Richard F Patterson

Professor • of Mathematics and Statistics, Graduate Program Director and Advising Coordinator

Mathematics & Statistics • College of Arts & Sciences

Areas of Expertise

Discrete Functional Analysis-Summability and Classical Statistics

Education

 

Doctor of Philosophy, 1997

Kent State University

            Dissertation: Analysis\Summability

            Dissertation Director: John Fridy, Ph. D.

 

Master of Arts in Mathematics, 1993

Kent State University,

            Major: Applied Mathematics

 

Bachelor of Science in Mathematics, 1989

Saint Paul’s College

            Major: Mathematics

Biography

 

2014 - Present    Graduate Program Director & Advising Coordinator        

As the Graduate Program Director for the Department of Mathematics and Statistics, I serve as the primary point of contact for all stakeholders (both external and internal) and provide academic advising to students within the program. I assist the department chair in representing the department on college, university, and community committees. I also serve as an interim department chair as needed in the absence of the chair.

           

            2009 - Present                       Professor

                                                University of North Florida, Jacksonville, FL

                                                 Department of Mathematics and Statistics

            2004 - 2009                 Associate Professor (Tenured)

                                                University of North Florida, Jacksonville, FL

                                                Department of Mathematics and Statistics

            1999 - 2004                Assistant Professor

                                                University of North Florida, Jacksonville, FL

                                               Department of Mathematics and Statistics

                1997 - 1999                              Assistant Professor

                             Duquesne University, Pittsburgh, PA

                                               Department of Mathematics and Computer Sciences

 

 

TEACHING EXPERIENCE

University of North Florida (1999-Present)                                      

Duquesne University (1997-1999)                            

Kent State University (1992-1997)                           

Awards

 

2010                Outstanding Faculty Scholarship Award

2007                Disability Appreciation Award     

1998                Duquesne University Presidential Research Scholarship Award

1997-1998       Project Next Fellow

1989-1992       Patricia Harris Fellow

Publications & Presentations

 

Nuray, F. & Patterson, R. F. (2015). Entire bivarate function of exponential type. Bulletin

           of Mathematical Sciences, DOI 10.1007/s13373-015-0066-x

 

Nuray, F. & Patterson, R. F. (2015). Some Tauberian theorems for four-dimensional Euler

          and Borel summability. Advances in Difference Equations, 50(1), 8pp.

 

Patterson, R. F. & Savas E., (2014). Four-dimensional matrix of geometrically dominated 

          double series. Numerical Functional Analysis and Optimization, 36(2), 20-247.

 

Patterson, R. F., (2014). Inclusion relations among methods of four-dimensional  

          summability compounded from given four-dimensional methods. Acta

          Mathematica Vietnamica, 39(3), 277–285.

 

Patterson, R. F. & Savas, E., (2013). Characterization of asymptotic statistical equivalent

          double and single sequences.  Applied Mathematics and Computation, 224(11),

          484-491.

 

Patterson, R. F. & Savas E., (2013). On sequence of continuous functions having

          continuous limit. Publication Mathematicae Debrecen, 82(1), 43-58.

 

Patterson, R. F., (2013). A Theorem on entire four-dimensional summability methods.

          Applied Mathematics and Computation, 219(14), 7777-7782.

 

Patterson, R. F. & Savas E., (2013). On sequence of continuous functions having

          continuous limit II. Filomat, 27(5), 931-935.

 

Patterson, R. F., (2012). Four-dimensional matrix characterization of P-convergent field

          of summability method. Applied Mathematics and Computation, 219(12), 6783-

          6791.

 

Patterson, R. F., (2013). RH-regular transformations which sums a given double

           Sequence. Filomat, 27(4), 625-627.

 

Patterson, R. F. & Savas E., (2013). RH-regular of unbounded double sequence.

           The journal Rendiconti dell'Istituto di Matematica dell'Università di Trieste, 45, 1-

           9.

 

Patterson, R. F. & Savas E., (2012). Asymptotic equivalence of double sequences.

           Hacettepe Journal of Mathematics and Statistics, 41(4), 1-11.

