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Partial List of Publications

I have publications in the following areas: Approximation Theory, Numerical Analysis, Wavelet Analysis, Multivariate Splines, Enumerative Combinatorics, Number Theory, Theory of Functions, and Optimization.

MathSciNet Listing

Books

  1. With P. J. S. Shiue and Z. Li, Analysis, Combinatorics and Computing, Nova Science Publishers, Inc., 2002.
  2. Dimensionality Reducing Expansion of Multivariate Integration, Birkh\"auser, Boston, March, 2001.
  3. Wavelet Analysis and Multiresolution Methods, Marcel Dekker, May, 2000.
  4. With L.C. Hsu and Y. S. Zhou, Some Topics on Multidimensional Numerical Integration, Anhui Education Press, 1985.
  5. The Theory of Advanced Mathematics and the Skill for Solving Problems, Anhui Education Press, 1984.
  6. Solutions of Mathematics Problems of Qualifying Examinations Volumes I, II, III, Anhui Education Press, 1982.
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Papers

  1. ``The Pascal Matrix Function and Its Applications to Bernoulli Numbers and Bernoulli Polynomials and Euler Numbers and Euler Polynomials.'' (with J. H.-C. Liao and P. J.-S. Shiue), J. Combin. and Number Theory, 6 (2015), No. 3, 189--207.
  2. ``Algorithms for enumeration problem of linear congruence modulo m as sum of restricted partition numbers.'' (with Peter J.-S. Shiue), Frontiers of Mathematics in China, 10 (2015), no. 1, 69 - 89.
  3. ``Matrix characterizations of Riordan arrays.'' Linear Algebra and Its Appl., 465 (2015), 15-42.
  4. ``On an extension of Riordan array and its application in the construction of convolution-type and Abel-type identities.'' (with L. C. Hsu and X. R. Ma), European Journal of Combinatorics, 42 (2014), 112-134.
  5. ``Polynomials that have golden ratio zeros.'' (With J. Maier and K. Vanness), J. Adv. Math. Stud., Vol. 7 (2014), No. 1, 151-175.
  6. ``Hyperbolic expressions of polynomial sequences and parametric number sequences defined by linear recurrence relations of order 2.'' (With Peter J.-S. Shiue and T.-W. Weng), J. Concr. Appl. Math., 12 (2014), No. 1-2, 63-85.
  7. ``Enumeration problems for a linear congruence equation.'' (With Wun-Seng Chou and Peter J.-S. Shiue), Taiwanese J. Math. 18 (2014), no. 1, 265?275.
  8. ``Impulse response sequences and construction of number sequence identities.'' J. Integer Seq. 16 (2013), no. 8, Article 13.8.2, 23 pp.
  9. ``Q-analogues of symbolic operators.'' (With Michael J. Dancs), J. Discrete Math., 2013 (2013), Article ID 487546, 6 pages.
  10. ``Characterization of ( c)-Riordan arrays, Gegenbauer-Humbert-type polynomial sequences, and ( c)-Bell polynomials.'' (With Henry W. Gould), J. Math. Research Appl., 33 (2013), No. 5, 505-527.
  11. ``Schroder matrix as inverse of Delannoy matrix.'' (With S.-L. Yang, S.-N. Zheng, S.-P. Yuan), Linear Algebra and Its Appl., 439 (2013), No. 11, 3605-3614.
  12. ``Expression and computation of generalized Stirling numbers.'' J. Combin. Math. Combin. Comput., 86 (2013), 239-268.
  13. ``On the construction of number sequence identities.'' (With Wun-Seng Chou), J. Concr. Appl. Math., 11 (2013), No. 3-4, 277-291 to appear, 2012.
  14. ``Parametric Catalan numbers and Catalan triangles.'' Linear Algebra and Its Appl., 438 (2013), No. 3, 1467-1484.
  15. ``A unified approach to generalized Stirling functions.'' J. Math. Research Appl., 32 (2012), No. 6, 631-646.
