Journal of Computational Analysis and Applications

Vitae

Editor in Chief
George Anastassiou
Department of Mathematical Sciences
University of Memphis
Memphis, TN 38152, U.S.A.

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RESEARCH AND PUBLICATIONS
(in Analysis, especially
in Approximation Theory and Probability)

50. "Differentiated Shift-invariant Multivariate Integral operators," in S.W.J. Pure and Appl. Math, Electronic Journal, Vol. 1, p.p. 13-19, 1995.

51. "On Ostrowski Type Inequalities," Proc. A.M.S., Vol. 123, No. 12, Dec 1995, p.p. 3775-3781.

52. With Mi Zhou. "Asymptotic Expansions of the (c₀) m-Parameter Operator Semigroups," "Num. Funct. Anal. & Optim," 16, (9&10), 1273-1291, 1996.

53. "Differentiated Shift-invariant Integral Operators," Approx. Th. VIII, Vol. 1, Approx. and Interp., C.k Chui and L.L. Schumaker (eds.) pp 1-6, 1995, World Scientific Publishing Co., Inc.

54. Zhou, Mi and G. Anastassiou, "Asymptotic Expansions Related to (c₀) m-Parameter Operator Semigroups," Approx. The. VIII, Vol. 1, Approx. and Interp., C.K. Chui and L.L. Schumaker (eds), pp, 563-570, 1995, World Scientific Publ. Co., Inc.

55. With Mi Zhou. "Representation Formulae for (c₀) m-Parameter Operator Semigroups," "Annales Polonici Mathematici," LXIII.3, p.p. 247-272, 1996.

56. "Global Smoothness Preservation by Singular Integrals," Proyecciones revista de Mathematica," Chile, Vol 14, No. 2, pp. 83-88, 1995.

57. With A. Bendikov, "A Sharp Error Estimate for the Numerical Solution of Multivariate Dirichlet Problem," "J. Computational and Applied Math." 75 (1996) 215-229.

58. With Zhou, Mi, "On Simultaneous Approximation of Feller Operator," "Computers and Mathematics with Appl." 31, (1996) No. 10, 31-44.

59. "Lattice Homomorphism - Korovkin Type Inequalities for Vector Valued Functions," Hokkaido Math. J., Vol. 26 (1997) 337-364.

60. "Shape and Probability preserving Univariate Wavelet Type Operators" in "Communications in Applied Analysis," 1 (1997) No. 3, 303-314.

61. "Rate of Convergence of Some Neural Network Operators to the unit-univariate Case." J. Math. Anal. and Appl. 212, 237-262 (1997).

62. "Optimal Bounds on the Average of a Bounded off Observation in the Presence of a Single Moment Condition," V. Benes and Stepan (eds.), Distributions with given Marginals and Moment Problems, p. 1-13, 1997, Kluwer Acad. Publ., The Netherlands.

63. "Multivariate Ostrowski Type Inequalities," "Acta Mathematica Hungarica," 76(4)(1997) 267-278.

64. With X.M Yu "Multivariable Probabilistic Scale Approximation," "Journal Fundamental Sciences and Appl." Plovdiv, Bulgaria, Vol. 5, 1997, 41-57.

65. "Differentiated Shift - Invariant Integral Operators, Multivariate Case," "Bulletin Inst. of Math., Academia Sinica", Vol. 25, Vo. 4, 1997, 243-275.

66. "Lattice Homomorphism Inequalities for Vector Valued Functions," "Proceedings Non-Linear Analysis," 2nd WCNA, 1996. Nonlinear Analysis, Theory, Methods and Applications, Vol. 30, No. 1, pp. 549-554, 1997.

67. With A. Bendikov, "A Discrete Analog of Kac's Formula and Optimal Approximation of the Solution of the Heat Equation," "Indian J. of Pure and Applied Math.," 28 (10) 1367-1389, 1997.

68. "Weak Convergence of Squashing Neural Network Operators Studied Asymptotically," "Neural, Parallel and Scientific Computation," 5 (1997) 439-448.

