Dragan Jukić

1. D. Jukić, K. Sabo, An existence criterion for the nonlinear $ell_p-$norm fitting problem, Central European Journal of Operations Research 29 (2021), 957-966
   Abstract

   In this paper, we give a necessary and sufficient criterion for the existence of the $ell_p-$norm estimate for the nonlinear $ell_p-$norm fitting problem. Our criterion is based on the existence level that describes the behavior of the objective function as its argument approaches the extended boundary of the parameter space.
2. D. Jukić, T. Marošević, An existence level for the residual sum of squares of the power-law regression with an unknown location parameter, Mathematica Slovaca 71/4 (2021), 1019-1026
   Abstract

   In a recent paper Jukic [1], a new existence level was introduced and then was used to obtain a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set. In this paper, we determined that existence level for the residual sum of squares of the power-law regression with an unknown location parameter, and so we obtained a necessary and sufficient condition which guarantee the existence of the least squares estimate.
3. D. Jukić, A necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function on a noncompact set, Journal of Computational and Applied Mathematics, 375 (2020)
   Abstract

   In this paper, we provide a necessary and sufficient criterion for the existence of the global minima of a continuous lower bounded function defined on a noncompact set. Our criterion is based on a new existence level introduced in this paper that describes the behavior of the function as its argument approaches the extended boundary of the minimization domain. Some examples are included to illustrate the efficiency of our criterion.
4. D. Jukić, An elementary proof of the quadratic envelope characterization of zero-derivative points, Optimization Letters 12/5 (2018), 1155-1156
   Abstract

   This note presents a simple and self-contained proof of Zlobec's theorem [J. Glob. Optim. 46(2010), 155-161] on quadratic envelope characterization of zero-derivative points for smooth functions in several variables with a Lipschitz derivative. Our proof does not require any knowledge about convexifiable functions.
5. D. Jukić, D. Marković, Nonlinear least squares estimation of the shifted Gompertz distribution, European Journal of Pure and Applied Mathematics 10/2 (2017), 157-166
   Abstract

   The focus of this paper is the existence of the best nonlinear least squares estimate for the shifted Gompertz distribution. As a main result, two theorems on the existence of the least squares estimate are obtained, as well as their generalization in the lp norm (1 ≤ p < ∞ ).
6. D. 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
   Abstract

   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.
7. D. Marković, D. Jukić, Total least squares fitting the three-parameter inverse Weibull density, European Journal of Pure and Applied Mathematics 7/3 (2014), 230-245
   Abstract

   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<∞).
8. D. Jukić, On nonlinear weighted least squares estimation of Bass diffusion model, Applied mathematics and computation 219/14 (2013), 7891-7900
   Abstract

   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.
9. D. Marković, D. 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
   Abstract

   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.
10. D. 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
    Abstract

    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.
11. D. Jukić, The L_p-norm estimation of the parameters for the Jelinski-Moranda model in software reliability, International Journal of Computer Mathematics 89 (2012), 467-481
    Abstract

    The exponential model of Jelinski and Moranda [Software reliability research, in Statistical Computer Performance Evaluation, W. Freiberg, ed., Academic Press, New York, 1972, pp. 465–484] is one of the earliest models proposed for predicting software reliability. The estimation of its parameters has been approached in the literature by various techniques. The focus of this paper is on the L p -norm (1≤p<∞) fitting approach. Special attention is paid to the nonlinear weighted least squares (LS) estimation. We show that it is possible for the best L p -norm estimate to not exist. As the main result, a necessary and sufficient condition for the existence of the best L p -norm estimate is obtained. This condition is theoretical in nature. We apply it to obtain two theorems on the existence of the LS estimate. One of them gives the necessary and sufficient conditions which guarantee the existence of the LS estimate. To illustrate the problems arising with the nonlinear normal equation approach for solving the LS problem, some illustrative examples are included.
12. D. Jukić, Total least squares fitting Bass diffusion model, Mathematical and Computer Modelling 53/9-10 (2011), 1756-1779
    Abstract

    This paper is concerned with the Bass model, which is widely used as a first-purchase diffusion model in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the nonlinear weighted total least squares (TLS) fitting approach. We show that it is possible that the TLS estimate does not exist. As a main result, two theorems on the existence of the total least squares estimate are obtained, as well as their generalization in the total l_s norm (1≤s<∞). Several illustrative numerical examples are given to illustrate the efficiency of our approach.
13. M. Marušić, D. Marković, D. Jukić, Least squares fitting the three-parameter inverse Weibull density, Mathematical Communications 15/2 (2010), 539-553
    Abstract

