113. Harmonic Analysis and The Euler Totient Function: Von Neumann Algebras over p-Adic Number Fields, Apr., 2014, Results in Mathematics (With Prof. Palle Jorgensen)

112. Calculus on Arithmetic Functions Determined by Primes, Apr., 2014, Pure and Applied Mathematics Quarterly

111. An Application of Free Probability to Arithmetic Functions, Mar., 2014, Complex Analysis and Operator Theory (With Prof. Palle Jorgensen) (accepted Apr. 2014)

110. Dynamical Systems on Arithmetic Functions Determined by Primes, **Feb., 2014**,

109. Dirichlet-Characters Acting on Arithmetic Functions, Feb., 2014, Bulletin of Korean Mathematical Society

108. Tensoring Arithmetic Functions and Free Probability, Dec., 2013 (With Prof. Palle Jorgensen)

Infinite Dimensional Analysis, Quantum Probability and Related Topics

107. On Classical Moment Problems: Determinants of Hankel Matrices and Convergent Real Sequences,

Nov., 2013 Involve A Journal of Mathematics (With Mr. *Ryan Golden* and Ms. *Ivelina Petrova*) Undergraduate Research

106. On Dynamical Systems Induced by p-Adic Number Fields, Nov., 2013 Opuscula Mathematica

105. Actions of Arithmetic Functions on Matrices and Corresponding Representations, Oct., 2013

(With Prof. Palle Jorgensen) Annals of Functional Analysis: Special Issues

104. Complex-Valued Functions Induced by Graphs, Oct., 2013 Complex Analysis and Operator Theory

103. Structure Theorems of von Neumann Algebras Induced by Bijective Monads, Oct., 2013

(With Prof. In Hyeon Kim) Method and Applications of Analysis

102. Arithmetic Functions in Harmonic Analysis and Operator Theory, Aug., 2013 (With Prof. Palle Jorgensen)

Springer Book Project: Handbook of Operator Theory

101. Asymptotic Free Probability for Arithmetic Functions and Factorization of Dirichlet Series, May, 2013 (With Prof. Palle Jorgensen and Dr. Tim Gillespie)

Journal of Mathematical Analysis and Applications

100. Arithmetic Functions and Corresponding Free Probability Determined by Primes, May, 2013 (With Dr. Tim Gillespie)

Rocky Mountain Journal of Mathematics

99. p-Adic Banach-Space Operators and Adelic Banach-Space Operators, Apr., 2013, Opuscula Mathematica (accepted Jun., 2013)

98. Krein-Space Operators Induced by Dirichlet Characters, Apr., 2013 (With Prof. Palle Jorgensen) Special Issue for Contemporary Mathematics, American Mathematical Society (accepted Apr., 2013)

97. Free Distributional Data of Arithmetic Functions and Corresponding Generating Functions

Determined by Gaps Between Primes, Mar., 2013, Complex Analysis and Operator Theory (accepted in Mar., 2013)

96. Free Probability on Arithmetic Functions Determined by Primes, Mar. 2013, Collectanea Mathematica

95. Krein-Space Representations of Arithmetic Functions Determined by Primes, Mar. 2013 (With Prof. Palle. Jorgensen) Central European Journal of Math

94. Classification on Arithmetic Functions and Corresponding Free-Moment L-Functions, Feb. 2013 Bulletin of Korean Mathematical Society (accepted May, 2013)

93. Group-Action Invariant Free Probability, Feb. 2013 Journal of Korean Mathematical Society

92. On Matricial Algebras over Arithmetic Functions, Feb., 2013, Methods and Applications of Analysis

91. Monad-Graphs, Opreators and Fractals, Dec., 2012 (With Prof. Palle Jorgensen) Reviews of Applied Physics

90. K-Groups of a C*-Algebra Generated by a Single Opearator, Nov. 2012, Complex Analysis and Operator Theory (accepted in Jan. 2013)