  16. ``The characterization of Riordan arrays and Sheffer-type polynomial sequences.'' 24th MCCCC. J. Combin. Math. Combin. Comput. 82 (2012), 249?268.
  17. ``Eulerian polynomials and B-splines.'' J. Comput. Appl. Math., 236 (2012), 3763-3773.
  18. ``A note on Horner's method.'' (With P. J.-S. Shiue), J. Concr. Appl. Math. 10 (2012), no. 1-2, 53?64.
  19. ``Generalized exponential Euler polynomials and exponential splines.'' Open J. Discrete Math., 1 (2011), 35-42. http://www.scirp.org/journal/PaperInformation.aspx?paperID=5766
  20. ``Some Dense Subsets of Real Numbers and their Applications.'' (With P. J.-S. Shiue and X. Zha), J. Adv. Math. Studies, 4(2011), No. 2, 25-32.
  21. ``Sequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials.'' (With Peter J.-S. Shiue and T.-W. Weng), ISRN Discrete Math., Vol. 2011, Article ID 674167, 16 pages, 2011. doi:10.5402/2011/ 674167
  22. ``Sequences of non-Gegenbauer-Humbert polynomials meet the generalized Gegenbauer-Humbert polynomials.'' (With Peter J.-S. Shiue), ISRN Algebra, Vol. 2011, Article ID 268096, 18 pages, 2011. doi:10.5402/2011/268096
  23. ``Riordan arrays associated with Laurent series and generalized Sheffer-type groups.'' Linear Algebra and Its Appl., 435 (2011), 1241?1256.
  24. ``Generalized zeta functions.'' J. Adv. Math. Studies, 4 (2011), No. 1, 43-48.
  25. ``Characterizations of orthogonal generalized Gegenbauer-Humbert polynomials and orthogonal Sheffer-type polynomials.'' J. of Compu. Anal. and Appl., 13 (2011), No. 4, 701-723.
  26. ``Boundary type quadrature formulas over axially symmetric regions.'' Journal of Concrete and Applicable Mathematics, 8 (2010), No. 3, 489-503.
  27. ``On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order $2$.'' (With Peter J.-S. Shiue), International Journal of Mathematics and Mathematical Sciences, Volume 2009 (2009), Article ID 709386, 1-21.
  28. ``Characterization of Compactly Supported Refinable Splines With Integer Matrix.'' (With Yu-jing Guan), Applicable Analysis, 88 (2009), 1397-1407.
  29. ``A Pair of Operator Summation Formulas and Their Applications.'' (With L. C. Hsu and D. Yin), Comp. & Math. with Applications, 58 (2009), 1340-1348.
  30. ``Sequence Characterization of Riordan Arrays.'' (With R. Sprugnoli), Discrete Math., 309 (2009), 3962-3974.
  31. ``Pade Spline Functions.'' J. Computational Analysis and Applications, 10(2008), No. 4, 495-508.
  32. ``A Symbolic Operator Approach to Power Series Transformation-Expansion Formulas.'' Journal of Integer Sequences, 11(2008), No. 2, Article 08.2.7, 1-19.
  33. ``A symbolic operator approach to several summation formulas for power series II.'' (With L. C. Hsu and P. J.-S. Shiue), Discrete Math., 308(2008), 3427-3440.
  34. ``The Sheffer Group and the Riordan Group.'' (With L. C. Hsu and P. J.-S. Shiue), Discrete Appl. Math., (155) 2007, 1895-1909.
  35. ``Symbolization of Generating Functions, An Application of Mullin-Rota's Theory of Binomial Enumeration.'' (With L. C. Hsu and P. J.-S. Shiue), Comp. & Math. with Applications, 2007, 54 (2007), 664-678.
  36. ``Construction of Biorthogonal B-spline Type Wavelet Sequences with Certain Regularities.'' J. Appl. Functional Analysis, 2(2007), No. 4, 339-360.
  37. ``Fourier Transform of Bernstein-B\'ezier Polynomials.'' (With C. K. Chui and Q. Jiang), Math. Anal. Appl., 325 (2007), 294-304.
