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Početna strana  > ŽIVOT NA MFN > Lične prezentacije > Predrag Rajković
Predrag Rajković

Prof. Dr Predrag Rajković



 Full Professor in Mathematics and  Informatics
(Special Functions, Numerical Analysis, Optimization,
Computer graphics and Programming)

Home-page   http://math.masfak.ni.ac.rs/math/~PredragRajkovic/
Office Location: 606a,

Faculty of Mechanical Engineering,

University of Nis, Serbia

A. Medvedeva 14, 18 000 Nis, Serbia

 

Job-phone: +381-18-500-721  

Fax:             +381-18-588-244

 

E-mail:  pedja.rajk@yahoo.com,

           pedja.rajk@gmail.com,

           pedja.rajk@masfak.ni.ac.rs

 

RESEARCH INTERESTS

¨    Special functions (MSC:33)

     Q-calculus (basic hypergeometric functions ), Special transformations

¨    Numerical Analysis (MSC: 65)

     Orthogonal polynomials,  Numerical integration, Approximation theory

¨    Combinatorics (MSC: 05)

¨    Computer graphics(MSC: 68U)

¨    Mathematical programming (MSC: 90C)

 

WORK EXPERIENCE

 

à      2009.   Full professor for mathematics and informatics

                 (special functions, analysis, programming, geometry, optimization)

                  University of Nis, Faculty of Mechanical Eng., Department for Mathematics

 

à      2004. High assistant professor for mathematics and informatics

                 (numerical analysis, programming and  geometry

                  University of Nis, Faculty of Mechanical Eng., Department for Mathematics

 

à      1999.  Assistant Professor for Numerical Analysis,

                  Computer Programming and  Geometry

                  University of Nis, Faculty of Mechanical Eng., Department for Mathematics

 

à      1984.  Research and teaching assistant for mathematics

            (Numerical Analysis, Computer Programming, Geometry and Calculus)

                  University of Nis, Faculty of Mechanical Eng., Department for Mathematics

 

EDUCATION

 

Doctoral  Dissertation (1998)

 “New Types of Orthogonality of Polynomials  and Their Applications”

  Scientific Area: Numerical Analysis

University of Niš, Faculty of Sciences and Mathematics.

 

 

Master’s Thesis (1991)

 “ Complex Orthogonal Polynomials and Their Applications”,  

Scientific Area: Numerical Analysis, Approximating theory, Quadrature, Orthogonal Polynomials, Differential Equations, Programming.

University of Niš, Faculty of Sciences and Mathematics.

 

            Bachelor of Mathematics (1983)

 University of Niš, Faculty of Sciences and Mathematics.  

INTERNATIONAL  RESEARCH  PROJECTS

 

  1. Multimedia Technology for Mathematics and Computer Science Education, 2002.-2008.

 Partner in the project within the DAAD-Sonderprogramm Akademischer Neuaufbau Südosteuropa  in the framework of the Stability Pact for South Eastern Europe (leader of the project: prof. dr Konrad Polthier)

       2.  Tempus project 145009-Tempus-2008-RS-JPHES, 2010-2012, 

               Conversion Courses for Unemployed University Graduates in Serbia CONCUR.

                3. Integral Transform Methods, Special Functions And Applications, 

               (Project ID_02_2009),  National Science Fund, Ministry of Education and   

               Science of Bulgaria, Project Leader: Dr. Virginia Kiryakova, Bulgarian  

               Academy of Sciences (as a foreign member of the team with  other researchers

              from Bulgaria, Germany, Spain,  Belarus).

 

 

SCHOLARSHIPS AND AWARDS
     

  1. DAAD-scholarship, Germany

      November-December, 2004. at University in Kassel, Germany

           Host:   prof. dr. Wolfram Koepf , 

   AG Computational Mathematics Fachbereich Mathematik / Informatik
             http://www.mathematik.uni-kassel.de/~koepf/

   Theme: “On q-differrence equations and their role in the investigation of

   the orthogonal polynomials and special number sequences”

  1. DAAD-scholarship, Germany,

      University in Kassel, Germany, 2008.