89. Real Numbers Acting on Arithmetic Functions, Nov., 2012, (With Dr. Tim Gillespie) INTEGERS: The Electronic Jornal of Combinatorics and Number Theory (r)

88. Non-Archimedean Matricial Algebras over the Adele Ring, Oct., 2012, Journal of Combinatorics and Number Theory

87. Von Neumann Algebras Generated by the Adele Ring, Aug. 2012, Ukrainian Mathematical Journal

86. Actions on Groupoids Induced by Monads, Aug. 2012 Publicationes Mathematicae

85. The Index Semigroup and K-Groups of Graph-Groupoid C*-Algebras, Jun. 2012, Complex Analysis and Operator Theory (accepted Oct. 2012)

84. Operator Algebras Induced by Monads, May. 2012 (With Prof. Palle Jorgensen) Journal of Applied Mathematics and Computing (accepted July 2012)

83. Operators Induced by Prime Numbers, May. 2012 Method and Applications of Analysis (accepted Jan., 2013)

82. The Index Semigroup and K-Groups of Graph-Groupoid C*-Algebras, Apr. 2012, ISRN Geometry (rejceted May 2012)

81. Von Neumann Algebras Generated by the Adele Ring and p-Adic Number Fields, Mar. 2012, ACTA Applied Math (rejected Jul. 2012)

80. On the Von Neumann Algebra Generated by the Adele Ring, Feb. 2012 (With Dr. Tim Gillespie) Journal of Math Physics (rejected Jun. 2012)

79. K-Theory Induced by a single Partial Isometry, Feb. 2012 Opuscula Mathematica (accepted in June 2012)

78. C*-Algebraic K-Theory Induced by Graphs, Jan. 2012, Americal Journal of Mathematics and Mathematical Science (accepted in Mar. 2012)

77. Operators Induced by Prime Numbers, Jan. 2012, Journal of Physics A: Mathematical and Theoretical (IOP) (rejected in May, 2012: Good rejection!)

76. Index Semigroup and Indexing on von Neumann Algebras, Oct., 2011, Complex Analysis and Operator Theory (accepted Nov. 2011)

75. K-Theory on Groupoid C*-Algebras, Oct., 2011, ACTA Applied Math (rejected Jan. 2012)

74. Embeddings of Graphs in Manifolds, Sep., 2011, (With Prof. Palle Jorgensen), Anaylsis in Theory and Applications

73. Algebras of Operators and Discrete Laplacians in Energy Hilbert Space, Aug., 2011, (With Prof. Palle Jorgensen) Mediterranean Journal of Mathematics (rejected Jul. 2012)

72. Index-Morphism on Finite Trees and Classification of von Neumann Algebras Induced by Finite Trees, Apr., 2011, Invited Paper (Chapter) in a Book: "Quantum Mechanics," InTech Open Access Publisher (accepted in Apr., 2011)

71. Histories Distorted by Partial Isometries, Mar., 2011, Journal of Physical Mathematics. (accepted in May, 2011) DOI:10.4303/jpm/P110301

70. Operators Induced by Graphs, Mar., 2011, (With Prof. Palle Jorgensen) Letters in Mathematical Physics (accepted in May 2012)

69. Entropy of Graphs and Information-Theoretical Characterization of Graphs with Fractal Property, Mar., 2011, Advances and Applications in Mathematical Sciences (accepted in May, 2011)

68. Algebras in Resistance Networks and Their Representations, Feb., 2011, (with Prof. Palle Jorgensen) Functional Analysis and Other Mathematics (accepted in Jul., 2011)

67. Operator Algebraic Quotient Structures Induced by Graphs II, Feb. 2011, Complex Analysis and Operator Theory (accepted in Oct., 2011)

66. Free Probability on Operator Algebras Induced by Currents of Electric Resistance Networks, Jan. 2011 (with Prof. Palle Jorgensen) (accepted in Jun., 2011) International Journal of Functional Analysis, Operator Theory & Applications

