LIST OF PUBLICATIONS

    To see Dr. Don Hong's papers listed in the Math Reviews of American Mathematical Society, click here

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    Books/Proceedings

  1. QUANTITATIVE MEDICAL DATA ANALYSIS USING MATHEMATICAL TOOLS AND STATISTICAL TECHNIQUES , (with Yu Shyr ), World Scientific Publication , 2007. ISBN: 978-981-270-461-0.

  2. Real Analysis with an introduction to wavelets and applications, Graduate Textbook, (with Jianzhong Wang and Robert Gardner), Elsevier/Academic Press, 2004. ISBN: 0-12-354861-6.

    Book Cover

  3. Proceedings of Wavelets and Approximation Theory , (edited with Michael Prophet ), A Special Issue in Journal of Computational Analysis and Applications , 5:1 (2003).

  4. Proceedings of Approximation Theory and Numerical Analysis , (edited with Tianxiao He ), A Special Issue in Journal of Computational and Applied Mathematics , 155 (2003).

  5. Wavelets and Statistical Applications , a special issue in the Journal of Concrete and Applicable Mathematics , (editing with Yu Shyr ), 4 (2006).

  6. 2010 Special Issue on Computational Biology and Data Mining for IJMCS , (edited with Ji-Ping Wang ).

    Articles in Journals

  7. D. Hong, Spaces of bivariate spline functions over triangulations, Approx. Theory and Applications, 7 (1) 1991, 56-75. MR 92f: 65016.

  8. C. K. Chui, D. Hong, and S. T. Wu, On the degree of multivariate Bernstein polynomial operators, J. of Approx. Theory , 78 (1994), 77-86. MR 95j: 41032.

  9. D. Hong and S. T. Wu, Some properties of Bernstein polynomials on a simplex, J. of Math. Res. and Expos., 14 (1994), 355-366. MR 95h: 41057.

  10. D. Hong , A Bernstein-B\'ezier based smoothness condition for $pp$ functions, Approx. Theory and Applications, 11 (1995), 67-75. CMP 1 370 767 (96:07).

  11. C. K. Chui, D. Hong, and R. Q. Jia, Stability of optimal order approximation by bivariate splines over arbitrary triangulations, Trans. of Amer. Math. Soc. , 347 (1995), 3301-3318. MR 96d: 41012.

  12. D. Hong , Optimal triangulations using edge swappings, in Approximation Theory VIII, Vol. 1, C. K. Chui and L. L. Schumaker (eds.), pp. 249-256, World Scientific Publishing Co., Inc., 1995. CMP 1 471 736 (98:01), MR 98d: 41001.

  13. C. K. Chui and D. Hong , Construction of the local $C^1$ quartic spline elements for optimal order approximation, Math. of Computation , 65 (01/1996). 85-98. MR 96d: 65023.

  14. C. K. Chui and D. Hong , Swapping edges of arbitrary triangulations to achieve the optimal order of approximation, SIAM J. Numer. Anal. 34 (08/1997), 1472-1482. MR 98h: 41036.

  15. D. Hong , Recent Progress on Multivariate Splines , in Approximation Theory: In Memory of A.K. Varma (N.K. Govil et al. Eds.), pp.265-291, Marcel Dekker, Inc., New York, NY, 1998. MR 99c: 41022.

  16. D. Hong and R. Mohapatra, Optimal order of approximation by mixed three-directional spline elements, Computers and Mathematics with Applications, 40 (2000), 127-135. CMP 1 768 969 (2000:15)

  17. D. Hong and Huan-Wen Liu, Some new formulation of smoothness conditions and conformality conditions of bivariate splines , Computers and Mathematics with Applications , 40 (2000), 117-125. CMP 1 768 968 (2000:15).

  18. D. Hong, On optimal order of approximation from bivariate spline spaces , In " Proceedings of the Sixth International Colloquium on Numerical Analysis and Computers with Applications" (D.D. Bainov Ed.), pp.219-226, VSP, International Sciences Publishers, Utrecht, The Netherlands, 1998. CMP 1 644 943 (99:01), MR 99d: 00026.

  19. D. Hong, Huanwen Liu, and Ram Mohapatra, Optimal triangulations and smoothness conditions for bivariate splines, in "Approximation Theory IX, Vol. 2: Computational Aspects", Charles K. Chui and Larry L. Schumaker (eds.), pp. 129-136, Vanderbilt University Press, Nashville, TN, 1998. CMP 1 743 040 (2000:11), MR 00k: 41002.

  20. H.-W., Liu and D. Hong , Some smoothness conditions and conformality conditions for bivariate quartic and quintic splines, CALCOLO: A Quarterly on Numerical Analysis and Theory of Computation ,(1999), 43 -- 61. CMP 1 742 430.

  21. Don Hong and Yuchun Anna Mu, On construction of minimum supported piecewise linear prewavelets over triangulations, In: " Wavelets and Multiresolution Methods," (T.X. He ed.), pp. 181--201, Marcel Decker Pub., New York, 2000.

  22. H.W. Liu and D. Hong , Bivariate $C^1$ cubic spline spaces over even stratified triangulations, J. of Computational Analysis and Applications, B> 4:1 (2002), 19-35.

  23. D. Hong , On scattered data representation using bivariate splines , In: Handbook on Analytic-Computational Methods in Applied Mathematics , pp.997--1029, Chapman & Hall/CRC Press, Boca Raton, 2000. CMP 1 770 944 (2000:16).

  24. Don Hong and Aidi Wu, Orthogonal multiwavelets of multiplicity four , Computers and Mathematics with Applications , 40 (2000), 1153--1169.