  38. ``Multivariate Expansion Associated with Sheffer-type Polynomials and Operators.''(With L. C. Hsu, P. J.-S. Shiue), Bulletin Institute of Mathematics, Academia Sinica, New Series, 1(2006), No. 4.
  39. ``Numerical Approximation to $\zeta (2n+1)$.'' (With M. J. Dancs), J. Comput. Appl. Math., August, 196( 2006), 150-154.
  40. ``An Euler-Type Formula for $\zeta (2k+1)$.'' (With M. J. Dancs), J. Number Theory 118 (2006), no. 2, 192--199.
  41. ``On the Generalized M\"obius Inversion Formulas.'' (With L. C. Hsu, P. J.-S. Shiue), the Blletin of the Australian Mathematical Society, 73(2006), 79-88.
  42. ``On the Convergence of the Summation Formulas Constructed by Using a Symbolic Operator Approach.'' (With L. C. Hsu, P. J.-S. Shiue), Comp. & Math. with Applications, 51(2006), 441-450.
  43. ``On an Extension of Abel-Gontscharoff's Expansion Formula.'' (With L. C. Hsu, P. J.-S. Shiue), Anal. Theory Appl., 21(2005), 359-369.
  44. ``A symbolic operator approach to several summation formulas for power series.'' (With L. C. Hsu, P. J.-S. Shiue, and D. C. Torney), J. Comput. Appl. Math., 177( 2005), 17-33.
  45. ``If $F(x)=\int^{2x}_xf(t)dt$ is constant, must $f(t)=c/t$?'' (With Z. Sinkala and X. Zha), College Math. J., 36(2005), 199-204.
  46. ``MRA frame wavelets associated with the refinable generators of shift invariant spaces.'' Advances in Mathematics Volume 6, Nova Science Publishers, Inc., 2005, 157-178.
  47. ``Biorthogonal spline type wavelets.'' Computers & Mathematics with Applications, 48/9(2004), 1319-1334.
  48. ``On Multivariate Abel-Gontscharoff Interpolation.'' Advances in Constructive Approximation, Nashboro Press, Brentwood, 2004, 219-226.
  49. ``Dimension-reducing expansion, boundary type quadrature formulas, and the boundary element method.'' Advances in Boundary Element Techniques V, EC Ltd., UK, 2004, 287-292.
  50. ``On Abel-Gontscharoff-Gould's polynomials.'' (With L. C. Hsu and P. J. S. Shiue), Anal. Theory Appl. 19 (2003), no. 2, 166--184.
  51. ``Boundary-type quadrature and boundary element method.'' (With R. Zhang and Y. S. Zhou), J. Comput. Appl. Math. 155 (2003), no. 1, 19--41.
  52. ``Multivariate interpolation using Carlitz's inversion formulas.'' J. Comput. Anal. Appl. 5 (2003), no. 1, 103--118.
  53. ``Dimensionality-reducing expansion, boundary type quadrature formulas, and the boundary element method.'' Analysis, Combinatorics and Computing (T.X. He, P. J. S. Shiue and Z. Li eds.), Nova Science Publishers, Inc., 2002, 235-250.
  54. ``Stable refinable generators of shift invariant spaces with certain regularities and vanishing Moments.'' Approximation Theory X (C. K. Chui, L. L. Schumaker, and J. St\"ockler eds.), Vanderbilt University Press, Nashville, 2002, 305-322.
  55. ``Biorthogonal Wavelets with Certain Regularities,'' Applied and Computational Harmonic Analysis, 11(2001), No.2, 227-242.
  56. ``A brief biography of Professor L. C. Hsu. In celebration of Professor Hsu for his 80's birthday.'' Approximation Theory and Its Applications, 16 (2000), no.3, 1--9.
  57. "Boundary quadrature formulas and their applications," Handbook of Analytic-Computational Methods in Applied Mathematics, G. Anastassiou (ed.), Chapman & Hall/CRC, New York, 2000, 773-800.
  58. "C^1 Quadratic Macroelements and C1 Orthogonal Multiresolution Analyses in 2D." Computers and Mathematics with Applications, 40(2000), 95-106.
