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International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 473582, 12 pages
http://dx.doi.org/10.1155/2012/473582
Research Article

An Upper Bound of the Bezout Number for Piecewise Algebraic Curves over a Rectangular Partition

School of Mathematical Sciences, Ocean University of China, Qingdao, Shandong 266100, China

Received 24 March 2012; Accepted 10 June 2012

Academic Editor: Raül Curto

Copyright © 2012 Feng-Gong Lang and Xiao-Ping Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. H. Wang, “Structure of multivariate splines, and interpolation,” Acta Mathematica Sinica, vol. 18, no. 2, pp. 91–106, 1975, English translation, vol. 18, pp. 10–39. View at Google Scholar
  2. R.-H. Wang, Multivariate Spline Functions and Their Applications, Science Press, Beijing, China; Kluwer Academic, New York, NY, USA, 1994/2001.
  3. R. Hartshorne, Algebraic Geometry, Springer, New York, NY, USA, 1977. View at Zentralblatt MATH
  4. R. J. Walker, Algebraic Curves, Dover, New York, NY, USA, 1950.
  5. D. X. Gong, Some Research on Theory of Piecewise Algebraic Variety and RBF Interpolation [Ph.D. thesis], Dalian University of Technology, Dalian, China, 2009.
  6. X. Shi and R. Wang, “The Bezout number for piecewise algebraic curves,” BIT Numerical Mathematics, vol. 39, no. 2, pp. 339–349, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. R. Wang and Z. Xu, “Estimation of the Bezout number for piecewise algebraic curve,” Science in China A, vol. 46, no. 5, pp. 710–717, 2003, English translation, vol. 46, no. 5, pp. 710–717. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. R.-H. Wang, “Recent researches on multivariate spline and piecewise algebraic variety,” Journal of Computational and Applied Mathematics, vol. 221, no. 2, pp. 460–471, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. G. H. Zhao, On Some Problems for Multivariate Splines [Ph.D. thesis], Dalian University of Technology, Dalian, China, 1996.
  10. Z. X. Luo, Researches On Nonlinear Splines [Ph.D. thesis], Dalian University of Technology, Dalian, China, 1991.
  11. F.-G. Lang and R.-H. Wang, “Intersection points algorithm for piecewise algebraic curves based on Groebner bases,” Journal of Applied Mathematics and Computing, vol. 29, no. 1-2, pp. 357–366, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. X. Zhang and R. Wang, “Isolating the real roots of the piecewise algebraic variety,” Computers and Mathematics with Applications, vol. 57, no. 4, pp. 565–570, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. R. Wang and C. Zhu, “Nöther-type theorem of piecewise algebraic curves,” Progress in Natural Science, vol. 14, no. 4, pp. 309–313, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. C. Zhu and R. Wang, “Nöther-type theorem of piecewise algebraic curves on quasi-cross-cut partition,” Science in China A, vol. 52, no. 4, pp. 701–708, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. R.-H. Wang and C.-G. Zhu, “Cayley-Bacharach theorem of piecewise algebraic curves,” in Proceedings of the International Symposium on Computational Mathematics and Applications (Dalian, 2002), vol. 163, no. 1, pp. 269–276, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH