A Multi-component Matrix Loop Algebra and Its Application

A set of multi-component matrix Lie algebra is constructed. It follows that a type of new loop algebra AM-1 is presented. An isospectral problem is established. Integrable multi-component hierarchy is obtained by Tu pattern, which possesses tri-Hamiltonian structures. Furthermore, it can be reduced to the well-known AKNS hierarchy and BPT hierarchy. Therefore, the major result of this paper can be regarded as a unified expression integrable model of the AKNS hierarchy and the BPT hierarchy.

REPRESENTATIONS OF A LOOP LIE ALGEBRA ASSOCIATED WITH QUANTUM PLANE

In this article, some modules over a loop Lie algebra associated to quantum plane are constructed. The isomorphism classes among these modules are also determined.

A Higher Dimensional Loop Algebra and Integrable Couplings System of Evolution Equations Hierarchy

An extension of the Lie algebra A_~n-1 has been proposed [Phys. Lett. A, 2003, [STHZ]310:19-24]. In this paper, the new Lie algebra was used to construct a new higher dimensional loop algebra [AKG～]. Based on the loop algebra [AKG～], the integrable couplings system of the NLS-MKdV equations hierarchy was obtained. As its reduction case, generalized nonlinear NLS-MKdV equations were obtained. The method proposed in this letter can be applied to other hierarchies of evolution equations.

Two types of loop algebras and their expanding Lax integrable models

Though various integrable hierarchies of evolution equations were obtained by choosing proper U in zero-curvature equation Ut-Vx ＋[U, V] = 0, but in this paper, a new integrable hierarchy possessing bi-Hamiltonian structure is worked out by selecting V with spectral potentials. Then its expanding Lax integrable model of the hierarchy possessing a simple Hamiltonian operator ^~J is presented by constructing a subalgebra ^~G of the loop algebra -^~A2. As linear expansions of the above-mentioned integrable hierarchy and its expanding Lax integrable model with respect to their dimensional numbers, their （2＋1）-dimensional forms are derived from a （2＋1）-dimensional zero-curvature equation.

ON INVERSES AND ALGEBRAIC LOOPS OF CO-H-SPACES

In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primarily interested in the algebraic loops which have inversive, power-associative and Moufang properties for some comultiplications.

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.

Vector Loop Algebra and Its Applications to Tu Hierarchy

A vector loop algebra and its extended loop algebra are proposed, which are devoted to obtaining the Tu hierarchy. By making use of the extended trace identity, the Harniltonian structure of the Tu hierarchy is constructed. Furthermore, we apply the quadratic-form identity to the integrable coupling system of the Tu hierarchy.

A New Loop Algebra and Its Corresponding Multi-component Integrable Hierarchy

A type of new loop algebra GM is constructed by making use of the concept of cycled numbers. As its application, an isospectral problem is designed and a new multi-component integrable hierarchy with multi-potential functions is worked out, which can be reduced to the famous KN hierarchy.

A New Loop Algebra and Corresponding Computing Formula of Constant γ in Quadratic-Form Identity

A new loop algebra containing four arbitrary constants is presented, -whose commutation operation is concise, and the corresponding computing formula of constant γ in the quadratic-form identity is obtained in this paper, which can be reduced to computing formula of constant γ in the trace identity. As application, a new Liouville integrable hierarchy, which can be reduced to AKNS hierarchy is derived.

嵌合流行毒株G-H环基因重组口蹄疫病毒的拯救及其免疫原性分析

为了研究能有效免疫防控当前流行的O型3个拓扑型口蹄疫病毒(foot-and-mouth disease virus,FMDV)的疫苗候选株,本研究利用FMDV反向遗传操作技术,通过基因替换,构建同时含当前流行的O型三个拓扑型病毒株结构蛋白基因的重组全长克隆,转染表达T7RNA聚合酶的细胞后拯救重组FMDV,分析结构蛋白基因的重构对病毒生物学特性的影响;拯救病毒制备灭活疫苗,免疫猪和牛,用体外中和试验初步研究其作为O型FMD疫苗候选株的潜力。结果表明FMD流行毒株结构蛋白VP1 G-H环基因的替换没有明显影响重组病毒的噬斑表型和复制能力,但不同FMDV G-H环抗原表位对猪诱导机体产生交叉中和抗体水平影响较大,对牛诱导机体产生交叉中和抗体的影响较小,表明FMDV G-H抗原表位是猪免疫优势的表位。本研究为未来FMDV疫苗的设计提供了重要参考。