  59. "Short Time Fourier Transform, Integral Wavelet Transform, and Wavelet Functions Associated with Splines." Journal of Mathematical Analysis and Applications, 224(1998), 182-200.
  60. ``Biorthogonal Spline Approximation and Its Wavelet Analysis." Approximation Theory IX, C. K. Chui and L. L. Schumaker (eds.), Vanderbilt University Press, 1998, 113-120.
  61. "Positivity and Convexity Criteria for Bernstein-Bézier Polynomials Over Simplices." Curves and Surfaces with Applications in CAGD, A. Le M\'ehaut\'e, C. Rabut, and L.L. Schumaker (eds.), Vanderbilt University Press, Nashville, 1997, 169-176.
  62. "Spline Wavelet Transforms II." Wavelet Applications in Signal and Image Processing IV, M. A. Unser (ed.), Proc. SPIE 2825, 488-491, 1996.
  63. "Spline Wavelet Transforms." Proceedings of the International Conference on Science Computing & Modeling, S. K. Dey and J. Ziebarth (eds.), 139-142, 1996.
  64. "Shape Criteria of Bernstein-Bézier Polynomials Over Simplexes." Computers & Mathematics with Applications, 30, 317-333, 1995.
  65. With C. K. Chui, "Bivariate Interpolatory Rational Splines." Numerical Algorithms, 9, 277-291, 1995.
  66. "Construction of Boundary Quadrature Formulas Using WAvelets." Wavelet Applications in Signal and Image Processing IV, M. A. Unser (ed.), Proc. SPIE 2569, 825-836, 1995.
  67. "Spline Interpolation and its Wavelet Analysis." Approximation Theory VIII, Vol. 2: Wavelets and Multilevel Approximation, C.K. Chui and L. L. Schumaker (eds.), 143-150, 1995.
  68. "Admissible Location of Sample Points of Interpolation by Bivariate C1 Quadratic Splines." Proceedings of the First International Conference on Approximation, Probability, and Related Fields, G. Anastassiou and S. T. Rachev (eds.), Plenum Publisher, 1994, 283-296.
  69. With C. K. Chui and H. C. Chui, "Shape Preserving Interpolation by Bivariate C1 Quadratic Splines." Workshop on Computational Geometry, by A. Conte, V. Demichelis, F. Fontanella, and I. Galligani (eds.), World Scientific, New Jersey, 1993, 21-75.
  70. ``C1 Quadratic Finite Element Analysis and Its Applications.'' Thesis (Ph.D.) Texas A&M University, 1991. 285 pp, ProQuest LLC.
  71. With C. K. Chui, "On Bivariate C1 Quadratic Finite Elements and Vertex Splines." Mathematics of Computation, 54(1990), 169-187.
  72. With C. K. Chui, "Computation of Minimally and Quasi-minimally Supported Bivariate Splines." Journal of Computational Mathematics, 8(1990), 108-117.
  73. With A. K. Chan and C. K. Chui, "Application of Generalized Vertex Splines to Boundary Element Method for Electromagnetic Scattering." The 6th Annual Review of Progress in Applied Computational Electromagnetics at the Naval Postgraduate School, Monterey, California, March 19-22, 1990, 329-337.
  74. With C. K. Chui, "On the Dimension of Bivariate Super Spline Spaces." Mathematics of Computation, 53(1989), 219-234.
  75. With G. Q. Zhu, "On the Researches of Multivariate Spline Functions,'' Journal of Hefei University of Technology (Natural Science) 24(1989), No. 2, page number.
  76. With R. H. Wang, X. Y. Liu, and S. C. Wang, "An Integral Method for Constructing Bivariate Spline Functions." Journal of Computational Mathematics, 7(1989), 244-261.
  77. With C. K. Chui and L.C. Hsu, "On a General Class of Multivariate Linear Smoothing Operators." Journal of Approximation Theory, 55(1988), 35-48.
  78. With C. K. Chui and L.C. Hsu, "Asymptotic Properties of Positive Summation-integral Operators." Journal of Approximation Theory, 55(1988), 49-60.