    The inverse Weibull model was developed by Erto [10]. In practice, the unknown parameters of the ppropriate inverse Weibull density are not known and must be estimated from a random sample. Estimation of its parameters has been approached in the literature by various techniques, because a standard maximum likelihood estimate does not exist. To estimate the unknown parameters of the three-parameter inverse Weibull density we will use a combination of onparametric and parametric methods. The idea consists of using two steps: in the first step we calculate an initial nonparametric density estimate which needs to be as good as possible, and in the second step we apply the nonlinear least squares method to estimate the unknown parameters. As a main result, a theorem on the existence of the least squares estimate is obtained, as well as its generalization in the l_p norm (1 p < 1). Some simulations are given to show that our approach is satisfactory if the initial density is of good enough quality.
14. D. Jukić, D. Marković, On nonlinear weighted errors-in-variables parameter estimation problem in the three-parameter Weibull model, Applied mathematics and computation 215/10 (2010), 3599-3609
    Abstract

    This paper is concerned with the three-parameter Weibull distribution which is widely used as a model in reliability and lifetime studies. In practice, the Weibull model parameters are not known in advance and must be estimated from a random sample. Difficulties in applying the method of maximum likelihood to three-parameter Weibull models have led to a variety of alternative approaches in the literature. In this paper we consider the nonlinear weighted errors-in-variables (EIV) fitting approach. As a main result, two theorems on the existence of the EIV estimate are obtained. An illustrative example is also included.
15. D. Jukić, D. Marković, On nonlinear weighted least squares fitting of the three-parameter inverse Weibull distribution, Mathematical Communications 15/1 (2010), 13-24
    Abstract

    In this paper we consider nonlinear least squares fitting of the three-parameter inverse Weibull distribution to the given data (wi; ti; yi), i = 1,...,n, n>3. As the main result, we show that the least squares estimate exists provided that the data satisfy just the following two natural conditions: (i) 0 < t1 < t2 < ... < tn and (ii) 0 < y1 < y2 <... < yn < 1. To this end, an illustrative numerical example is given.
16. D. Marković, D. Jukić, On nonlinear weighted total least squares parameter estimation problem for the three-parameter Weibull density, Applied Mathematical Modelling 34/7 (2010), 1839-1848
    Abstract

    The three-parameter Weibull density function is widely employed as a model in reliability and lifetime studies. Estimation of its parameters has been approached in the literature by various techniques, because a standard maximum likelihood estimate does not exist. In this paper we consider the nonlinear weighted total least squares fitting approach. As a main result, a theorem on the existence of the total least squares estimate is obtained, as well as its generalization in the total l_q norm ($q\geq 1$). Some numerical simulations to support the theoretical work are given.
17. D. Marković, D. Jukić, M. Benšić, Nonlinear weighted least squares estimation of a three-parameter Weibull density with a nonparametric start, Journal of Computational and Applied Mathematics, 228/1 (2009), 304-312
    Abstract

    This paper is concerned with the parameter estimation problem for the three-parameter Weibull density which is widely employed as a model in reliability and lifetime studies. Our approach is a combination of nonparametric and parametric methods. The basic idea is to start with an initial nonparametric density estimate which needs to be as good as possible, and then apply the nonlinear least squares method to estimate the unknown parameters. As a main result, a theorem on the existence of the least squares estimate is obtained. Some simulations are given to show that our approach is satisfactory if the initial density is of good enough quality.
18. D. Jukić, On the existence of the best discrete approximation in $l_p$ norm by reciprocals of real polynomials, Journal of Approximation Theory 156/2 (2009), 212-222
    Abstract

    For the given data (wi,xi,yi), i=1,…,M, we consider the problem of existence of the best discrete approximation in l_p norm (1≤p<∞) by reciprocals of real polynomials. For this problem, the existence of best approximations is not always guaranteed. In this paper, we give a condition on data which is necessary and sufficient for the existence of the best approximation in $l_p$ norm. This condition is theoretical in nature. We apply it to obtain several other existence theorems very useful in practice. Some illustrative examples are also included.
19. D. Jukić, M. Benšić, R. Scitovski, On the existence of the nonlinear weighted least squares estimate for a three-parameter Weibull distribution, Computational Statistics & Data Analysis 52/9 (2008), 4502-4511
    Abstract

