PUBLICATIONS

After 1990 [Some of the following hyperlinks link to the pdf-files of the drafts of the papers before they were published. The formal published versions of these papers are referred to the web sites of the journals.]

  1. Jianzhong Wang, ˇ°Geometric Structure of High-Dimensional Data and Dimensionality Reductionˇ±, Higher Education Press (China) and Springer, Beijing, 2011 (ISBN 978-7-04-031704-6)
  2. Jianzhong Wang, Construction of local nonlinear filter without staircase effect in image restoration, special issue ˇ°Wavelet analysis in PDE and Mathematical imageryˇ±, Applicable Analysis 90 (8) (2011) 1257-1273. 
  3. C.K. Chui and Jianzhong Wang, Dimensionality Reduction of Hyper-Spectral Imagery Data for Feature Classification, in "Handbook of Geomathematics", W. Freeden, Z. Nashed and T. Sonar eds., Springer, Berlin, 2010.
  4. C.K. Chui and Jianzhong Wang, Randomized Anisotropic Transform for Nonlinear Dimensionality Reduction, International Journal on Geomathematics, 1(1) (2010) 23-50.
  5. C.K. Chui and Jianzhong Wang, PDE models associate with the bilateral filter, Advances in Computational Mathematics, 31 (2009) 131-156.
  6. Jianzhong Wang, Higher Order Difference Schemes for Heat Equation, Applications and Applied Mathematics, 4(2) (2009) 263 – 272.
  7. Jianzhong Wang, Multiscale Randomized Algorithms for Approximation to Symmetric Matrices, Proceedings of the 5th Asian Mathematical Conference, L.S. Keong and H.K. Haili eds., Malaysia Vol. I ISBN: 978-967-5417-53-5 (2009) 436-441.
  8. C.K. Chui and Jianzhong Wang, Methods and algorithms for dimensionality reduction of HSI data, The 2nd Workshop on Advancing the Automation of Image Analysis, AAIA Workshop II, UCLA, Los Angles, July, 29-31, 2008.
  9. Jianzhong Wang, Wavelet approach to numerical differentiation of noisy functions, Communications on Pure and Applied Analysis, Vol. 6, No. 3, (2007) 873-897.
  10. C.K. Chui and Jianzhong Wang, Wavelet-Based Minimal-Energy Approach to Image Restoration, Applied and Computational Harmonic Analysis Vol. 23 (2007) 114–130.
  11. Jianzhong Wang, On Spline Wavelets, in the book "Wavelets and Splines—Athens 2005" Ed. by G. Chen and M-J Lai, (2006) 456-483.
  12. Jianzhong Wang, Variational method and wavelet regression, Journal of Concrete and Applicable Mathematics: the special issue on ˇ°Wavelets and Applicationsˇ±, 4 (4) (2006) 485-504.
  13. C.K. Chui and Jianzhong Wang, Image Clean-up and Pre-coding, U. S. Patent Application #11/153,461 (filing date: 06/14/2004) and PCT International Application #61586-5000WO (filing date: 06/14/2005).

14.  D. Hong, Jianzhong Wang, and R. Gardner, ˇ°Real analysis with an Introduction to Wavelets and Applicationsˇ±, Elsevier Academic Press, 2005.