  25. Lutai Guan, Don Hong , and Aidi Wu, On smoothness and convergence of orthogonal multiwavelets, Journal of Engineering Matheamtics, 18:2 (2001), 1--11.

  26. Hao Gu, Don Hong , and M. Barrett, On still image compression, J. of Computational Analysis and Applications 5(2003), 45--75.

  27. Bradley Dyer and Don Hong , An algorithm for optimal triangulations on $C^1$ quartic spline approxiamtion and MatLab implementation, , J. of Computational Analysis and Applications 5(2003), 25-43.

  28. Jiansheng Cao and Don Hong , Best approximation for symmetric semi-definite positive solutions of the left and right inverse problems on a subspace, Journal of Concret and Applicable Mathematics , 1:3 (2003) 217-227.

  29. Huanwen Liu and Don Hong, An explicit representation of a local basis in $C^1$ cubic spline space over a triangulated quadrangulation, Journal of Computational and Applied Mathematics , 155 (2003), 187-200.

  30. Doug Hardin and Don Hong, On Piecewise Linear Wavelets and Prewavelets over Triangulations, Journal of Computational and Applied Mathematics, 155 (2003), 91-109.

  31. Don Hong, Martin Barrett, and Panrong Xiao, Biorthogonal Spline Wavelets and EZW Coding for Image Compression, Lecture Notes in Control and Information Sciences, Vol. 299 (Tarn, Tzyh-Jong; Chen, Shan-Ben; Zhou, Changjiu (Eds.)) , Springer-Verlag Berlin Heidelberg, 2004, pp.281-303.

  32. Don Hong and Larry L. Schumaker, Surface Compression Using a Basis of $C^1$ Cubic Bivariate Spline Spaces, Computing, 72 (2004), 79-92.

  33. Don Hong and Qingbo Xue, Construction of Piecewise Linear Prewavelets over Regular Triangulations, Journal of Concrete and Applicable Mathematics , 4 (2006), 451-471.

  34. Don Hong and Yu Shyr, Wavelets in Biostatistics, Journal of Concrete and Applicable Mathematics , 4 (2006), 505-521.

  35. Huan-Wen Liu, Don Hong , and Dun-Qian Cao, Bivariate $C^1$ cubic spline space over non-uniform type-2 triangulation and its subspaces with boundary conditions, Journal of Computers and Mathematics with Applications, 49 (2005), 1853-1865.

  36. Renee Ferguson and Don Hong , On airline revenue optimization problems, Journal of Concrete and Applicable Math, 5 (2007), 153-167.

  37. Jiansheng Cao, Don Hong, and Wenjun Huang, Construction of Small Support Piecewise Linear Prewavelets over Type-2 Triangulations, In: Splines and Wavelets: Athens 2005 (G.R. Chen and M.J. Lai Eds.), pp. 105-122, Nashboro Press, Brentwood, 2006.

  38. Xingchen Yuan, Don Hong, and Yu Shyr, Survival Model and Estimation for Lung Cancer Patients, In: Quantitative Medical Data Analysis Using Math Tools and Statistical Techniques, pp. 201-222, World Scientific Publications, LLC., Singapore, 2007.

  39. Don Hong, Huiming Li, Ming Li, and Yu Shyr, Wavelets and Projecting Spectrum Binning for Proteomic Data Processing, In: Quantitative Medical Data Analysis Using Math Tools and Statistical Techniques, pp. 159-178, World Scientific Publications, LLC., Singapore, 2007.

  40. Jiansheng Cao and Don Hong, Parameterized Piecewise Linear Prewavelets over Type-2 Triangulations, Journal of Applicable Analysis, 86 (2007) 83-98.

  41. Shuo Chen, Don Hong, and Yu Shyr, Wavelet-Based Procedures for Proteomic MS Data Processing, Computational Statistics and Data Analysis, 52 (2007), 211-220.

  42. Don Hong and Yu Shyr, Mathematical Framework and Wavelets Applications in Proteomics for Cancer Study, In: Handbook of Cancer Models With Applications to Cancer Screening, Cancer Treatment and Risk Assessment, (Wai-Yuan Tan and Leonid Hannin Eds.), pp. 471-499, World Scientific Publication, Singapore, 2008. ISBN: 981-277-947-7.

  43. Shuo Chen, Ming Li, Don Hong, Dean Billheimer, Huiming Li, Baogang J. Xu, and Yu Shyr, A Novel Comprehensive Wave-form MS Data Processing Method, Bioinformatics, Vol. 25, no. 6, 2009, 808--814.

  44. Don Hong and Zoe Zhang, Weighted Elastic Net Model for Mass Spectrometry Imaging Processing, Math. Model. Nat. Phenom. , Vol. 5, No. 3, 2010, pp. 115-133.

  45. Don Hong, Shiyin Qin, and Fengqing (Zoe) Zhang, Mathematical Tools and Statistical Techniques for Proteomic Data Mining, for International Journal of Mathematics and Computer Science, 5(2010), no. 2, 123-140.

  46. Wenjun Huang, Huanwen Liu, and Don Hong, Triangulation based method for constructing molecular surfaces, Proceedings on Multimedia and Computational Intelligence of IEEE, 2010 2nd International Conference on MCI of IEEE, Wuhan, China, September 29-30, 2010, pp. 423-426.

  47. Zoe Zhang and Don Hong, Elastic-Net Model for Imaging Mass Spectrometry Data Processing , Statistics in Medicine , 30 (2011), 753-768. DOI: 10.1002/sim.4147, March 2011.

  48. Rong Lu and Don Hong, A NONPARAMETRIC PHENOTYPIC CODING OF THE UNIVARIATE FAMILY-BASED ASSOCIATION TEST IN THE LATE TIME-TO-ONSET ANALYSIS, manuscript, 2011.

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