  79. With C. K. Chui, "On Minimal and Quasi-minimal Support Bivariate Splines." Journal of Approximation Theory, 52(1988), 217-238.
  80. With C. K. Chui, "On the Location of Sample Points for Interpolation by Bivariate C1 Quadratic Splines." Numerical Approximation Theory, ed. by L. Collatz etc., Birkhauser, Basel, 1987, 30-43.
  81. With C. K. Chui and R. H. Wang, "The C2 Quadratic Spline Space on a Four-directional Mesh." Journal of Approximation Theory and Its Applications, 3(1987), 32-38.
  82. With C. K. Chui and R. H. Wang, "Interpolation by Bivariate Linear Splines." Colloquia Mathematica, J. Szbadas ed., North-Holland Pub., 1986, 247-255.
  83. With C. K. Chui, "On Quasi-minimal Support Bivariate Splines." in Approximation Theory V, C. K. Chui, L. L. Schumaker, and J. D. Ward (eds.), Academic Press, New York 1986, 303-306.
  84. With Y. S. Zhou, "The Multivariate Zolodaliev-Korkin Theorem and Its Application,'' Journal of Hefei University of Technology (Natural Science) 21(1986), No. 4, page number.
  85. With R. H. Wang, "A Basis of the Multivariate Spline Space on a Quasi-cross-cut Grid Partition." Scientia Sinica (Series A), 29(1986), No. 7, 673-680.
  86. With L.C. Hsu, "On a Kind of Multivariate Rational Interpolation." Numerical Mathematics Journal of Chinese Universities, 8(1986), No. 2, 144-152. MR. 87k:41005.
  87. "Pad\'e Spline Interpolation,'' Journal of Hefei University of Technology (Natural Science) 21(1986), No. 3, page number.
  88. "Bivariate B-Spline Bases,'' Journal of Hefei University of Technology (Natural Science) 20(1985), No. 3, page number.
  89. "A Kind of Numerical Integration Formulas Over Unbounded Regions,'' Journal of Hefei University of Technology (Natural Science) 20(1985), No. 3, page number.
  90. With R. H. Wang, "The Spline Spaces with Boundary Conditions on Non-uniform Type-2 Triangulations," Scientific Bulletin, 30(1985), No. 7, 858-861. MR. 87b:41011 41A15.
  91. "An Algebraic Method for Constructing Boundary-type Quadrature Formulas," Mathematics Numerical Sinica, 7(1985), No. 1, 1-5. MR. 87b:65029 65D32.
  92. With G. Q. Zhu, "The Applications of Pade Approximation in the Numerical Analysis.'' Journal of Huaibai Coal Normal University, 6(1985), No. 1.
  93. With G. Q. Zhu, "A Numerical Method for Pad\'e Spline Interpolation,'' Journal of Hefei University of Technology (Natural Science) 20(1985), No. 1, page number.
  94. "Some Notes on the Quasi-Local Positive Linear Operator,'' Journal of Hefei University of Technology (Natural Science) 20(1985), No. 1, page number.
  95. "The Asymptotic Estimate of Hermite-Fej\'er Interpolation on the Chebyshev Nodes of the Second Kind,'' Journal of Hefei University of Technology (Natural Science) 20(1985), No. 1, page number.
  96. With R. H. Wang, "The Asymptotic Estimate of the Process on the Chebyshev Nodes III," Mathematics Numerical Sinica, 6(1985), No. 1, 1-7. MR. 87a:65033.
  97. With Y. S. Zhou and Y. T. Chang, "Multivariate Interpolation Methods I," Journal of Engineering Mathematics, 4(1984), 12-16.
  98. "The Precision of Interpolation by Hermite-Fej\'er Polynomials with Chebyshev Nodes of the Second kind,'' Journal of Hefei University of Technology (Natural Science) 19(1984), No. 3, page number.
  99. With G. Q. Zhu, "The spline functions with the minimum rectangular compact supports under the type three triangulation.'' Journal of Huaibai Coal Normal University, 5(1984), No. 1.
