Dragan Jukić

 

Full Professor
Department of Mathematics
Josip Juraj Strossmayer University of Osijek
Trg Ljudevita Gaja 6
Osijek, HR-31000, Croatia
phone: +385-31-224-800
fax: +385-31-224-801
email:  jukicd @ mathos.hr
office:  35/I

 


Research Interests

As a mathematician, my fields of interest are numerical and applied mathematics. Specifically, my research focuses on the following areas:
  • Parameter estimation
  • Nonlinear least squares problems
  • Curve fitting
  • Smoothing methods
  • Mathematical modelling

Degrees

PhD in mathematics, Department of Mathematics, University of Zagreb, 1996.
MSc in mathematics, Department of Mathematics, University of Zagreb, 1990.
BSc in Mathematics and Physics, Josip Juraj Strossmayer University of Osijek, 1986.
 

Publications

 
Journal Publications

  1. Dragan Jukić, A simple proof of the existence of the best estimator in a quasilinear regression model, Journal of optimization theory and applications 162 (2014), 293-302
    We provide a theorem on the existence of the best estimator in a quasilinear regression model, from which the existence of the best estimator for the whole class of nonlinear model functions follows immediately. The obtained theorem both extends and generalizes the previously known existence result. Our proof is elementary and rests on the basic knowledge of linear algebra and calculus.
  2. Darija Marković, Dragan Jukić, Total least squares fitting the three-parameter inverse Weibull density, European Journal of Pure and Applied Mathematics 7/3 (2014), 230-245
    The focus of this paper is on a nonlinear weighted total least squares fitting problem for the three-parameter inverse Weibull density which is frequently employed as a model in reliability and lifetime studies. As a main result, a theorem on the existence of the total least squares estimator is obtained, as well as its generalization in the l_q norm (1≤q<∞).
  3. Dragan Jukić, On nonlinear weighted least squares estimation of Bass diffusion model, Applied mathematics and computation 219/14 (2013), 7891-7900
    The Bass model is one of the most well-known and widely used models of first-purchase demand. Estimation of its parameters has been approached in the literature by various techniques. The focus of this paper is on a nonlinear weighted least squares fitting approach. As a main result, two theorems on the existence of the least squares estimate are obtained. One of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate. Some numerical experiments are given to illustrate the efficiency of our approach.
  4. Darija Marković, Dragan Jukić, On parameter estimation in the bass model by nonlinear least squares fitting the adoption curve, International Journal of Applied Mathematics and Computer Science 23/1 (2013), 145-155
    The Bass model is one of the most well-known and widely used first-purchase diffusion models in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the parameter estimation approach for the Bass model based on nonlinear weighted least squares fitting of its derivative known as the adoption curve. We show that it is possible that the least squares estimate does not exist. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the ls norm (1 ≤ s < ∞). One of them gives necessary and sufficient conditions which guarantee the existence of the least squares estimate. Several illustrative numerical examples are given to support the theoretical work.
  5. Dragan Jukić, On the $l_s$-norm generalization of the NLS method for the Bass model, European Journal of Pure and Applied Mathematics 6/4 (2013), 435-450
    The best-known and widely used model in diffusion research is the Bass model. Estimation of its parameters has been approached in the literature by various methods, among which a very popular one is the nonlinear least squares (NLS) method proposed by Srinivasan and Mason. In this paper, we consider the l_s-norm (1≤s<∞) generalization of the NLS method for the Bass model. Our focus is on the existence of the corresponding best l_s -norm estimate. We show that it is possible for the best l_s-norm estimate not to exist. As a main result, two theorems on the existence of the best l_s -norm estimate are obtained. One of them gives necessary and sufficient conditions which guarantee the existence of the best l_s-norm estimate.



Refereed Proceedings

  1. Darija Marković, Dragan Jukić, A review of some existence results on parameter estimation problem in the three-parameter Weibull model, 12th International Conference on Operational Research, Pula, Croatia, 2008, 103-111
  2. Dragan Jukić, Rudolf Scitovski, Alfonzo Baumgartner, Kristian Sabo, Localization of the least squares estimate for two-parametric regression models, 10th International Conference on Operational Research KOI 2004, Trogir, 2005, 165-174
  3. Dragan Jukić, Rudolf Scitovski, Kristian Sabo, Total least squares problem for the Hubbert function, Conference on Applied Mathematics and Scientific Computing, Brijuni, 2003, 217-234
  4. Rudolf Scitovski, Gordana Kralik, Dragan Jukić, Radoslav Galić, Estimation of the saturation level and asymmetry coefficient of the generalized logistic model, 9th International Conference on Operational Research KOI 2002, Trogir, 2002, 57-66
  5. Dragan Jukić, Kristian Sabo, Goran Bokun, Least squares problem for the Hubbert function, 9th International Conference on Operational Research KOI 2002, Trogir, 2002, 37-46



