SOLUTION OF SIMULTANEOUS EQUATIONS OF COSINE LAW ARISING FROM SUBJECTIVITY GEOMETRY

This paper discusses the solution of a group of two-order six elements rooted algebraic simultaneous equations set up by cosine law arising from the application example of subjectivity geometry[1]. By means of the implicit function theorem, this paper proves that there exists a unique real solution of those equations. Transforming this problem into an unconstrained nonlinear optimization problem, the solution can be found by known methods. 4 numerical example by descent method is given.

THE GENERIC PROPERTIES OF SOLUTIONS OF A CONSERVATION LAW

In this paper we answer all the questions about the conjectures of Glimm and Lax on genericproperties of solutions. We prove that the discotinuous points of almost every solution with L∞,bounded varistion or contrinuous data are dense in the upper half-plane minus the closure of the setof central simple waves. It is also proved that if the equation is analytic,then the solutions withpiecewise analytic data are piecewise analytic,and the shock curves are also piecewise analytic. Wedisprove the conjecture which claims that almost every solution with C^k data is 'bad' enough, and provethat every solution with C^k data possesses nice propetied, i.e. when k≥4 the generic property ofsolutions is piecewise C^k,and hence is 'good' enough.For the proof of the generic property withC^k (k≥4) data, the idea of transversality in the theory of singular points is essential.

Multi-symplectic method for generalized Boussinesq equation

The generalized Boussinesq equation that represents a group of important nonlinear equations possesses many interesting properties. Multi-symplectic formulations of the generalized Boussinesq equation in the Hamilton space are introduced in this paper. And then an implicit multi-symplectic scheme equivalent to the multi-symplectic Box scheme is constructed to solve the partial differential equations （PDEs） derived from the generalized Boussinesq equation. Finally, the numerical experiments on the soliton solutions of the generalized Boussinesq equation are reported. The results show that the multi-symplectic method is an efficient algorithm with excellent long-time numerical behaviors for nonlinear partial differential equations.

Multi-symplectic method for the generalized(2+1)-dimensionalKdV-mKdV equation

In the present paper, a general solution involv- ing three arbitrary functions for the generalized （2＋1）- dimensional KdV-mKdV equation, which is derived from the generalized （1＋1）-dimensional KdV-mKdV equa- tion, is first introduced by means of the Wiess, Tabor, Carnevale （WTC） truncation method. And then multi- symplectic formulations with several conservation laws taken into account are presented for the generalized （2＋1）- dimensional KdV-mKdV equation based on the multi- symplectic theory of Bridges. Subsequently, in order to simulate the periodic wave solutions in terms of rational functions of the Jacobi elliptic functions derived from thegeneral solution, a semi-implicit multi-symplectic scheme is constructed that is equivalent 1：o the Preissmann scheme. From the results of the numerical experiments, we can con- clude that the multi-symplectic schemes can accurately sim- ulate the periodic wave solutions of the generalized （2＋1）- dimensional KdV-mKdV equation while preserve approxi- mately the conservation laws.

Nonlinear optimal predictive controller for static var compensator to improve power system damping and to maintain voltage

The main objectives of this paper are to simul-taneously improve power system damping and to maintain voltage at the static var compensator(SVC)location bus simultaneously.A new controller for SVC with closed-form analytic solution nonlinear optimal predictive control(NOPC)law was presented.The controller does not require online optimization and the huge calculation burden can be avoided,so that the demand of real-time control can be sat-isfied.In addition,there are only two design parameters,which are the predictive period and control order;so it is easy to implement and test in practical use.Simulation results have shown that the controller can not only attenuate power system oscillation effectively but can also maintain voltage at the SVC bus location.