69. With X.M. Yu "Shape preserving bivariate shift-invariant operators", to appear "Rev. Academia de Ciencias,"Zaragoza, 52(1997), pp. 43-50.

70. With A. Bendikov, "A Sharp error estimate for the Numerical Solution of Multivariate Dirichlet Problem for the Heat Equation," "Stochastic Analysis and Applications," 16(3), 403 -422 (1998) .

71. With M. Ganzburg, "L-positive Approximation," "Revue Roumaine de Math. Pures et Appl.," 43(5-6) (1998), 475-494.

72. "Higher Order Univariate Wavelet Type Approximation, "Approximation Theory," "In Memory of A. K. Varma," pp. 43-60, Marcel Dekker, 1998.

73. "Differentiated Shift - Invariant Integral Operators, Univariate Case," "Applicable Analysis," Vol. 68(3-4), pp 281-311, 1998.

74. With T. Rychlik, "Moment Problems on Random Rounding Rules Subject to Two Moment Conditions," "Comp. & Math. with Appl., Vol. 36, No. 1, pp. 9-19, 1998.

75. "Opial Type inequalities for Linear Differential operators," "Math. Ineq. Appl.," Vol 1, No 2, April 1998, 193-200.

76. "Weak Convergence of Cardaliaguet Euvrard Neural Network operators studied Asymptotically," "Results in Mathematics", 34(1998) 214-223.

77. "General Fractional Opial type Inequalities", "Acta Applicandae Mathematicae", 54:303-317, 1998.

' Accepted:

78. "Opial type inequalities involving fractional derivatives of functions," "Nonlinear Studies", Vol. 6, No. 2, 1999, 207-230.

79. "The Degree of Convergence of Sequences of Multivariate Wavelet Type Operators," "Approx. Th. 98," Proc. Int. Conf., Nashville, TN: Approx. Th. XI, Vol 1,Theoretical aspects, 1-6, 1998, editied by C.K. Chui, R.L. Schumaker.

80. With Sorin Gal, "On some shift invariant integral operators, Univariate case, revisited," "J. of Computational Analysis and Appl", Vol. 1, No. 1, 3-23, 1999

81. "Inequalitites for Local Moduli of Continuity", "Applied math. Letters", 12 (1999), 7-12.

82. With S.G. Gal "General theory of global smoothness preservation by Singular Integrals, Univariate case", "Journal of Computational Analysis and Applications", Vol. 1, No. 3, 1999, pp. 289-317.

83. With S.G. Gal, "Global Smoothness preservation by Multivariate Singular Integrals," "Bulletin of Australian Math. Soc.11, 61,(2000), 489-506.

84. With T. Rychlik, "Rates of Uniform Prokhorov convergence of probability measures with given three moments to a Dirac one","Computers and Math. with Appl.11, 38(1999), 101-119.

85. With S.T. Rachev, "Solving moment problems with applications to stochastics", "Monografii Mathematice", Univ. of the West from Timisoara, Romania, No. 65/1998, pp. 77.

86. With J. Pecaric, "General Weighted Opial Inequalities for Linear Differential Operators", J. of Math. Anal. and Appl., 239, 402-418(1999).

87. With T. Rychlik, "Refined rates of bias convergence for generalized L-Statistics in the I.I.D. case," "Applicationes Mathematicae", (Warsaw) 26 (1999), 437-455.

88. With S. Gal, "On some differentiated shift invariant integral operators, Univariate case, revisited", "Advances in Nonlinear Variational Inequal", (1999), 2(2) 71-83.

89. With S. Gal, "on some differentiated shift-invariant integral operators, multivariate case, revisited", "Advances In Nonlinear Variational Inequal", 1999, 2(2), 97-109.

90' "Rate of Convergence of Some Multivariate Neural Network Operators to the Unit," to appear, "J. Comp. and Math. with Appl." 1999.

91'. With Stamatis Cambanis, "Non-orthogonal Wavelet Approximation with Rates of Deterministic Signals," to appear, J."Comp. and Math. with Appl." 1999.

92'. "General Moments Optimization Problems", accepted "Encyclopedia of Optimization," eds. C. Floudas, P. Pardalos, Kluwer.