  100. "On Reducing Dimension Expansions of Multivariate Integration with Algebra Precisions,'' Journal of Hefei University of Technology (Natural Science) 19(1984), No. 2, page number.
  101. "An Asymptotic Estimate Formula on Hermite-Fej\'er Interpolation Polynomials,'' Journal of Hefei University of Technology (Natural Science) 19(1984), No. 1, page number.
  102. With G. Q. Zhu, "Pade Spline Interpolation," Scientific Bulletin, 3(1983), 1020-1021.
  103. With R. H. Wang, "The Asymptotic Estimate of the Process on the Chebyshev Nodes II," Mathematics Numerical Sinica, 5(1983), No. 4, 372-377. MR. 86j:41001 41A05.
  104. With R. H. Wang, "The Asymptotic Estimate of the Process on the Chebyshev Nodes," Mathematics Numerical Sinica, 5(1983), No. 3, 260-266. MR. 85j:41056 41A60.
  105. With G. Q. Zhu, "The Number-Theortical Method for Constructing Boundary-Type Quadrature Formulas,'' Journal of Hefei University of Technology (Natural Science) 18(1983), No. 1, page number.
  106. "A Method of Numerical Integration Over Hypercube and the Estimation of Its Convergence Rate,'' Journal of Hefei University of Technology (Natural Science) 18(1983), No. 3, page number.
  107. "The optimal estimate of the Hermite-Fej\'er Interpolatory operators of the first kind.'' Journal of Huaibai Coal Normal University, 4(1983), No. 2.
  108. With Y. S. Zhou, "A Method for Constructing a Kind of Boundary Type Quadrature Formulas," Acta Science Natural University of Jilin, 1983, No. 4, 40-46. MR. 86f:65054 65D32.
  109. With Y. Q. Huang, "A Note on the Convergence Rate of the Polak-Ribieré Algorithm," Numerical Mathematics Journal of Chinese Universities, 5(1983), No. 1, 59-62. MR. 84h:65053 65H05.
  110. "A Generalization of Contractive Mappings,'' Journal of Hefei University of Technology (Natural Science) 18(1983), No. 2, page number.
  111. With G. Q. Zhu, "Spline functions with the minimum local supports under the third triangulation," Journal of Huaibai Coal Normal University, 1(1983), page number.
  112. With G. Q. Zhu, "Notes on Rational Approximation with Constraints,'' Journal of Hefei University of Technology (Natural Science) 17(1982), No. 2, page number.
  113. With L.C. Hsu, "On the Optimal Estimation of the Remainders in Dimensionality-lowering Expansions with Algebraic Precision," Journal of Mathematics (Wuhan), 2(1982), No. 3, 247-255. MR. 84m:41043 41A55(65D32).
  114. With G. Q. Zhu, "A Note on Rational Spline Functions," Numerical Mathematics Journal of Chinese Universities, 3(1981), No. 3, 276-278. MR. 84b:41010 41A15 (65D07).
  115. With G. Q. Zhu, "A Method of Calculation for the N-point Sectional Pade Approximation," Mathematics Numerical Sinica, 3(1981), No. 2, 179-182. MR. 82k:65009 65D15.
  116. "Boundary type Quadrature Formulas Without Derivative Terms," Journal of Mathematical Research & Exposition, 1(1981), No. 2, 93-102. MR. 83d:65066 65d32 (41A25).
  117. With S. C. Wang, "A Note on the Opial-Hua Inequality," Journal of Mathematical Research & Exposition, 1981, First Issue, 61-62. MR. 83a:26023 26D10.
  118. With G. Q. Zhu, "The Best Boundary-type Quadrature Formula for High-Dimensional Cube,'' Journal of Hefei University of Technology (Natural Science) 16(1981), No. 4, page number.
  119. "A Note on an Iteration Method,'' Journal of Hefei University of Technology (Natural Science), 16 (1981), No. 3, page number.
  120. "Boundary-Type Quadrature Formulas over Some Regions," Journal of Huaibai Coal Normal University, 1(1980), page number.
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