 

Patterson, R. F. & Savas E., (2012). Multidimensional matrix characterization of

           equivalent double sequences. Studia Scientiarum Mathematicarum Hungarica,

           49(2), 269-281.

 

Patterson, R. F. & Savas E., (2012). Rate of P-convergence over equivalent classes of

            double sequence spaces. Positivity, 16(4) 739-749.

 

Patterson, R. F. & Savas E., (2012). RH-conservative matrix characterization of P-

           convergence in probability. Journal of Computational and Applied Mathematics,

          63(6), 1020-1025.

 

Patterson, R. F. & Savas E., (2011). Matrix summability of statistically P-convergence

            Sequences. Filomat, 25(4), 55-62.

 

Patterson, R. F. & Savas E., (2011). Double sequence transformations that guarantee a

            given rate of P-convergence. Filomat, 25(1), 129-135.

 

Savas, E. & Patterson, R. F. (2011). Some double lacunary sequence spaces defined

            by Orlicz functions. Southeast Asian Bulletin of Mathematics, 35(1), 103-110.

 

Patterson, R. F., (2011). Equivalence of methods for the summation of double

             sequences. Applied Mathematics Letters, 24(2), 107-110.

 

Savas, E. & Patterson, R. F., (2011). Double sequence spaces defined by a

           Modulus. Mathematica Slovaca, 61(2), 245-256.

 

Patterson, R. F. & Savas E., (2011). A category theorem for double sequences. Applied

            Mathematics Letters, 24(10), 1680-1684.

 

Patterson, R. F. & Sen, P., (2011). Characterization of the central limit theorem by the 

           Burmann power series. International Journal of Mathematical and Statistics,

           9(S11) 68-77.

 

Patterson, R. F. & Rhoades, B. E., (2010). Four Dimensional Matrix that induces the

           Double   Gibbs Phenomenon. Acta Mathematica Hungarica, 129(1-2), 142-15.2

 

Patterson, R. F. & Savas, E., (2010). P-asymptotically equivalent in probability,

           Sarajevo Journal of Mathematics, 6(19), 2, 217-228.

 

Patterson, R. F. & Savas, E., (2010). Consistent classes of double summability

           methods. Applied Mathematical Letters, 23990, 831-835.

 

Patterson, R. F. & Savas, E., (2010). Double sequence transformations that guarantee

            a given rate of P-convergence. FILOMAT, 25(2) 129-135.

 

Patterson, R. F. & Rhoades, B. E., (2009). Four-Dimensional Matrix Transformation

            and the double Gibbs’ Phenomenon. Mathematical Communications, 14(4), 7-12.

 

Patterson, R. F. & Savas, E., (2009).  Double σ-convergence lacunary statistical

             sequences. Journal of Computational Analysis and Applications, 11(4), 610-615.

 

Patterson, R. F. (2009). Analogues of some Tauberian Theorems for Bounded

           Variation. Acta Mathematica Hungarica (Szeged), 122(3), 255-271.

 

Savas, E. & Patterson, R. F., (2009). On double statistical P-convergence of fuzzy

             numbers, Journal of Inequalities and Applications, Art. ID 423792, 8pp.

 

Patterson, R. F. & Savas, E., (2009). Regularity characterizations of asymptotically

            probability equivalent sequences.  Applied Mathematics Letters, 22(10), 1491-95.

 

Savas, E. & Patterson, R. F., (2008). An extension asymptotically lacunary statistical

             equivalent  sequences. The Aligarh bulletin of mathematics, 27(2), 109-113.

 

Patterson, R. F. & Savas, E. (2008). Summability of double independent random

           variables. Journal of Inequalities and Applications, Art ID 948195 12pp.

 

Patterson, R. F. & Lemma, M. (2008). Four Dimensional Matrix Characterization of

           double Oscillation via RH-conservative and RH-multiplicative matrices. Central

         European Journal of Mathematics, 6(4) 581-594.

 

Patterson, R. F., Connor, J., & Kline, J. (2008). Matrix characterization of oscillation for

           double  sequences. Central European Journal of Mathematics, 6(3), 488-496.

