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Dr. Khristo Boyadzhiev

Professor of Mathematics
Mathematics & Statistics Dept.
230 Mathile Science Center
525 S. Main Street
Ada, OH 45810
(419) 772-2349
Professional Experience: 
  • 2000 - Present: Professor of Mathematics at ONU.
  • 1993- 1999: Associate Professor of Mathematics at ONU.
  • 1990- 1993: Assistant Professor of Mathematics at ONU.
  • 1990: Visiting Associate Professor of Mathematics for two quarters at Ohio University.
  • 1989: Senior Research Fellow at the Institute of Mathematics, Bulgarian Academy of Sciences, and the University of Sofia.

1981- Present: Reviewer for Mathematical Reviews.

1988- Present: Reviewer for Zentralblatt für Mathematik.

- My Google Site -

Department of Mathematics and Statistics - Seminar Organizer

Education: 
  • Ph.D. in Mathematics, University of Sofia, Bulgaria, 1978. Thesis: Order Characterization of Operator Algebras.
  • M.S. in Mathematics, University of Sofia, Bulgaria, 1972. Thesis: The Spectral Theorem via Extreme Points.
Teaching Interests: 

Undergraduate and graduate courses in Calculus, Geometry, Linear Algebra, Differential Equations, Complex Variables, College Algebra and Trigonometry, Foundations of Mathematics, Real Analysis, Functional Analysis, Fourier Analysis and Partial Differential Equations.

Awards: 
Research Interests: 

Classical Analysis. Theory of Series. Integral Transforms. Functional calculus for operators. Commutation relations. Trace formulas for commutators and differences of operators. Hyponormal operators. Operator and functional inequalities. Operator monotone functions.  Semigroups of operators and the Abstract Cauchy Problem. Fractional powers and imaginary powers of operators. Order properties of operator algebras. Banach Jordan algebras.

Selected Publications: 
  1. Euler sums of hyperharmonic numbers (with Ayhan Dil), Journal of Number Theory, Volume 147 (2015), Pages 490–498.

  2. Series with zeta values and infinite products. Integral Transforms and Special Functions 26 (2015), no. 3, 173–176.

  3. Poisson's formula with principal value integrals and some special Gradshteyn and Ryzhik integrals, SCIENTIA. Series A: Mathematical Sciences, 25 (2014), 27-37.

  4. Power Series with Binomial Sums and Asymptotic Expansions, Int. Journal of Math. Analysis, Vol. 8 (2014), no. 28, 1389-1414.

  5. Evaluation of series with binomial sums, Analysis Mathematica, 40 (1), (2014), 13-23.

  6. Binomial transform and the backward difference, Advances and Applications in Discrete Mathematics, 13 (1) (2014), 43-63.

  7. Power series with skew-harmonic numbers, dilogarithms, and double integrals, Tatra Mountain Math. Publications, 56, (2013), 93–108.

  8. Evaluation of one exotic Furdui type series, Far East Journal of Mathematical Sciences, Volume 75, Issue 2 (2013), 359 - 367.

  9. The integrals in Gradshteyn and Ryzhik.Part 21: Hyperbolic functions (with Victor Moll), SCIENTIA: Series A: Mathematical Sciences, v. 22 (2012), 109-127.

  10. Close encounters with the Stirling numbers of the second kind, The Mathematics Magazine, 85, No. 4, (October 2012), 252-266.

  11. Series with Hermite polynomials and applications, (with  Ayhan Dil ) Publicationes Mathematicae Debrecen,  80, Fasc. 3-4, (2012) 387-406.

  12. Series with Central Binomial Coefficients, Catalan Numbers, and Harmonic Numbers,  Journal of Integer Sequences, v. 15 (2) 2012 ; 12.1.7

  13. Series Transformation Formulas of Euler Type, Hadamard Product of Functions, and Harmonic Number Identities, Indian Journal of pure and Applied mathematics, 42 (2011), 371-387.

  14. The integrals in Gradshteyn and Ryzhik. Part 17, The Riemann Zeta Function (with Victor Moll) ,  SCIENTIA: Series A: Mathematical Sciences, v. 20 (2010), 61-71.

  15. Calculus, radio dials and the straight-line frequency variable capacitors,      “International Journal of Mathematical Education in Science and Technology”, Vol. 41, No. 5, 15 July 2010, 667–710.

  16. The Euler Series Transformation and the Binomial Identities of Ljunggren,  Munarini, and Simons, “INTEGERS”, 10 A22 (2010) 265-271.