Others

  1. Dragan Jukić, Kristian Sabo, Najbolja aproksimacija rezultata eksperimentalnih mjerenja, Osječki matematički list 10 (1997)
  2. Dragan Jukić, The matrix of a linear operator in a pair of ordered bases, Mathematical Communications 2/1 (1997), 77-82
    In the lecture it is shown how to represent a linear operator by a matrix. This representation allows us to define an operation with matrices.
  3. Dragan Jukić, Djeljivost cijelih brojeva, Osječki matematički list (1996), 41-45
  4. Dragan Jukić, The existence theorem for the solution of a nonlinear least squares problems, Mathematical Communications 1/1 (1996), 61-66
    In this paper we prove a theorem which gives necessary and sufficient conditions which guarantee the existence of the global minimum for a continuous real valued function bounded from below, which is defined on a non-compact set. The use of the theorem is illustrated by an example of the least squares problem.
  5. Dragan Jukić, The problem of the initial approximation for a special nonlinear least squares problems, Mathematical Communications 1/1 (1996), 25-32
    In [6] the existence theorem for the best least squares approximation of parameters for the exponential function is proved. In this paper we consider the problem of choosing a good initial approximation of these parameters.



Books

  1. Dragan Jukić, Mjera i integral, Odjel za matematiku, Osijek, 2012.
  2. Dragan Jukić, Uvod u teoriju mjere i integracije-I dio, Odjel za matematiku, Osijek, 2008.
  3. Dragan Jukić, Rudolf Scitovski, Matematika I, Odjel za matematiku, Osijek, 1998.
  4. Miljenko Crnjac, Dragan Jukić, Rudolf Scitovski, Matematika, Ekonomski fakultet, Osijek, 1994.



Projects

    • 2007- 2013 head of  scientific program (2352818)  "Various aspects of parameter estimation problem in nonlinear mathematical models (Ministry of Science, Education and Sports)

    • 2007- 2013 head of  scientific project (235-2352818-1034)  "Nonlinear parameter estimation problems in mathematical models“ (Ministry of Science, Education and Sports)

    • 2002- 2005 -  scientific project (0235001) "Parameter estimation in mathematical models“ (Department of Mathematics, University of Osijek - Ministry of Science, Education and Sports), investigator

    • 1996 - 2000 - scientific project (165021) "Parameter identification problems in mathematical models“ (Department of Mathematics, University of Osijek - Ministry of Science and Technology), investigator

    • 1991-1995 -  scientific project (1-01-129) "Application of numerical and finite mathematics“ (Ministry of Science, Technology and Computing), investigator

    • 1986 - 1990 -  project task (2.08.01.03.02) "Operationalization of categories and relationships of value laws“ that was carried out within project (2.08.01) "Fundamental research in economy“ (Ministry of Science, Technology and Computing), investigator


     

 

 


Professional Activities

Editorial Boards

 


 

Committee Memberships
  • Member of the Scientific Committee of the international Conference on Applied Mathematics and Scientific Computing,  2013 (ApplMath13)

  • Member of the  Scientific Committee of the 5th Croaatian Congress of Mathematics (Rijeka, 2012)
  • Member of the Scientific Committee of the international Conference on Applied Mathematics and Scientific Computing,  2011 (ApplMath11)

  • Member of the Scientific Committee of the international Conference on Applied Mathematics and Scientific Computing,  2009 (ApplMath09)

  • Member of the Scientific Committee of the 4th Croaatian Congress of Mathematics (Osijek, 2008) 

  • Member of the Organizing Committee of the International Conference on Operational Research, Croatian Operational Research Society (1996, 1998, 2000, 2002, 2004)

  • Member of the Program Committee of the International Conference on Operational Research, Croatian Operational Research Society (2000, 2002, 2004, 2006, 2008, 2010)

  • Member of the National  Commission for Mathematics  (since 2005)

 


 

Refereeing/Reviewing

Periodically refereeing for journals:

  • Journal of Computational and Applied Mathematics

  • Mathematical and Computer Modelling

  • European Journal of Operational Research

  • Computational Statistics and Data Analysis

  • Communications in Statistics – Theory and Methods

  • International Journal of Mathematics and Mathematical Sciences

  • Information and Software Technology

 


 

Service Activities
  • Assistant Head of the Department of Mathematics, University of Osijek, 2007-2013

  • Head of the  Department of Mathematics, University of Osijek,  2003 -2007

  • Vice-Head of the Department of Mathematics, University of Osijek, 1999-2003

  • Head of Engineering Section of the Croatian Mathematical Society-Division Osijek (since 1993)

  • Member of the National  Commission for Mathematics  (since 2005)

 


Teaching

Konzultacije (Office Hours): Srijeda (Wed) 11:30am. Konzultacije su moguće i po dogovoru.

 

Konveksni skupovi

Matematički modeli

Realna analiza

Uvod u teoriju mjere

Uvod u teoriju integracije

 

Matematika 1 (Odjel za kemiju)

Matematika 2 (Odjel za kemiju)

 

 


Personal

  • Birthdate: February 26, 1962
  • Birthplace: Bračević (near Split), Croatia
  • Citizenship: Croatian
  • Family: Married, two children