Lie algebras and related Liouville integrable hierarchies

Based on the generalization of Lie algebra An- 1, two types of new Lie algebras were worked out and the integrability of the related hierarchies of evolution equations were proved in the sense of Liouville.