 

Harry, M. & Patterson, R. F. (2008). Core theorems for double subsequences and

            rearrangements. Acta Mathematica Hungarica (Szeged),

            http://www.springerlink.com/content/a8u448376m463jn2

 

Savas, E. & Patterson, R. F. (2008). (\bar{λ},σ) - double sequence spaces via Orlicz

           function and  double statistical convergence. Journal of Computational Analysis

           and Applications, 10(1), 101-111.

 

Savas, E. & Patterson, R. F. (2007). (Aσ)Δ - double sequence spaces  via Orlicz

           function and double statistical convergence. Iranian Journal of Science and

           Technology, Transaction A, 31(4), 357-367.

 

Savas. E. & Patterson, R. F. (2007). Erratum to “Lacunary statistical convergence of

         Multiple sequences.” [Applied Mathematical Letters, 19, 527-534]. Applied

         Mathematical Letters, 20(11), 1174-1174.

 

Patterson, R. F. (2007). λ – rearrangements characterization of double sequences

           Pringsheim limit points. International Journal of Mathematics and Mathematical

           Sciences,  Art. ID 28205, 9pp.

 

Savas, E. & Patterson (2007). Double sequence spaces defined by Orlicz functions.  

           Iranian Journal of Science and Technology, Transaction A, 31(2), 183-188.

 

Savas, E. & Patterson, R. F. (2007). Double sequence spaces characterized by lacunary

            sequences. Applied Mathematical Letters, 20(9) 964-970.

 

Patterson, R. F. & Savas, E. (2007). Uniformly summable double sequences. Studia

            Scientiarum Mathematicarum Hungarica, 44(1), 147-158.

 

Patterson, R. F. & Savas, E. (2007). Multidimensional matrix characterizations of the

           Banach and Pringsheim core. Applied Mathematical Letters, 20, 357-365.

 

Patterson, R. F. & Savas, E. (2006). On asymptotically lacunary statistical equivalent

           sequences. Thai Journal of Mathematics, 4(2), 267-272.

 

Savas, E. & Patterson, R. F. (2006). Some σ - double sequence spaces defined by Orlicz

            function. Journal of Mathematical Analysis and Applications, 324(1), 525-531.

 

Savas, E. & Patterson, R. F. (2006). Generalization of two asymptotically statistical

            equivalent theorems. FILOMAT (Niš), 20(2), 81-86.

 

Savas, E. & Patterson, R. F. (2006). σ–Asymptotically lacunary statistical equivalent

            sequences. Central European Journal Mathematics, 4(4), 648-655.

 

Savas. E. & Patterson, R. F. (2006). Lacunary statistical convergence of multiple

            sequences. Applied Mathematical Letters, 19, 527-534.

 

Savas, E. & Patterson, R. F. (2005).  On some double almost lacunary sequence spaces

           defined by Orlicz functions. FILOMAT (Niš), 19, 35-44.

 

Savas, E. & Patterson, R. F. (2005). An Orlicz extension of some new sequence spaces.

           Rendiconti dell'Istituto di Matematica dell'Università di Trieste, 37, 145-154.

 

Sen. P. & Patterson, R. F. (2005). A general probability distribution using Bürmann

           power series. Journal of Mathematics and Statistics, 1(3), 189-193.

 

Patterson, R. F., Sen, P. & Rhoades, B. (2005). A Tauberian theorem for generalize

           power series method. Applied Mathematical Letters, 18(10), 1127-1133.

 

Patterson, R. F. & Savas, E. (2005). Korovkin and Weierstrass approximation via

           lacunary statistical convergent. Journal of Mathematics and Statistics, 1(2), 165-

           167.

 

Savas E., Vatan Karakaya, & Patterson, R. F. (2005). Inclusion theorems for double

           lacunary sequence spaces. Acta Mathematica Hungarica, (Szeged), 20, 63-73.

 

Patterson, R. F. & Savas, E. (2005). Lacunary statistical convergence of double

   sequences. Mathematical Communications, 10(1), 55-61.