  17. Exponential polynomials, Stirling numbers, and evaluation of some Gamma integrals, Abstract and Applied Analysis, Volume 2009, Article ID 168672 (electronic, open source).

  18. Harmonic Number Identities Via Euler's Transform, J. Integer sequences, 12(6), (2009), Article 09.6.1 (electronic).

  19. Alternating Euler sums at the negative integers (with  H. Gopalkrishna Gadiyar, and R. Padma),  Hardy-Ramanujan Journal, 32(2009), 24-37.

  20. On the Taylor Coefficients of the Hurwitz Zeta Function, JP Journal of Algebra, Number Theory and Applications, 12(1) (2008), 1 - 127.

  21. Derivative polynomials for Tanh, Tan, Sech and Sec in explicit form, Fibonacci Quarterly, 45.4 (2007), 291-303. 

  22. The integrals in Gradshteyn and Ryzhik. Part 11: The incomplete beta function, arXiv.org, (2008)

  23. Polyexponentials, arXiv.org, (2007)

  24. The values of an Euler sum at the negative integers and a relation to a certain convolution of Bernoulli numbers (with  H. Gopalkrishna Gadiyar, and R. Padma), Bulletin of the Korean Mathematical Society. Vol. 45, No. 2, (2008), 277-283.

  25. Evaluation of some simple Euler-type series, Far East Journal of Mathematical Sciences (FJMS),
    Volume 29, Issue 1, Pages 1 -11 (2008).

  26. Apostol-Bernoulli functions, derivative polynomials and Eulerian polynomials, Advances and Applications in Discrete Mathematics, Volume 1, Issue 2, Pages 109 -122 (2008).

  27. Equiangular surfaces, self-similar surfaces and the geometry of sea shells, College Mathematics Journal, 30, no. 4, (2007), 265-271.

  28. Evaluation of series with Hurwitz and Lerch zeta function coefficients by using Hankel contour integrals, Applied Mathematics and Computation, Vol 186/2, (2007),1559-1571.