  1. Foreign examiner for doctoral dissertation, Ireland, 2011

      Waterford Insitute, candidate: Aoife Hennessy

      Host: prof. dr Paul Barry  
   

ADVISOR’S  WORK

 

A)    Advisor of doctoral dissertation in mathematics

 

            1. candidate: mr Slađana D. Marinković,

         The Applications Of The Basic Hypergeometric Functions In The  Theory Of

          Orthogonality And Numerical Mathematics,

         doctoral dissertation in mathematics, University of Niš, Faculty of Mathematics

         and Natural Sciences, Niš, 2005.

 

B)    Coadvisor of doctoral dissertation in mathematics

 

 

2.      candidate:  Marko D. Petković,

          The Symbolic Computing Of Hankel Determinants And Generalized Matrix    

           Inverses,

           doctoral dissertation in mathematics and informatics, University of Niš,

           Faculty of Mathematics and Natural Sciences,  2008.

 

C)    Coadvisor of master thesis in mathematics

 

 

3.      candidate: Savić Nataša, coadvisor,

     Generating Functions And Riordan Sequences With Applications On

     Hankel Determinants And Combinatorial Interpretation

           Magister thesis in mathematics and informatics, University of Niš, Faculty of   

           Mathematics and Natural Sciences,  2012.

 

 

D)     Member of commissions for doctoral dissertations 

 

1.      Marko Miladinović, comission member for Ph. D thesis in mathematics and  

     informatics, 2011., University of Niš.

2.      Aoife Hennessy, comission foregn member for Ph. D thesis in mathematics

and   informatics, 2011., Waterford Insitute, Ireland.

 

 

 

REVIEWER

 

I am reiviewer for in the following journals:

 

  1. Applied Mathematics and Compupation;
  2. Journal of Compuational and Applied Mathematics;
  3. Mathematical Computation and Modelling;
  4. Discrete Mathematical Analisys and Applications;
  5. Fractional calculus and applied analysis;
  6. Facta Universitatis;
  7. FILOMAT
  8. Mathematical Journal of Novi Sad

 

 

 

MONOGRAPHS AND BOOKS

 

1) P.M. Rajkovic, S.D. Marinkovic and M.S. Stankovic

                Differential And Integral Calculus Of Basic Hypergeometric Functions

                (monography) Nis, 2008.

         (Mathematical Subject Classification:

        33D15, 33D60, 33D45, 33C45, 39A13,11B65, 26D15, 26A33, 30C15, 41A30)

 

2) Lj. Petkovic, S.Trickovic and P.M. Rajkovic,

                A Collection Of Tasks In Numerical Mathematics,        

                 Faculty of Mechanical Engineering, Nis, 1997.

 

         

PARTICIPATION IN SERBIAN SCIENTIFIC PROJECTS

 

 

1)      Dynamical Stability And Unstability  Of  Mechanical    

2)      Systems Under Stochastical Disruption,

                        Project of Ministry of  Republic Serbia,  2011-2014. 

3)      Deterministic and stochastic  stability of mechanical systems,

        Project of Ministry of  Republic Serbia,  2006-2010.

4)      Stability and nonlinear oscilations of viscoelastic composite platforms,   

        Project of Ministry of  Republic Serbia,  2001-2005.

5)      Methods and Models in theoretical and Applied Mathematics,

Project of Mathematical Institute of Republic Serbia,  1996 - 2001.

6)      Project of Faculty of Mechanical Engineering in Nis, 1996-2001.

7)      Mathematics with Applications, Project of Mathematical Institute of Republic  Serbia, 1991-1995.