 

Patterson, R. F. (2005). Four-dimensional Tauberian theorems via block dominate

           matrices. Tamkang Journal of Mathematics, 36(1), 81-85.

 

Patterson, R. F. and Rhoades, B. (2004). Summability of λ – rearrangements for double

           sequences. Analysis (Munich), 24, 213-225.

 

Patterson, R. F. (2004). Four dimensional characterizations of bounded double                                                                          sequences. Tamkang Journal of Mathematics, 35(2), 129-134.

 

Patterson, R. F. (2004). Four dimensional characterization of absolute summability.

           Soochow Journal of Mathematics, 30(1), 21-26.

 

Patterson, R. F. (2004). Four dimensional matrix characterization of Pringsheim core.

           Southeast Asian Bulletin of Mathematics, 27(5), 899-906.

 

Patterson, R. F. (2003). On asymptotically statistical equivalent sequence. Demonstratio

          Mathematica, 36(1), 149-153.

 

Patterson, R. F. (2002). Rate preservation of double sequences under l-l type

           transformation. International Journal of Mathematics and Mathematics Sciences,

          30(10), 637- 643.

 

Patterson, R. F. (2002). Comparison theorems for four-dimensional regular matrices.

          Southeast Asian Bulletin of Mathematics, 26(2), 299-305.

 

Patterson, R. F. (2002). Rate of convergence for double sequences. Southeast Asian

           Bulletin of Mathematics, 26(3), 469-478.

 

Patterson, R. F. (2002). Characterization for the limit points of stretched double

           sequences. Demonstratio Mathematica, 35(1), 103-109.

 

Patterson, R. F. (2001). Analogues of some Tauberian theorems for stretchings.

           International Journal of Mathematics and Mathematical Sciences, 27(2), 99-109.

 

Patterson, R. F. (2000). Analogues of some fundamental theorems of summability                     Theory. International Journal of Mathematics and Mathematical Sciences,              23(1), 1-9.

 

Patterson, R. F. (2000). Invariant core theorems for double sequences. Southeast Asian

           Bulletin of Mathematics, 24(3), 421-429.

 

Patterson, R. F. (1999). Subseries of double series, which are not absolutely P- 

           convergent. Soochow Journal of Mathematics, 25(3), 249-257.

 

Patterson, R. F. (1999). Double sequences core theorems. International Journal of

          Mathematics and Mathematical Sciences, 22(4), 785-793.

 

Patterson, R. F. (1999). A characterization for limit points of double sequences.

           Demonstratio Mathematica, 32 (4), 775-780.

 

 

 

CITATIONS:

 

Citations to scholarship by Richard F. Patterson (includes edited publication) are found in several books, dissertations, scholarly papers, and proceedings. This scholarship is also cited in the following peer review journals:

 