  29. A note on Bernoulli polynomials and solitons, Journal of Nonlinear Mathematical Physics, 14 (2), (2007), 174 -178
  30. A Series transformation formula and related polynomials, International Journal of Mathematics and Mathematical Sciences ,Vol. 2005 (2005), Issue 23, Pages 3849-3866
  31. Integral representation of functions on sectors, functional calculus and norm estimates, Collect. Math. 53,3 (2002), 287-302.
  32. Consecutive evaluation of Euler sums, Internat. J. Math. Math. Sci., 29:9 (2002), 555-561
  33. Evaluation of Euler-Zagier sums, Internat. J. Math. Math. Sci., 27:7 (2001) 407-412.
  34. Krein's trace formula and spectral shift function, Internat. J. Math. Math. Sci., 25:4 (2001), 239-252.
  35. A characteristic property of differentiation, American Mathematical Monthly, 106, no.4, (1999), 353-355.
  36. Spirals and conchospirals in the flight of insects, College Mathematics Journal, 30, no.1, (1999), 23-31.
  37. Norm estimates for commutators of operators,  Journal of the London Mathematical Society, 57 (1998), 739-745..
  38. Functional calculus for Hilbert space operators with bounded imaginary powers, ( in Interaction Between Functional Analysis, Harmonic Analysis, and Probability, ed. N. Kalton et al.). Lecture Notes in Pure and Appl. Math. v. 175 (1996), 97-104.
  39. Strong stability of Hilbert space contraction semigroups, (With N.Levan), Studia Sci.Math.Hungarica 29(1994), 1-18.
  40. Logarithms and imaginary powers of operators on Hilbert space, Collectanea Mathematica, 45(1994), 287-300.
  41. Spectral theorem for unbounded strongly continuous groups on Hilbert space,(With R.deLaubenfels) Proc.Amer.Math.Soc. 120(1994), 127-136.
  42. Boundary values of holomorphic semigroups, (With R.deLaubenfels) Proc.Amer.Math.Soc. 118(1993), 113-118.
  43. Generation of generators of holomorphic semigroups, (With C.Berg and R.deLaubenfels). J.Australian Math.Soc. 55(1993), 245-269.
  44. Mean value theorems for traces, Mathematica Japonica 38(1993), 217-224.
  45. Semigroups and resolvents of bounded variation, imaginary powers and  H inf -functional calculus, (With R.deLaubenfels) Semigroup Forum 45(1992), 372-384.
  46. Introducing the equiangular spiral by using LOGO to model Nature,(With I.Boyadzhiev), J. of Computers in Math. and Math. Education 11(1992), 155-162.
  47. Trace formula for commutators of unitary operators with rank one commutator, Proc.Amer.Math.Soc. 113(1991), 157-162.
  48. Hinf-functional calculus for perturbations of generators of holomorphic semigroups, (With R.deLaubenfels) Houston J.Math. 17(1991), 131-147.
  49. Some inequalities for generalized commutators, Publ. RIMS, Kyoto Univ. 26(1990), 521-527.
  50. Poisson integrals of the Pincus principal function for hyponormal operators, Review Roumaine Math.Pures et Appl. 34(1989), 197-211.
  51. Sinclair type inequalities for the local spectral radius and related topics, Israel J.Math. 53(1987), 272-284.
  52. An asymptotic Fuglede theorem for generators of Co-groups, Acta Math.Hungarica 49(1987), 145-150.
  53. A many-variable Landau-Kolmogorov inequality, Math.Proc.Cambridge Philos.Soc. 101(1987), 123-129.
  54. Generalizations of the Landau-Hadamard inequality and inequalities for quadratic polynomials of operators, Proc.Roy.Soc.Edinburgh Sect. A, 102(1986), 123-129.
  55. New applications of Bernstein's inequality to the theory of operators: A local Sinclair lemma and a generalization of the Fuglede-Putnam theorem, Complex Analysis and Applications'85, Sofia, 1986, 97-104.
  56. The Liouville Theorem. A Survey, Math. and Math. Education, Proc.15th Conf. Sunny Beach, Bulgaria, April 6-9, 1986, 24-56.
  57. Commuting Co-groups and the Fuglede-Putnam theorem, Studia Math. 81(1985), 303-306.
  58. Commuting one-parameter groups of operators, operator and functional inequalities and the Fuglede-Putnam theorem, C.R.Acad. Bulgare Sci. 38(1985), 19-22.
  59. Characterization of the generators of Co-semigroups which leave a convex set invariant. Comment.Math.Univ.Carolinae25(1984),no.1, 158-170.
  60. Linear operators satisfying a minimum principle. C.R.Acad.Bulgare Sci. 37(1984), 721-724.
  61. A note on a paper of Watanabe (The boundedness of closed linear maps in C*-algebras), Acta Sci.Math. (Szeged) 46(1983), 303-304.
  62. A generalization of Fuglede-Putnam's theorem, C.R.Acad.Bulgare Sci. 36(1983), 1503-1505.
  63. Some notes on numerical ranges and dissipative operators,C.R.Acad.Bulgare Sci. 36(1983), 1371-1374.
  64. An inequality for bounds of successive derivatives, Math.Student 50(1982), 214-218.
  65. Unbounded generators of positive semigroups on B*-algebras, C.R.Acad.Bulgare Sci. 35(1982), 1033-1036.
  66. Unbounded dissipative operators on Jordan Banach algebras and B*-algebras, C.R.Acad.Bulgare Sci. 35(1982), 291-293.
  67. Some notes on unbounded symmetric operators in Banach spaces, Annuare Univ.Sofia Fac.Math.Mech.,Livre 1, 75(1981), 19-25.
  68. Alternators on Banach Jordan algebras,(with M.Youngson) C.R.Acad.Bulgare Sci. 33(1980), 1589-1590.
  69. Order characterization of some Banach Jordan algebras, C.R.Acad. Bulgare Sci. 32(1979), 1019-1021.
  70. Some notes on real Banach algebras, Serdica 5(1979), 307-309.
  71. Partially ordered B*-equivalent Banach algebras, Serdica 4 (1978), 12-18.
  72. Characterization of B*-equivalent Banach algebras by means of their positive cones, Serdica 3(1977), 20-24.
  73. Commutativity in Banach algebras and elements with real spectrum, C.R.Acad.Bulgare Sci.29(1976), 1401-1403.
Mathematics and Statistics Department

Heidi Leek

419-772-2346
mathematics@onu.edu
Mathile 240
525 South Main Street
Ada, Ohio 45810
Monday: 8 a.m.-4:30 p.m.
Tuesday: 8 a.m.-4:30 p.m.
Wednesday: 8 a.m.-4:30 p.m.
Thursday: 8 a.m.-4:30 p.m.
Friday: 8 a.m.-4:30 p.m.
Saturday: Closed
Sunday: Closed