 

 

 

CONFERENCE ORGANAZING COMMITTEE

 

 

I was the member of organizing and scientific committee of the next conferences:

 

 

  1. MASHING - The Second International Conference “Mechanical Engineering In The Xxi Century”, Nis, 2013.
  2. SAUM - XI Conference on Systems, Automatic Control and Measure, Niš, 2012.
  3. MASHING - The Second International Conference “Mechanical Engineering In The Xxi Century”, Nis, 2011.
  4. SAUM - X Conference on Systems, Automatic Control and Measure, Niš, 2009.

 

 

 

PROFESSIONAL MEMBERSHIP

 

  1. Serbian Society of Mathematics, Belgrade, Kneza Milosa 35, Serbia

 

 

PUBLICATIONS

 

Total: 84

 

A)  Papers published in  refereed journals (SCI-list):  25

B)  Papers published in  journals with  international editorial board: 17

C)  Papers published in the proceedings of international conferences: 33

D)  Papers published in  abstract-book of international conferences: 9

 

Cited by : 164

 

 

A)  Papers published in  refereed journals (SCI-list)

 

 

  1. Predrag M. Rajković , Paul Barry and Marko D. Petković,

            Sobolev orthogonal polynomials in computing of Hankel determinants,

             Linear algebra and applications 437 (10) (2012), 2417–2428 (M21)

            Cited by 1

 

  1. Slađana D. Marinković,  Miomir S. Stanković, Predrag M. Rajković,

            Functions induced by iterated deformed Laguerre derivative: analytical and  

           operational approach,

            Abstract and Applied Analysis (2012) 1-17.

            Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2012,

             Article ID 190726, 17 pages  (M21)

 

  1. Marko D. Petković, Paul Barry and Predrag M. Rajković,

Closed-form expression for Hankel determinants of the Narayana polynomials,

            Czechoslovak Mathematical Journal, 62 (137) (2012), 39–57 (M23)

 

  1. Miomir S. Stanković, Slađana D. Marinković, Predrag M. Rajković,

            The deformed exponential functions of two variables in the context of various

            statistical mechanics,

             Applied Mathematics and Computation 218 (2011) 2439–2448 (M21)

           Cited by 2

 

  1. Miomir S. Stanković, Slađana D. Marinković, Predrag M. Rajković,

             Deformed and modified Mittag-Leffler polynomials,

             Mathematical and Computer Modelling 54 (2011) 721–728. (M21)

           Cited by 3

 

  1. Marko D. Petković, Predrag M. Rajković and Paul Barry,

The Hankel transform of generalized central trinomial coefficients and related sequences,

            Integral Transforms and Special Functions,  Vol. 22, Issue 1  (2011),  29–44

            (M22)

             Cited by 1

 

  1. Miomir S. Stanković, Predrag M. Rajković, Slađana D. Marinković,

           On The Fractional  q-Derivative Of Caputo Type,

           Comptes rendus de l'Acad_emie bulgare des Sciences 63, No 2, 2010, 1-8. (M23)

 

  1. Paul Barry, Predrag M. Rajković and Marko D. Petković,

            An Application of Sobolev Orthogonal Polynomials to the Computation of a

           Special Hankel Determinant,     

            chapter of the book “Approximation and Computation” (In Honor of Gradimir V.

            Milovanović) Series:  

            Springer Optimization and Its Applications, Vol. 42  (2010), pp. 1-8.  (M13)

             Cited by 9

 

  1. Predrag M. Rajković, Slađana D. Marinković, Miomir S. Stanković,

            A generalization of the concept of q--fractional integrals, 

            Acta Mathematica Sinica, English version, Vol. 25, No. 10 (2009), 1635-1646. 
 
            (M22)

            Cited by 5

 

  1. Bratislav Danković, Predrag M. Rajković, Slađana  D. Marinković,

            On a class of almost orthogonal polynomials,

            Lecture Notes in Computer Science 5434, (M23) Numerical Analysis and its

            Aplications, Springer-Verlag

            Berlin Heidelberg,  (2009) 241—248. S. Margenov, L.G. Vulkov, and J.