  1. Abstract and Applied Analysis
  2. Acta Mathematica Hungarica (Hungary)
  3. Acta Mathematica Sinica  (China)
  4. Acta Mathematica Vietnamica (Vietnam)
  5. Acta Scientiarum Technology (Brazil)
  6. Acta Universitatis Apulensis (Romania)
  7. Acta Universitatis Matthiae Belii, series Mathematics (Solvakia)
  8. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (Czech Republic)
  9. Advances in Difference Equations
  10. Advances in Inequalities and Applications
  11. Afrika Matematika (South Africa)
  12. Aligarh bulletin of mathematics
  13.  Analele stiintifice Ale UniversitiiAlexnndru Ioan Cuza” Din Iasi-(SN) Matematica (Romania)
  14. Analele Universitatii "Ovidius" Constanta - Seria Matematica (Romania)
  15. Analysis (Germany)
  16. Annals of Fuzzy Mathematics and Informatics (Korea)
  17. Annals of the Alexandru Ioan Cuza University (Romania)
  18. Annals of the University of Craiova, Mathematics and Computer Science Series (Romania)
  19. Annali Dell’universita Di Ferrara (Italy)
  20. Applied Mathematics and Computation
  21. Applied Mathematics & Information Sciences
  22. Applied Mathematics Letters
  23. Arab Journal of Mathematical Sciences (Saudi Arabia)
  24. Boletim da Sociedade Paranaense de Matemática (Brazil)
  25. Bulletin of the Belgian Mathematical Society (Belgium)
  26. Bulletin of the Iranian Mathematical Society (Iran)
  27. Bulletin of the Korean Mathematics Society (Korea)
  28. Bulletin of Mathematical Sciences
  29. Central European Journal of Mathematics (Poland)
  30. Chinese Journal of Mathematics (China)
  31. College Mathematics (China)
  32. Communications de La Faculte Des Sciences De L’Universite Ankara - Series A1 (Turkey)
  33. Communications of the Korean Mathematical Society (Korea)
  34. Computers & Mathematics with Applications
  35. Contemporary Analysis and Applied Mathematics (Turkey)
  36. Cubo, A Mathematical Journal (Brazil)
  37. Czechoslovak Mathematical Journal (Czech Republic)
  38. Demonstratio Mathematica (Poland)
  39. Electronic Journal of Mathematical Analysis and Applications
  40. Far East Journal of Mathematical Sciences (India)
  41. Fasciculi Mathematici (Poland)
  42. Filomat (Serbia)
  43. General Mathematics Notes (Jordan)
  44. Global Journal of Mathematical Analysis (Germany)
  45. Hacettepe Journal of Mathematics and Statistics (Turkey)
  46. Information Sciences
  47. International Journal of Algebra and Statistics
  48. International Journal of Analysis
  49. International Journal of Mathematical Analysis
  50. International Journal of Mathematics and Mathematical Sciences
  51. International Journal of Mathematics and its Applications
  52. International Journal of Mathematics Trends and Technology (India)
  53. International Journal of Science and Research
  54. International Journal of Scientific and Innovative Mathematical Research (India)
  55. International Journal of Modeling and Optimization
  56. International Mathematical Forum (Bulgaria)
  57. International Scholarly Research Network
  58. International Scholarly Research Notices
  59. Iranian Journal of Fuzzy Systems (Iran)
  60. Iranian Journal of Science & Technology (Iran)
  61. Istanbul Ticaret Üniversitesi Fen Bilimleri Dergisi (Turkey)
  62. Journal of Functions Spaces
  63. Journal of Huaqiao University (Natural Sciences)
  64. Journal of Intelligent and Fuzzy Systems (Netherlands)
  65. Journal of Inequalities and Application
  66. Journal of Jimei University (Natural Sciences)
  67. Journal of Mathematical Analysis Journal of Function Spaces and Applications
  68. Journal of Mathematical Analysis and Applications
  69. Journal of Mathematical Study (China)
  70. Journal of Mathematics (China)
  71. Journal of Mathematics and Statistics
  72. Journal of Ningde Teachers College (Natural Sciences) (China)
  73. Journal of Sanming University (China)
  74. Journal of Shaoguan University (Natural Sciences) (China)
  75. Journal of Southwest China Normal University (Natural Sciences) (China)
  76. Journal of Xiamen University (Natural Sciences) (China)
  77. Journal of the Egyptian Mathematical Society (Egypt)
  78. Kathmandu University Journal of Science, engineering and Technology (Nepal)
  79. Lobachevskii Journal of Mathematics (Russia)
  80. МАТЕМАТИЧКИ ВЕСНИ (Russia)
  81. Mathematical and Computer Modelling
  82. Mathematical Communications (Croatia)
  83. Mathematical Inequalities & Applications
  84. Mathematical Sciences (Russia)
  85. Mathematica Slovaca (Solvak Republic)
  86. Michigan Journal of Mathematics
  87. Miskolc Mathematical Notes (Hungary)
  88. Nepal Journal of Science and Technology (Nepal)
  89. New Mathematics and Natural Computation
  90. Note di Matematica (Italy)
  91. Numerical Functional Analysis and Optimization
  92. Periodica Mathematica Hungarica (Hungary)
  93. Positivity
  94. Proyecciones Journal of Mathematics (Chile)
  95. Progress in Applied Mathematics
  96. Proceedings of the Estonian Academy of Sciences (Estonia)
  97. Publicationes Mathematicae Debrecen (Hungary)
  98. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences (India)
  99. Published in IET Signal Processing (United Kingdom)
  100.  Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics (Italy)
  101. Rendiconti del Seminario Matematico Università e Politecnico di Torino (Italy)
  102. Research and Reviews: Discrete Mathematical Structures (India)
  103. Results in Mathematics
  104. Ricerche di matematica (Nepal)
  105. Sarajevo Journal of Mathematics (Bosnia Herzegovina)
  106.  Science in China Series A: Mathematics (China)
  107.  Selcuk Journal of Applied Mathematics (Turkey)
  108.  Soochow Journal of Mathematics (China)
  109. Southeast Asian Bulletin of Mathematics (China)
  110.  Studia Universitatis Babes-Bolyai, Mathematica (Romania)
  111.  Studies in Mathematical Sciences (Canada)
  112. Studia Scientiarum Mathematicarum Hungarica (Hungary)
  113.  Tamkang Journal of Mathematics (Taiwan)
  114. Tatra Mountains Mathematical Publications (United Kingdom)
  115. Taiwanese Journal of Mathematics  (Taiwan)
  116.  Tbilisi Mathematical Journal (London)
  117. Thai Journal of Mathematics (Thailand)
  118.  Theory and Applications of Mathematics & Computer Science (Poland)
  119.  World Academy of Science, Engineering and Technology (France)