    The problem of nonlinear weighted least squares fitting of the three-parameter Weibull distribution to the given data (wi,ti,yi), i=1,…,n, is considered. The part wi>0 of the data stands for the data weights. It is shown that the best least squares estimate exists provided that the data satisfy just the following two natural conditions: (i) 0<t1<t2<⋯<tn and (ii) 0<y1<y2<⋯<yn<1. To support this, an illustrative numerical example is given.
20. D. Jukić, K. Sabo, R. Scitovski, A review of existence criteria for parameter estimation of the Michaelis-Menten regression model, Annali dell'Universita' di Ferrara 53 (2007), 281-291
    Abstract

    In this paper we consider the least squares (LS) and total least squares (TLS) problems for a Michaelis-Menten enzyme kinetic model $f(x ; a, b)=ax/(b+x)$, $a, b>0$. In various applied research such as biochemistry, pharmacology, biology and medicine there are lots of different applications of this model. We will systematize some of our results pertaining to the existence of the LS and TLS estimate, which were proved in papers [16] and [17]. Finally, we suggest a choice of good initial approximation and give one numerical example.
21. K. Hadeler, D. Jukić, K. Sabo, Least squares problems for Michaelis Menten kinetics, Mathematical Methods in the Applied Sciencies 30 (2007), 1231-1241
    Abstract

    The Michaelis-Menten kinetics is fundamental in chemical and physiological reaction theory. The problem of parameter identification, which is not well-posed for arbitrary data, is shown to be closely related to the Chebyshev sum inequality. This inequality yields sufficient conditions for existence of feasible solutions both for non-linear and for linear least squares problems. The conditions are natural and practical as they are satisfied if the data show the expected monotone and concave behavior.
22. D. Jukić, R. Scitovski, K. Sabo, Total least squares fitting Michaelis-Menten enzyme kinetic model function, Journal of Computational and Applied Mathematics, 201 (2007), 230-246
    Abstract

    The Michaelis-Menten enzyme kinetic model $f(x ; a, b)=ax/(b+x)$, $a, b>0$, is widely used in biochemistry, pharmacology, biology and medical research. Given the data $(p_i, x_i, y_i)$, $i=1, \ldots, m$, $m\geq 3$, we consider the total least squares (TLS) problem for the Michaelis-Menten model. We show that it is possible that the TLS estimate does not exist. As the main result, we show that the TLS estimate exists if the data satisfy some natural conditions. Some numerical examples are included.
23. D. Jukić, R. Scitovski, Least squares fitting Gaussian type curve, Applied mathematics and computation 167/1 (2005), 286-298
    Abstract

    Given the data (pi, ti, yi), i = 1, …, m, m ⩾ 3, we give necessary and sufficient conditions which guarantee the existence of the weighted least squares estimate for a Gaussian type function. To this end, we suggest a choice of the suitable initial approximation for an iterative minimization, and give some numerical examples.
24. D. Jukić, A necessary and sufficient criteria for the existence of the least squares estimate for a 3-parametric exponential function, Applied mathematics and computation 147/1 (2004), 1-17
    Abstract

    Given the data (pi,ti,yi), i=1,…,m, m⩾3, we give necessary and sufficient conditions which guarantee the existence of the least squares estimate for a 3-parametric exponential function. To this end, we suggest a choice of the initial approximation and give some numerical examples.
25. D. Jukić, G. Kralik, R. Scitovski, Least squares fitting Gompertz curve, Journal of Computational and Applied Mathematics, 169/2 (2004), 359-375
    Abstract

    In this paper we consider the least-squares (LS) fitting of the Gompertz curve to the given nonconstant data (pi,ti,yi), i=1,…,m, m⩾3. We give necessary and sufficient conditions which guarantee the existence of the LS estimate, suggest a choice of a good initial approximation and give some numerical examples.
26. D. Jukić, R. Scitovski, Solution of the least-squares problem for logistic function, Journal of Computational and Applied Mathematics, 156/1 (2003), 159-177
    Abstract

    Given the data (pi,ti,fi), i=1,…,m, m>3, we consider the best least-squares approximation of parameters for the logistic function . We give necessary and sufficient conditions which guarantee the existence of such optimal parameters.
27. R. Scitovski, D. Jukić, I. Urbiha, Solving the parameter identification problem by using $TL_p$ spline, Mathematical Communications - Supplement 1/1 (2001), 81-91
28. D. Jukić, R. Scitovski, The best least squares approximation problem for a 3-parametric exponential regression model, ANZIAM Journal 42/2 (2000), 254-266
    Abstract