  1. R-Q. Jia, Jianzhong Wang, and D-X Zhou, Compactly supported wavelet bases for Sobolev spaces, Applied and Computational Harmonic Analysis 15 (2003) 224-241.
  2. C. K. Chui and Jianzhong Wang, Shannon wavelet approach to sub-band coding, International Journal of Wavelets, Multiresolution and Information Processing, 1 (2003) 233-242.
  3. Jianzhong Wang, Interpolating cubic spline wavelet packet on arbitrary partitions, J. of Comput. Anal. And Appl. 5 (2003) 179-193.
  4. Jianzhong Wang, Spline wavelets in numerical resolution of partial differential equations, in Wavelet Analysis and their Applications, D.Deng, D. Huang, R-Q. Jia, W. Lin, and Jianzhong Wang (eds.) 25 of AMS/IP Studies Advanced Mathematics, Series Editor: S. T. Yau, International Press, (2002) 257-277.
  5. Jianzhong Wang, On Linear Independence of Generators of FSI Distribution Spaces on R, in Approximation Theory X, Splines and Applications, C.K. Chui, L. L. Schumaker, and J. Stockler (eds.),  (2002) 453-472.
  6. Jianzhong Wang, A necessary and sufficient condition for a perfect filter bank, SPIE Proceedings, Vol. 3813 (1999) 682--690.
  7. D. Ruch, W. So, and Jianzhong Wang, Global support of a scaling vector, Applied and Computational Harmonic Analysis 5 (1998), 493--498.
  8. D. Ruch and Jianzhong Wang, Connection between the support and linear independence of refinable distributions, J. Approx. Theory 92 (1998), 472--485.
  9. Jianzhong Wang, Stability and linear independence associated with scaling vectors, SIAM Mathematical Analysis 29 (1998), 1140--1156.
  10. D. Eubank, P. Van Fleet and Jianzhong Wang, Moment computation in invariant spaces, Journal of Applied Mathematics and Stochastic Analysis 11 (1998), 465--479.
  11. Jianzhong Wang, Study of linear independence and accuracy of scaling vectors via two-scale factors, in ˇ°Advances in Waveletsˇ± ed. by K.S. Lau et al., Springer (1998) 229--260.
  12. C. K. Chui and Jianzhong Wang, A study of asymptotically optimal time-frequency windows of scaling functions and wavelets, Annals of Numerical Mathematics 4 (1997), 193--216.
  13. W. So and Jianzhong Wang, Estimating the support of a scaling vector, SIAM J. Matrix Analysis and Applications 18 (1997), 66--73.
  14. W. Cai and Jianzhong Wang, Adaptive multiresolution collocation methods for initial boundary value problems of nonlinear PDE's, SIAM Journal of Numerical Analysis 33 (1996), 937--970.
  15. Jianzhong Wang, Cubic spline wavelet bases for Sobolev space and multilevel interpolation, Applied and Computational Harmonic Analysis 3 (1996), 154--163.
  16. C. K. Chui and Jianzhong Wang, High order orthonormal scaling functions and wavelets give poor time-frequency localization, Fourier analysis and applications 2 (1996), 415--426.
  17. Jianzhong Wang, Interpolating spline wavelet packets, in ˇ°Approximation theory VIII, Vol 2.ˇ± ed. by C. K. Chui and L. L. Schumaker, (1995), 399—406.
  18. Jianzhong Wang and Z. Zhang, On necessary and sufficient conditions for duals of wavelet frames, Acta Math Scientia 15 (1995), 6--14.
  19. Jianzhong Wang, On solutions of two-scale difference equations, Chinese Ann. Math. (Series B) 15 (1994), 23--34.
  20. C. K. Chui and Jianzhong Wang, A study of compactly supported scaling functions and wavelets, in ˇ°Curve and Surfaces IIˇ±, ed. by P. J. Laurent, A. Le Mehaute, and L. L. Schumaker, (1994), 121--140.
  21.  C. K. Chui and Jianzhong Wang, Quasi-interpolation functional on the space of EP splines, J. Approx. Theory 76 (1994), 303--325.
  22. S. Xiao, Jianzhong Wang, and Y. Yang , Image mosaic and its boundary problems, Pattern Recognition and Artificial Intelligence 6 (1993), 198--195.
  23. Rong-Qing Jia and Jianzhong Wang, Stability and linear independence associated with wavelet decompositions, Proc. Amer. Math. Soc 117 (1993), 1115--1124.
  24. C. K. Chui and Jianzhong Wang, Computational and algorithmic aspects of cardinal spline wavelets, Approx. and Its Appl. 2 (1993), 53--75.
  25. C. K. Chui and Jianzhong Wang, An analysis of cardinal-spline wavelets, J. Approx. Theory 72 (1993), 54—68.
  26. C. K. Chui and Jianzhong Wang, A general framework of compactly supported splines and wavelets, J. Approx. Theory 71 (1992), 263--304.
  27. C. K. Chui and Jianzhong Wang, On compactly supported spline wavelets and a duality principle, Trans. Amer. Math. Soc. 330 (1992), 903--916.
  28. C. K. Chui and Jianzhong Wang, A cardinal spline approach to wavelets, Proc. Amer. Math. Soc. 113 (1991), 785--793.
  29. Jianzhong Wang, Wavelet theory and its application to engineering and physics, Math. Advance 2 (1991).
  30. Jianzhong Wang, Approximation of Cauchy principal value integral by cubic spline, Acta. Math. Scientia 1 (1991).
  31. Jianzhong Wang, A point-valued dual functional to the B-net basis, Math. Numer. Sinica 3(1991).