PRESENTATIONS: Referred National and International Conferences

Patterson, R. F. (2004). Four-dimensional characterizations of λ-rearrangement of  double sequences. Midwest Regional Summability Conference.

Patterson, R. F. (2002). Four-dimensional characterizations Pringsheim core sequences. Midwest  Regional Summability Conference.

Patterson, R. F. (2001). Rate of convergence of double sequences. Midwest Regional Summability Conference.

Patterson, R. F. (1999). Four-dimensional characterizations of almost P-convergent double sequences. Midwest Regional Summability Conference.

Patterson, R. F. (1999). Four-dimensional characterization of double sequence limit points. American Mathematics Society Conference; San Antonio, Texas.

Patterson, R. F. (1998).  Four-dimensional characterizations of double sequences limit points. Joint Meeting: The Mathematical Association of America and American Mathematics Society (MAA & AMS).

 

Invited Presentations

Patterson, R. F. (2013). Analogues of some Tauberian theorems for bounded variation.

2nd International Eurasian Conference on Mathematical Sciences and Application. International Sarajevo of University, Sarajevo, Bosnia and Herzegovina

Patterson, R. F. (2011). Rearrangement of double sequences. International Conference  on Analysis and its Applications. Aligarh Muslim University Uttar Pradesh, India

                                 Patterson, R. F. (2008). Four-dimensional matrix characterization of double sequences.  Istanbul Ticaret University, Turkey

Patterson, R. F. (2008). Matrix characterization of bounded variation via double subsequences stretching, Summability workshop days, Istanbul, Turkey

 Patterson, R. F. (2008). Pringsheim convergence and rate of convergence.  Istanbul   Aydin University, Turkey

        Patterson, R. F. (2008). Summability and Matrix Transformations. Colloquium Istanbul  Ticaret University, Turkey

  Patterson, R. F. (2005). Matrix Characterization of Pringsheim. Colloquium Yüzüncü Yil  University, Turkey

 Patterson, R. F. (2005). Title:  Summability λ–rearrangement for double sequences,   Colloquium Ohio University

 Patterson, R. F. (2001). Title: Graduate Studies in Mathematics and Statistics University of North Florida, Savannah State          University, Savannah, GA (2001).

Patterson, R. F. (2001). Title: Graduate Studies in Mathematics and Statistics at University of North Florida. The National Association of Mathematicians –   Undergraduate MATHFest XI

PattersonContact Information

(904) 620-3714

rpatters@unf.edu