Algebraic structure and Poisson＇s theory of mechanico-electrical systems

The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.

ALGEBRAIC STRUCTURES AND POISSON INTEGRALS OF RELATIVISTIC DYNAMICAL EQUATIONS FOR ROTATIONALSYSTEMS

The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the special nonholonomic rotational relativistic systems have Lie's algebraic structure, and the dynamical equations of the general holonomic rotational relativistic systems and the general nonholonomic rotational relativistic systems have Lie admitted algebraic structure. At last the Poisson integrals of the dynamical equations for the rotational relativistic systems are given.

Algebraic structure and Poisson method for a weakly nonholonomic system

The algebraic structure and the Poisson method for a weakly nonholonomic system are studied.The differential equations of motion of the system can be written in a contravariant algebra form and its algebraic structure is discussed.The Poisson theory for the systems which possess Lie algebra structure is generalized to the weakly nonholonomic system.An example is given to illustrate the application of the result.

LIE ALGEBRAIC STRUCTURE OF AKNS MATRIX SYSTEM

For an AKNS matrix system,Lie algebraic structure and its mastersymmetry are obtained by a purely algebraic approach;and by using the reduced technique,two similar algebraic structures for MKdV and KdV matrix systems are given.

Batalin-Vilkovisky Structure on Hochschild Cohomology of Self-Injective Quadratic Monomial Algebras

We give a complete description of the Batalin-Vilkovisky algebra structure on Hochschild cohomology of the self-injective quadratic monomial algebras.

Two new discrete integrable systems

In this paper,we focus on the construction of new（1＋1）-dimensional discrete integrable systems according to a subalgebra of loop algebra A 1.By designing two new（1＋1）-dimensional discrete spectral problems,two new discrete integrable systems are obtained,namely,a 2-field lattice hierarchy and a 3-field lattice hierarchy.When deriving the two new discrete integrable systems,we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy.Moreover,we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.

Isomorphic Transformations of Uncertaintiesfor Incorporating EMYCIN-Style andPROSPECTOR-Style Systems intoa Distributed Expert System

In the past, expert systems exploited mainly the EMYCIN modeland the PROSPECTOR model to deal with uncertainties. In other words, a lot ofstand-alone expert systems which use these two models are available. If we can usethe Internet to couple them together, their performance will be improved throughcooperation. This is because the problem-solving ability of expert systems is greatlyimproved by the way of cooperation among different expert systems in a distributedexpert system. Cooperation between different expert systems with these two het-erogeneous uncertain reasoning models is essentially based on the transformations ofuncertainties of propositions between these two models. In this paper, we discoveredthe exactly isomorphic transformations uncertainties between uncertain reasoningmodels, as used by EMYCIN and PROSPECTOR.