           Wa´sniewski (Eds.): NAA 2008

            Proceedings of The Fourth Conference on Numerical Analysis and Applications,

           June (2008), Lozenetz, Bulgaria.

                Cited by 6

 

  1. Slađana D. Marinković,  Predrag M. Rajković, Miomir S. Stanković,

           The inequalities for some types of q-integrals,

           Computers and Mathematics with Applications 56 (2008) 2490–2498 (M21)

           Cited by 12

 

  1. Ratko Pavlović, Predrag Rajković, and Ivan Pavlović,

     Almost Sure Stability of a Moving Elastic Band,

           Journal of Applied Mechanics, July 2008, Volume 75, Issue 4, 041016 (M22)

 

  1. Ratko Pavlović,  Predrag M.  Rajković, I. Pavlović,

            Dynamic stability of the viscoelastic rotating shaft subjected to random

            excitation,

            International Journal of Mechanical Sciences, 50(2008), PP. 359-364.  (M21)

            Cited by 7

 

  1. Wolfram Koepf, Predrag M. Rajković , Slađana D. Marinković,

            Properties of q-Holonomic Functions,

           Journal of Difference Equations and Applications, Vol. 13, No. 7  (2007), 621–

            638. (M21)

                  Cited by 2

 

  1. Predrag M. Rajković, M.D. Petković, P. Barry,

            The Hankel Transform of the Sum of  Consecutive Generalized Catalan

            Numbers,

             Integral Transforms and Special Functions, Vol. 18, Issue 4, 2007, 285--296.  

             (M22)

                Cited by 15

 

  1. Predrag Kozić, Ratko Pavlović, Predrag M.  Rajković,  

            Moment Lyapunov Exponents  and Stochastic Stability of a Parametrically

           Excited Oscillator,

            Meccanica,  Vol. 42 (2007) 323–330. (M22)

             Cited by 1

   
       
  1. Ratko Pavlović, Predrag Kozić, Predrag  M.       Rajković and I. Pavlović,      
     
    2.   
    
            Dynamic Stability of a Thin-Walled Beam Subjected to Axial Loads and End 
 
    
           Moments, 
 
    
            Journal of Sound and Vibration 301 (2007) 690–700)   (M21)
 
    
            Cited by 7
 
    
 
    
       
  1. Miloš      Ivković, Ivan Đordjević, Predrag M. Rajković,      Bane      Vasić,
     
    2.   
    
            Pulse Energy Probability Density Functions For Long-Haul Optical Fiber 
 
    
           Transmission Systems  By Using  
 
    
            Instantons And Edgeworth Expansion, 
 
    
            IEEE Photonics Technology Letters, vol 19, No 20,(2007), 1604-1606. (M21)
 
    
                 Cited by 13
 
    
 
    
19.  Predrag  M.  Rajković , Slađana D. Marinković, Miomir S. Stanković,
 
    
           On q-Orthogonal Polynomials Over  A Collection Of Complex Origin Intervals  
 
    
           Related To Little q-Jacobi Polynomials, 
 
    
           The Ramanujan Journal , Vol. 12, No. 2 (2006), 245-255. (M22)
 
    
            Cited by 1
 
    
 
    
       
  1. Predrag  M. Rajković , Slađana  D. Marinković and Miomir      S.      Stanković,
     
    2.   
    
            On q-Newton-Kantorovich Method  for Solving Systems of Equations,  
 
    
           Applied Mathematics and Computation,  vol. 168/2 (2005 ) 1432-1448 . (M22) 
 
    
              Cited by 5
 
    
 
    
21.  Slađana D. Marinković, Predrag M. Rajković,
 
    
            The q--Analogues Of Laguerre Polynomials  Over a Collection of Complex 
 
    
            Origin Intervals, 
 
    
            Integral Transforms and Special Functions, Vol. 16, No. 2 (2005), 159-169. 
 