65. Toeplitz Operators in Hilbert Space Induced by Infinite Graphs, Jan., 2011, Journal of Korean Mathematics Society

64. Free Probability Induced by Electric Resistance Networks on Energy Hilbert Spaces, Jan., 2011, Opuscula Mathematica (with Prof. Palle Jorgensen) (accepted in Mar., 2011)

63. Representations and Operator Algebras Induced by Systems of Resistors in Networks, Jan., 2011, Results in Mathematics (with Prof. Palle Jorgensen)

62. Algebras in Resistance Networks and Their Representations, Dec. 2010, Advances in Computational Mathematics (With Prof. Palle Jorgensen) (rejected in Jan. 2010 => Good rejection)

61. Graph-Matrices and Matricial Graph C*-Algebras, Nov., 2010, Bulletin of Korean Mathematics Society (accepted in Dec. 2010)

60. Free Probability on Operator Algebras Induced by Currents in Electric Resistance Networks, Nov., 2010, SIAM journal on Discrete Mathematics (SIDMA) (with Prof. Palle Jorgensen) (rejected in Jan. 2010 => The referee did not even read Introduction of the paper. Yeah.. whatever..)

59. Groupoid Actions Induced by Electric Resistance Networks and Dissipation Hilbert Space, Oct., 2010, Infinite Dimentional Analysis, Quantum Probability and Related Topics (with Prof. Palle Jorgensen) (rejected in Jan., 2011)

58. Index on von Neumann Algebras Induced by Graphs, Oct., 2010, Applied Mathematical Sciences (accepted in Jan. 2010)

57. Representations and Operator Algebras Induced by Systems of Resistors in Networks, Oct., 2010, (With Prof. Palle Jorgensen) Representation Theory (rejceted in Dec. 2010 ==> See 63!)

56. Measure-Framing on Graphs, and Corresponding von Neumann Algebras, Sep., 2010, Applied Mathematics (accepted in Nov., 2010)

55. Operators Induced by Graphs, Sep., 2010 (With Prof. Palle Jorgensen) Analysis and Mathematical Physics (rejected in Feb. 2011)

54. Entropy of Fractal Graphs, Jul., 2010, (With Prof. Palle Jorgensen) New York Journal of Mathematics

53. Graph Fractaloids: Classification and Application of Graph Groupoids with Fractal Property, Jul., 2010 Invited Paper (a Chapter of a Book) Classification and Application of Fractals, NOVA Publishers (accepted in Jul., 2010)

52. Toeplitz Operators in Hilbert Space over Infinite Graphs, Jul., 2010 (With Prof. Palle Jorgensen) Algebras and Representation Theory (rejected Jan. 2011 ==> Good rejection!)

51. Frames, Fractals, and Radial Operators in Hilbert Space, Jun., 2010, Journal of Mathematics and Science: Advances and Application (accepted in Aug., 2010)

50. Operators Induced by Graphs, Jun., 2010 (With Prof. Palle Jorgensen) Central European Journal of Mathematics (rejected in Sep. 2010: Referees don't understand anything! I never have such referees before! See 55)

49. Fractals in Von Neumann Algebras, Jun., 2010 Applied Mathematics (accepted in Aug. 2010)

48. Diagram Groupoids and von Neumann Algebras, Apr. 2010 Complex Analysis and Operator Theory (accepted June, 2010)

47. Frames, Fractals, and Radial Operators in Hilbert Space, Apr., 2010 (With Prof. Palle Jorgensen) Journal of Math Physics (rejected June, 2010)

46. Directed Graphs, von Neumann Algebras, and Index, Mar., 2010 (With Prof. Palle Jorgensen) Algebras and Representation Theory (accepted June, 2010)

45. Algebraic Structures Induced by Pull-Back Graphs, Mar.. 2010 Applied Mathematics

44. Symmetry in Tensor Algebras over Hilbert Space, Feb.. 2010 (With Prof. Palle Jorgensen) Illinois Journal of Math (accepted in Jun., 2011)

43. Towers of von Neumann Algebras Induced by Graphs, Feb. .2010 Oriental Journal of Math (accepted Jul., 2010)

42. Entropy on Fractal Graphs, Jan., 2010 (With Prof. Palle Jorgensen) Journal of Mathematical Cryptology (rejected Jul., 2010 ==> Good rejection, though... See 54 above!)