A Complex Higher-Dimensional Lie Algebra with Real and Imaginary Structure Constants as Well as Its Decomposition

A new Lie algebra G of the Lie algebra sl（2） is constructed with complex entries whose structure constants are real and imaginary numbers. A loop algebra G corresponding to the Lie algebra G is constructed, for which it is devoted to generating a soliton hierarchy of evolution equations under the framework of generalized zero curvature equation which is derived from the compatibility of the isospectral problems expressed by Hirota operators. Finally, we decompose the Lie algebra G to obtain the subalgebras G1 and G2. Using the G2 and its one type of loop algebra G2, a Liouville integrable soliton hierarchy is obtained, furthermore, we obtain its bi-Hamiltonian structure by employing the quadratic-form identity.

Y（sl（2）） Algebra Application in Extended Hydrogen Atom and Monopole Models

We present the extended hydrogen atom and monopole-hydrogen atom theory through generalizing the usual hydrogen atom model and with a monopole model respectively, in which Y (sl(2) ) algebras are realized. We derive the Hamiltonians of the two models based on the Y(sl(2) ) and the generalized Pauli equation. The energy spectra of the systems are also given in terms of Yangian algebra and quantum mechanics.

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.

Insertion site of FLAG on foot-and-mouth disease virus VP1 G-H loop affects immunogenicity of FLAG

The G-H loop of the foot-and-mouth disease virus（FMDV） virion contains certain dominant immunogenic epitopes, as well as an arginine-glycine-aspartic acid（RGD） motif that is recognized by cell surface integrin receptors. Previous experiments indicate that it is critical to maintain virus structural integrity when inserting an exogenous epitope into the surface of an FMDV structural protein. However, it remains to be determined how factors such as different insertion positions affect interactions among the virus, cells and host immune system. In this study, one infectious c DNA clone of the swine FMDV Cathay topotype strain O/CHA/90 was constructed. Then, a FLAG marker（DYKDDDDK） was inserted upstream（–4） or downstream（＋10） of the RGD motif to generate tagged viruses vFLAG-O/CHA/90 or vO/CHA/90-FLAG, investigating the possibility of expressing foreign antigen and effect on its immunogenicity. Compared to the parental virus, both tagged viruses exhibited similar plaque phenotypes, suckling mouse pathogenicity and antigenicity. Additionally, the FLAGtag insertion position did not change the use of integrin-mediated cell entry by the tagged viruses. Interestingly, both tagged vaccines protected pigs against challenge with the parental virus O/CHA/90 and induced immune responses against FMDV in BALB/c mice and pigs, but only vaccination with vFLAG-O/CHA/90 generated anti-FLAG antibodies. Our findings demonstrated that two sites（RGD–4 and RGD＋10） tolerated the insertion of an exogenous gene in the swine FMDV O/CHA/90 strain. However, only RGD–4 was a novel and appropriate inserting site which could tolerate exogenous FLAG. The resultant tagged virus is a promising candidate for FMD vaccine which can be differentiating infected from vaccinated animals（DIVA）.

Monotonic Property in Field Algebra of G-Spin Model

Let F be the field algebra of G -spin model, D(G) the double algebra of a finite group G and D(H) the sub-Hopf algerba of D(G) determined by the subgroup H of G . The paper builds a correspondence between D(H) and the D(H) -invariant sub- C * -algebra A H in F, and proves that the correspondence is strictly monotonic.

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 Kinds of New Lie Algebras for Producing Integrable Couplings

Two types of Lie algebras are constructed, which are directly used to deduce the two resulting integrable coupling systems with multi-component potential functions. Many other integrable couplings of the known integrable systems may be obtained by the approach.

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.

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.