    
            (M22)
 
    
 
    
22.  Ratko Pavlović, Predrag Kozić and Predrag M. Rajković, 
 
    
22.Influence of  randomly varying damping coefficient on the dynamic stability of continuous systems, 
 
    
             European  Journal of Mechanics A/Solids,  24 (2005), 81-87.  (M21)
 
    
                Cited by 3
 
    
 
    
23.  Slađana D. Marinković, Bratislav Danković, Miomir S. Stanković, Predrag M. Rajković,  
 
    
Orthogonality Of Some Sequences  Of The Rational Functions  And The Muntz Polynomials, 
 
    
            Journal of Computational and Applied Mathematics vol. 163,  (2004), 419-427. 
 
    
            (R51b)
 
    
 
    
24.  Ratko Pavlović, Predrag Kozić, Predrag M. Rajković, 
 
    
24.Influence of transverse shear on the stochastic instability of viscoelastic beam,
 
    
24.International Journal of Solids and Structures, Stanford, California, Vol. 38,  
 
    
            Issues 38-39, September 2001, 6829-6837. (M21)
 
    
 
    
25.  Gradimir V. Milovanović, Predrag M.  Rajković,
 
    
           On Polynomials  Orthogonal on a Circular  Arc,
 
    
           J. Comp. Appl. Math., vol. 51, North Holland, 1994., 1-13 (M22)
 
    
              Cited by 11
 
    
 
    
B) Papers published in  journals with  international editorial board 
 
    
 
    
1.      Predrag M.  Rajković, Paul Barry, Nataša Savić, 
 
    
                  Number sequences in an integral form with a generalized 
 
    
                  convolution property and Somos-4 Hankel  determinants, 
 
    
               Mathematica Balkanica, New Series Vol. 26 (2012) Fasc. 1-2, 219-228.
 
    
 
    
2.      Predrag M. Rajković, Sladjana D. Marinković, 
 
    
A comparison between different concepts of almost orthogonal polynomials, 
 
    
Functional Analysis, Approximation and Computation 1:2 (2009), 37-46.
 
    
 
    
3.      Predrag M. Rajković, S.D. Marinković, M.S. Stanković,
 
    
 Fractional Integrals and Derivatives in q-Calculus,
 
    
Applicable Analysis and Discrete Mathematics, 1 (2007), 311–323.  (M51)
 
    
Cited by 27
 
    
 
    
4.      Predrag M. Rajković, S.D. Marinković, M.S. Stanković, 
 
    
On q–Analogs of Caputo Derivative and Mittag–Leffler Function, 
 
    
Fractional Calculus and Applied Analysis,  (ISSN 1311-0454) ,
 
    
vol. 10, No 4 (2007), 359-374.
 
    
Cited by 8
 
    
 
    
5.      M. Stanković , Predrag M. Rajković and S.D. Marinković,
 
    
Inequalities Which Include q-Integrals, 
 
    
Bulletin T. CXXXIII de l’Academie serbe des sciences et des arts, 
 
    
Classe des Sciences mathématiques et naturelles, 
 
    
Sciences Mathématiques, No 31, Beograd 2006, 137-146. (M51)
 
    
 
    
6.      Predrag M. Rajković, M.S. Stanković and S.D. Marinković, 
 
    
A Method For Numerical Evaluating Of  Inverse Z-Transform,
 
    
Facta Universitatis, Nis, Ser. Mechanics, Automatic Control and Robotics, 
 
    
Vol. 4, No 16, 2004 pp. 133-139 UDC 519.6(045) 
 
    
 
    
7.      Predrag M. Rajković, Milos Ivković,  Marko Petković,
 
    
A Conjecture About Positivity   Of The PolynomialsObtained By The Expanding Of A Product,
 
    
Mathematica Balkanica, New Series Vol. 18, 2004., Fasc. 3-4, 419-430.
 
    
(exposed at  Minisymposium "Transform Methods and Special Functions"
 
    
Part of The Congress is organized by MAthematical 
 
    
Society of SouthEastern Europe -MASSEE), 2003. Borovets, Bulgaria.  
 