41. Group-Framing on Graphs and Corresponding von Neumann Algebras, Jan., 2010, Advances and Applications in Mathematical Sciences (Accepted Mar., 2010)

40. Frames. Fractals and Radial Operators in Hilbert Space, Dec., 2009, (With Prof. Palle Jorgensen) Ergodic Theory and Dynamical Systems (rejected)

39. Operations on Graph-Groupoids, Nov., 2009, (With Prof. Palle Jorgensen) Mathematische Nachrichten (rejected May 2010)

38. Moment Computations of Graphs with Fractal Property, Sep., 2009, (With Prof. Palle Jorgensen) Journal of Applied Math and Computing (accepted in Aug., 2010)

37. Frames, Fractals, and Radial Operators in Hilbert Space, Aug., 2009 (With Prof. Palle Jorgensen) Fractals (rejected ==> "Good Rejection!" ==> See 40)

36. Free Graph Stochastic Processes, Jun., 2009 Journal of Applied Math and Informatics (accepted in Sep., 2009)

35. Moment Computations for Graphs with Fractal Property, May, 2009 (With Prof. Palle Jorgensen) Advanced Math Physics: Special Issues (Quantum Information and Entanglements)

(rejected ==> But... See here, 1 !)

34. Framed Groupoids and W*-Dynamical System, Apr., 2009 (With Prof. Palle Jorgensen) New Journal of Physics

33. C*-Dynamical Systems Induced by Partial Isometries, Apr., 2009 (With Prof. Palle Jorgensen) Advances and Applications in Mathematical Science (accepter in June. 2009)

32. Boundary-Fixed Glued Graphs and their Graph von Neumann Algebras. Mar., 2009, The Open Mathematics Journal

31. Non-commutative Geometry of Locally Finite Directed Graphs: Groupoids and Fractals, Mar., 2009, (With Prof. Palle Jorgensen) Mathematische Nachrichten

30. Fractals in Graph-von Neumann Algebras, Feb., 2009 (With Prof. Palle Jorgensen) Conformal Geometry and Dynamics (rejected ==> Modified to 37)

29. Fractal Property in B(H) Induced by Partial Isometries, Feb., 2009, Complex Analysis and Operator Theory (accepted in Apr., 2009)

28. Measure Framing on Graphs, Feb., 2009, (with Prof. Palle Jorgensen) Journal of Physics A: Mathematical and Theoretical (IOP) (rejected ==> Modified to 37)

27. Classification of Graph Fractaloids, Jan., 2009, (with Prof. Palle Jorgensen) Journal of Math Physics (rejected in May, 2009)

26. Graph Groupoids and Corresponding Representations, Dec., 2008, (Invited Paper: NOVA Publisher) Group Theory: Classes, Representations and Connections, and Applications (NOVA Publisher)

(accepted in Dec., 2008)

25. Graph Fractaloids: Graph Grouopoids with Fractal Property, Dec., 2008, (With Prof. Palle Jorgensen) Journal of Physics A: Mathematical and Theoretical (IOP) (rejected==> Modified to 31.)

24. Applications of Automata and Graphs: Labeling Operators in Hilbert Space II, Sep., 2008, (With Prof. Palle Jorgensen) Journal of Math Physics (accepted in Mar., 2009)

23. Measure Framing on Graphs and Corresponding von Neumann Algebras, Sep., 2008, Pacific Journal of Math (rejected in Oct. 2008 ==> What a beautiful rejection it is!)