93'. With T. Rychlik, "Moment Problems on Random Rounding Rules Subject to One Moment Condition," accepted, "Communications in Applied Analysis".

94'. "Opial Type Inequalities Involving Functions and Their ordinary and Fractional Derivatives", accepted "Communications in Applied Analysis".

95'. With S.G. Gal, "On Some Shift Invariant Multivariate Integral Operators, Revisited," accepted, "Communications in Applied Analysis."

96'. "Higher Order Multivariate Wavelet Type Approximation", to appear Proc. #941 AMS Meeting, "Wavelet Analysis and MultiResolution Methodso," Editor Tian He, Marcel Dekker; N.Y. 2000.

97'. With T. Rychlik "Prokhorov radius of a neighborhood of zero described by three moment constraints," accepted, J. of Global optimization.

98'. With S. Gal, "Convergence of generalized singular integrals to the unit, univariate case", accepted, "Mathematical Inequalities and Appl.," 2000.

99'. With S. Gal,"Convergence of generalized singular integrals to the unit, Multivariate case," accepted, "Appl. Math. Rev., Vol. 1/WSPC, 2000.

100'. "Degree of Approximation of Order Statistics Functionals, Dependent Caseff, to appear "Handbook of AnalyticComputational Methods in Applied Mathematics", Editor G. Anastassiou, CRC Press, 2000.

101*.With T. Rychlik, "Exact rates of Prokhorov convergence under three moment conditions," submitted.

In Preparation:
Papers:

102". "Korovkin theorems for random functions."

103". "Wavelets and Probability."

104". "Approximate Solutions of P.D.E."s - Probabilistic Approach."

105". "Approximation on Neural Networks."

106". "on Opial Inequalities."

107". "Asymptotic Expansions Related to Stationary Processes."

108". "On Prokhorov radius.,,

109". "Global Smootheness."

110"-115". With S. Gal: "On Fuzzy Approximation Theory".

116". "On Riemann Hypothesis."

New Books (In preparation)

1. With S. Gal "Approximation Theory: Moduli of Continuity and Global Smoothness Preservation," appeared Birkhauser Boston, 2000.

2. "Quantitative Approximations," accepted, CRC Press, 2000.

3. "Handbook of Analytic-Computational Methods in Appl. Math.," accepted CRC Press, 2000.

4. "Applied Math. Rev., Vol. l," accepted, World Scientific Publ. Co., 2000.

Much of this work is joint research. My collaborators list includes:
1. S.T. Rachev (U.C. at Santa Barbara)
2. 0. Shisha (Univ. of Rhode Island)
3. H. Gonska (University of Duisburg - Germany)
4. C. Cottin (Univ. of Duisburg - Germany)
5. X.M. Yu (Southwest Missouri State University)
6. S. Cambanis (U.N.C.)
7. A. Bendikov, University of Erlangen, Germany
8. M. Ganzburg (Courant Institute)
9. T. Rychlik (Polish Academy of Science)
10. S. Gal (U. Oradea, Romania)

All the above articles have appear/will appear in international journals, except numbers 2, 13 which appeared in a national journal. Also, all of them have been refereed.

Travel Research Grant from NATO for 1990-1993, going to W. Germany to collaborate with H. H. Gonska and Gonska visiting U.of M. to work with me. Research at Oberwolfach with all expenses paid. During July 93, research in Greece (Nea Makri) with H. Gonska under the NATO grant.

Renewal of NATO grant for 1992, 1993.

Outstanding young researcher's award from College of Arts and Sciences, M.S.U., 1990.

Distinguished Research Award in College Arts & Sciences, The University of Memphis, 1999.

Alumni Association Distinguished Research Award of The University of Memphis, 1999.

$8,500 N.S.F. grant to organize 6th S.E.A. Conference, 1991 in Memphis at M.S.U.

Organizer, 6th S.E. Approximation Theory International Conference, March 14-16, 1991.

University of Memphis Allumni Association Distinguished Research Award, 1999.

Instigator/Local organizer of #919 AMS Conference at The University of Memphis, March 21-22, 1997 and their organizer of a special session on "Approximation in Mathematics".

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