    
Cited by 2
 
    
 
    
8.     Predrag M. Rajković, M.S. Stanković and S.D. Marinković, 
 
    
8.On q-Iterative Methods For Equation Solving, 
 
    
                  Novi Sad Journal of Mathematics, vol 33, No 2,   2003., 127-137.  (M51)
 
    
( Exposed at Conference of Applied Mathematics PRIM 2002, May 2002, Zlatibor, Serbia, Yugoslavia).
 
    
Cited by 2
 
    
 
    
9.      Predrag M. Rajković, M.S. Stanković and S.D. Marinković, 
 
    
Mean Value Theorems In q-Calculus,
 
    
Matematicki vesnik 54 (2002),  Beograd, 171-178. (M51)
 
    
(Proceedings of  International Conference "Mathematical Analysis and Applications", 
 
    
October 2002, Nis, Yugoslavia).
 
    
Cited by 12
 
    
 
    
10.  Predrag M. Rajković,
 
    
On Integration Of Nearly Singular Functions By The Quadratures  Over The Semicircle With Equal Weights,
 
    
Facta Universitatis, Ser. Mechanics, Automatic Control and Robotics, vol. 3, No 12, 2002., 359-365 
 
    
(Proc. of V Yugoslav Symposium on Nonlinear Mechanics, Nis, Yugoslavia, 2000.)
 
    
 
    
11.  A. Cvetković, Predrag M.  Rajković and M. Ivković, 
 
    
Catalan Numbers, The Hankel Transform And Fibonacci Numbers, 
 
    
The electronic Journal of Integer Sequences, ISSN 1530-7638, Dep. of Comp. Sc., University of Arizona, USA, May 2002.
 
    
Cited by 46
 
    
 
    
12.  Predrag M. Rajković and S. Marinković, 
 
    
12.On q-Extensions Of Generalized Hermite Polynomials,
 
    
FILOMAT,  vol. 15, 2001, Nis, Yugoslavia. 277-283.
 
    
Cited by 7
 
    
 
    
13.  G.V. Milovanović, Predrag  M. Rajković, Z.M. Marjanović,
 
    
Zero Distribution Of Polynomials Orthogonal On The Radial Rays In The Complex Plane,
 
    
Facta Universitatis (Nis), Ser. Mathem. Inform. 12 (1997), 127-142.
 
    
 
    
14.  G.V. Milovanović, Predrag M. Rajković, Z.M. Marjanovic,
 
    
A Class Of Orthogonal Polynomials On The Radial Rays In The Complex Plane (II part),
 
    
Facta Univ., Ser. Math. Inform., Nis, vol. 11, 1996, 29-47
 
    
 
    
15.  G.V. Milovanović, Predrag M. Rajković, Z.M. Marjanović,
 
    
15.On Properties Of Some Nonclassical Orthogonal Polynomials,
 
    
15.Filomat, vol. 9, 101—111, Nis, 1995.
 
    
 
    
16.  G.V.Milovanović and Predrag M. Rajković, 
 
    
16.Complex  Orthogonal Polynomials With The Hermite Weight,
 
    
Publ. Elektrotehn. Fak. Ser. Mathem.,  Beograd, 1995., vol. 6, 63-73.
 
    
Cited by 2
 
    
 
    
17.  G.V.  Milovanović, Predrag M. Rajković,
 
    
Geronimus Concept Of Orthogonality  For Polynomials Orthogonal On A Circular  Arc,
 
    
Rendiconti di Mat., Ser. VII, vol.10, Roma, 1990., 383-390.
 
    
Cited by 4
 
    
 
    
 
    
C)  Papers published in the proceedings of international conferences 
 
    
 
    
 
    
 
    
1.      Bratislav Danković, Predrag M.  Rajković,  Miomir S. Stanković, Slađana Marinković, 
 
    
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