22. C*-Sublagebras Generated by a Single Operator in B(H), Sep., 2008, (With Prof. Palle Jorgensen) ACTA Appl. Math.: Banff Special Issues. (accepted in Dec., 2008)

21. Scalar-Valued Free Probability on a Graph von Neumann Algebra, Sep., 2008, Journal of Korean Mathematics Society. (accepted in Oct., 2008)

20. Von Neumann Algebras Generated by Automata, Apr., 2008 : NOVA Publishers, INC: Graphene: Research, Technology and Applications (accepted in Dec., 2008)

19. Operator Algebraic Quotient Structures Induced by Directed Graphs, Mar. 2008 : Complex Analysis and Operator Theory (accepted in Mar., 2008)

18. Towers of Graphs and Towers of Graph von Neumann Algebras, Mar. 2008 (Partially supported by FIC) Bulletin of Korean Mathematics Society (withdrawn because of the delay, but see 25)

17. Applications of Automata and Graphs: Labeling-Operators in Hilbert Space I, Mar. 2008 (With Prof. Palle Jorgensen, Math., U. of Iowa): Special Issues of ACTA Appl. Math: Signal Processing & Symbolic Dynamics (accepted in Oct. 2008)

16. Quotient Graphs and Quotient Groupoids, Feb. 2008 : Journal of Korean Mathematics Society (rejected in Apr., 2008 => Does the referee understand ...? The Application of this paper is accepted at CAOT. See 9)

15. Powers of Multinomials in Commutative Algebras, Feb. 2008 (With Mr. Steve Thompson, a Undergraduate Student, St. Ambrose) American Mathematical Monthly (rejected in Mar., 2008) This is a undergraduate research with my student.

14. Towers of Graphs and Towers of Graph von Neumann Algebras, Feb. 2008 : Trans. of AMS. (rejected in Mar. 2008 => Modified to 18)

13. C*-Subslgebras Generated by Partial Isometries, Dec. 2007 (With Prof. Palle Jorgensen, Math Dep., Univ. of Iowa) Journal of Math Physics (accepted in Aug., 2008)

12. Graph-Matrices over Additive Graph Groupoids, Dec. 2007 : Journal of Applied Math and Computing (accepted in Jan., 2009)

11. Vertex-Compressed Algebras of a Graph von Neumann Algebra, Oct. 2007 : ACTA Applied Math (accepted in Aug., 2008)

10. C*-Algebras Generated by Partial Isometries, Sep. 2007 (With Prof. Palle Jorgensen, Math Dep., Univ. of Iowa): Journal of Applied Math and Computing (accepted in Sep., 2007)

9. Characterization of Amalgamated Free Blocks of a Graph von Neumann algebra, Feb. 2007: Complex Analysis and Operator Theory (accepted in Mar., 2007)

8. Amalgamated Free Blocks of a Graph von Neumann Algebra and Graph-Free Products, Jan. 2007 : International J. of Math (rejected in Jan. 2007 ==> Modified to 9. See 5)

7. Graph Von Neumann Algebras, Oct. 2006 : ACTA Applied Math (accepted in Nov. 2006)

6. Strictly Free Additive Stable Free Random Variables, Oct. 2006 : Far East Journal of Mathematical Sciences (accepted in Nov. 2006)

5. The Moments of Certain Perturbed Operators of the Radial Operator in the Free Group Factor L(F_N), Oct. 2006: Journal of Analysis and Application (accepted in Feb. 2007)

4. Measures on Graphs and Certain Groupoid Measures, Aug. 2006 : Complex Analysis and Operator Theory (accepted in Aug. 2007)

3. Direct Producted W*-Probability Spaces and Corresponding Amalgamated Free Stochastic Integration, Apr. 2006 : Bulletin of Korean Mathematics Society (accepted in Feb. 2007)

2. Group Freeness and Certain Amalgamated Freeness, Mar. 2006 : Journal of Korean Mathematics Society (accepted in Nov. 2007)

1. Moments of Block Operators of Group von Neumann Algebras, Sep. 2005 : Manuscripta Mathematika.