RITT-WU'S CHARACTERISTIC SET METHOD FOR ORDINARY DIFFERENCE POLYNOMIAL SYSTEMS WITH ARBITRARY ORDERING

In this paper, a Ritt-Wu＇s characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed.

An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.

Characteristic Properties of Perspective Sets for Finite Stochastic Decision

For a perspective set that is derived by finite consequences with probabilities, this paper introduces the conception of basis that is proved and the uniqueness of basis over a perspective set holds. These give the characteristic properties of perspective sets and finite consequences with probabilities. These properties are applied to the utility defined by the consequences.

Differential characteristic set algorithm for the complete symmetry classification of partial differential equations

In this paper, we present a differential polynomial characteristic set algorithm for the complete symmetry classification of partial differential equations （PDEs） with some parameters. It can make the solution to the complete symmetry classification problem for PDEs become direct and systematic. As an illustrative example, the complete potential symmetry classifications of nonlinear and linear wave equations with an arbitrary function parameter are presented. This is a new application of the differential form characteristic set algorithm, i.e., Wu＇s method, in differential equations.

APPLICATION OF MECHANIZED MATHEMATICS TO ROTOR DYNAMICS

Based on the mechanized mathematics and WU Wen-tsun elimination method, using oil film forces of short-bearing model and Muszynska's dynamic model, the dynamical behavior of rotor-beating system and its stability of motion are investigated. As example, the concept of Wu characteristic set and Maple software, whirl parameters of short-bearing model, which is usually solved by the numerical method, are analyzed. At the same time, stability of zero solution of Jeftcott rotor whirl equation and stability of self-excited vibration are studied. The conditions of stable motion are obtained by using theory of nonlinear vibration.

ON A COLLISION PROBLEM

Traffic control is necessary for traffic safety in driving cars. To avoid collision of cars in crossroads is an important practical problem. We study in this paper the collision problem of two cars in elliptical forms which move with uniform speed on two crossroads orthogonal to each other. In applying Wb Wen-tsun's method of mathexnatics-mechanization we find conditions such that collision will not occur. We have also determined in the possible colliding case the time and place of first collision.

A SYMBOLIC COMPUTATION METHOD TO DECIDE THE COMPLETENESS OF THE SOLUTIONS TO THE SYSTEM OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS

A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method, and it can be carried out on the computer in the Maple environment.

Automated Reasoning and Equation Solving with the Characteristic Set Method

A brief introduction to the characteristic set method is given for solving algebraic equation systems and then the method is extended to algebraic difference systems. The method can be used to decompose the zero set for a difference polynomial set in general form to the union of difference polynomial sets in triangular form. Based on the characteristic set method, a decision procedure for the first order theory over an algebraically closed field and a procedure to prove certain difference identities are proposed.

Analyzing Boolean Functions via Solving Parametric Polynomial Systems

In this paper,a new method to analyze Boolean functions is proposed.By this method,one can analyze the balancedness,the nonlinearity,and the input-output correlation of vectorial Boolean functions.The basic idea of this method is to compute the refined covers of some parametric Boolean polynomial systems which are equivalent to these problems.By a refined cover,the parameter space is divided into several disjoint components,and on each component,the parametric Boolean polynomial system has a fixed number of solutions.An efficient algorithm based on the characteristic set method to compute refined covers of parametric Boolean polynomial systems is presented.The experimental results about some instances generated from cryptanalysis show that this new method is efficient and can solve some instances which can not be solved in reasonable time by other methods.

Exact Computation of the Topology and Geometric Invariants of the Voronoi Diagram of Spheres in 3D

In this paper, we are addressing the exact the Voronoi diagram of spheres using Wu＇s algorithm. computation of the Delaunay graph （or quasi-triangulation） and Our main contributions are first a methodology for automated derivation of invariants of the Delaunay empty circumsphere predicate for spheres and the Voronoi vertex of four spheres, then the application of this methodology to get all geometrical invariants that intervene in this problem and the exact computation of the Delaunay graph and the Voronoi diagram of spheres. To the best of our knowledge, there does not exist a comprehensive treatment of the exact computation with geometrical invariants of the Delaunay graph and the Voronoi diagram of spheres. Starting from the system of equations defining the zero-dimensional algebraic set of the problem, we are applying Wu＇s algorithm to transform the initial system into an equivalent Wu characteristic （triangular） set. In the corresponding system of algebraic equations, in each polynomial （except the first one）, the variable with higher order from the preceding polynomial has been eliminated （by pseudo-remainder computations） and the last polynomial we obtain is a polynomial of a single variable. By regrouping all the formal coefficients for each monomial in each polynomial, we get polynomials that are invariants for the given problem. We rewrite the original system by replacing the invariant polynomials by new formal coefficients. We repeat the process until all the algebraic relationships （syzygies） between the invariants have been found by applying Wu＇s algorithm on the invariants. Finally, we present an incremental algorithm for the construction of Voronoi diagrams and Delaunay graphs of spheres in 3D and its application to Geodesy.