Nonlinear differential equations and dynamical systems
Nonlinear differential equations and dynamical systems
Cayley-Bacharach theorem of piecewise algebraic curves
Journal of Computational and Applied Mathematics - Special issue on proceedings of the international symposium on computational mathematics and applications
Lagrange interpolation by bivariate splines on cross-cut partitions
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
Counting positive solutions for polynomial systems with real coefficients
Computers & Mathematics with Applications
The Bezout number for linear piecewise algebraic curves
Computers & Mathematics with Applications
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A piecewise algebraic curve is defined by a bivariate spline function. Using the techniques of the B-net form of bivariate splines function, discriminant sequence of polynomial (cf. Yang Lu et al. (Sci. China Ser. E 39(6) (1996) 628) and Yang Lu et al. (Nonlinear Algebraic Equation System and Automated Theorem Proving, Shanghai Scientific and Technological Education Publishing House, Shanghai, 1996)) and the number of sign changes in the sequence of coefficients of the highest degree terms of sturm sequence, we determine the number of real intersection points of two piecewise algebraic curves whose common points are finite. A lower bound of the number of real intersection points is given in terms of the method of rotation degree of vector field.