 

Before 1990

  1. Y. Chen and Jianzhong Wang, A remark on minimal support of bivariate polynomial splines, in ˇ°Approximation Theory IVˇ±, ed. by C. K. Chui, et al., (1989).
  2. Jianzhong Wang, The null splines of the quadratic box spline space, Applied Math. Journal of Chinese Univ. 1 (1988).
  3. Jianzhong Wang, Riemann problem with infinite many numbers of discontinuous points on real axis, Acta. Math. Scientia 1 (1988).
  4. Jianzhong Wang, On Cauchy principal value integral in case of kernel with infinite many numbers of discontinuous points, Acta. Math. Scientia 3 (1987). 
  5. Jianzhong Wang, On dual basis of bivariate box splines, Approx. theory and Its Appl. 3 (1987).
  6. Jianzhong Wang, Biorthogonal functional of box splines, Math. Numer. Sinica 1(1986).
  7. Jianzhong Wang, Local quasi-interpolating operators reproducing polynomials, J. Math. At Wuhan, 1 (1986).
  8. Jianzhong Wang, On multivariate splines interpolations, Chinese Ann. Math. (Series A) 2 (1986).
  9. Jianzhong Wang, Interpolation by bivariate splines on a three direction mesh, Numer. Math. Journal of Chinese Univ.  1 (1986).
  10. Jianzhong Wang, On coefficients of expansion in bivariate box splines, Chinese Ann. Math. 2 (1986).
  11. Jianzhong Wang, Representations of box splines by truncated powers, Math. Numer. Sinica 1 (1985).
  12. Jianzhong Wang, Exact estimates of remainders of Hermite interpolating splines--on conjuncture of Lipow and Schoenberg, J. Wuhan Univ. 4 (1985).
  13. Jianzhong Wang, Direct method of solution of singular integral equation with complex Hilbert kernel, J. Wuhan Univ. 1 (1984).
  14. D. Huang and Jianzhong Wang, The relation between the boundary condition and the convergence of interpolation splines, Acta. Math. Appl. Sinica 7(1984).
  15. D. Huang and Jianzhong Wang, The asymptotic expansions of quintic lacunary interpolation splines, Math. Numer. Sinica 2 (1984).
  16. Jianzhong Wang, On optimal error bounds for interpolating splines and corresponding linear width problems, J. Math. at Wuhan 4 (1984).
  17. D. Huang and Jianzhong Wang, Cubic L-spline interpolation at a bi-infinite knot sequence, J. Math. Research and Exposition 1 (1983).
  18. Jianzhong Wang, Lacunary polynomial splines with midpoint interpolation conditions, Chinese Ann. Math. (Series A) 4 (1983).
  19. D. Huang and Jianzhong Wang, Budan-Fourier theorem of $L$-spline and its application, Chinese Ann. Math. (Series A)  3 (1983).
  20. D. Huang and Jianzhong Wang, Inequality of Kolmogorov type bearing on self-conjugate differential operators, Acta. Math. Sinica 26 (1983).
  21. Jianzhong Wang, On optimal error bounds for interpolating splines, Scientia Sinica (Series A) 25 (1982).
  22. D. Huang and Jianzhong Wang, On quartic and quintic interpolating splines and their optimal error bounds, Scientia Sinica (Series A) 25(1982).
  23. Jianzhong Wang, Best simultaneous L1-approximations to n functions, Math. Numer. Sinica 1 (1982).
  24. Jianzhong Wang, Optimal error Lp bounds for polynomial interpolating splines, J. Zhejiang Univ. 4 (1982).
  25. Jianzhong Wang, Quartic lacunary polynomial spline, J. Zhejiang Univ. 1(1981).