    Given the data (pi, ti, fi), i = 1,…,m, we consider the existence problem for the best least squares approximation of parameters for the 3-parametric exponential regression model. This problem does not always have a solution. In this paper it is shown that this problem has a solution provided that the data are strongly increasing at the ends.
29. R. Scitovski, D. Jukić, Analysis of solutions of the least squares problem, Mathematical Communications 4/1 (1999), 53-61
    Abstract

    For the given data $(p_i,t_i,f_i),$ $i=1,\ldots,m$, we consider the existence problem of the best parameter approximation of the exponential model function in the sense of ordinary least squares and total least squares. Results related to that problem which have been obtained and published by the authors so far are given in the paper, as well as some new results on nonuniqueness of the best parameter approximation.
30. D. Jukić, R. Scitovski, H. Späth, Partial linearization of one class of the nonlinear total least squares problem by using the inverse model function, Computing 62/2 (1999), 163-178
    Abstract

    In this paper we consider a special nonlinear total least squares problem, where the model function is of the form f(x;a,b)=ϕ−1(ax+b) . Using the fact that after an appropriate substitution, the model function becomes linear in parameters, and that the symmetry preserves the distances, this nonlinear total least squares problem can be greatly simplified. In this paper we give the existence theorem, propose an efficient algorithm for searching the parameters and give some numerical examples.
31. R. Scitovski, Š. Ungar, D. Jukić, Approximating surfaces by moving total least squares method, Applied mathematics and computation 93/2-3 (1998), 219-232
    Abstract

    We suggest a method for generating a surface approximating the given data (xi, yi, zi) ϵ R^3, i = 1, …. m, assuming that the errors can occur both in the independent variables x and y, as well as in the dependent variable z. Our approach is based on the moving total least squares method, where the local approximants (local planes) are determined in the sense of total least squares. The parameters of the local approximants are obtained by finding the eigenvector, corresponding to the smallest eigenvalue of a certain symmetric matrix. To this end, we develop a procedure based on the inverse power method. The method is tested on several examples.
32. D. Jukić, T. Marošević, R. Scitovski, Discrete total lp-norm approximation problem for the exponential function, Applied mathematics and computation 94/2-3 (1998), 137-143
    Abstract

    In this paper we consider the total lp-norm (p > 0) approximation problem for the exponential function. We give sufficient conditions which guarantee the existence of such optimal parameters.
33. D. Jukić, R. Scitovski, Existence results for special nonlinear total least squares problem, Journal of Mathematical Analysis and Applications 226/2 (1998), 348-363
    Abstract

    In this paper we prove an existence theorem for a special nonlinear total least squares problem. We show that the optimal parameters of the generalized logistic function exist in the sense of total least squares, provided the data satisfy the Chebyshev's inequality.
34. T. Marošević, D. Jukić, Least orthogonal absolute deviations problem for exponential function, Student 2/2 (1997), 131-138
    Abstract

    We consider the existence problem of the optimal parameters for the exponential function, in the sense of the least orthogonal absolute deviations, and prove the existence of such optimal parameters for monotic data.
35. D. Jukić, R. Scitovski, Existence of optimal solution for exponential model by least squares, Journal of Computational and Applied Mathematics, 78/2 (1997), 317-328
    Abstract

    In this paper we prove the existence theorem for the best least squares approximation of the optimal parameters for the exponential model function. We give sufficient conditions which guarantee the existence of such optimal parameters. Using these results and methods, we are able to localize a sufficiently narrow area where one can choose a good initial approximation.
36. D. Jukić, R. Scitovski, The existence of the optimal parameters of the generalized logistic function, Applied mathematics and computation 77/2-3 (1996), 281-294
    Abstract

    The estimation of optimal parameters in a mathematical model described by the generalized logistic function with saturation level A and the asymmetry coefficient γ is a nonlinear least squares problem. In this paper we prove the existence of optimal parameters under considerably weaker conditions than those required in [1].
37. R. Scitovski, D. Jukić, A method for solving the parameter identification problem for ordinary differential equations of the second order, Applied mathematics and computation 74/2-3 (1996), 273-291
    Abstract

    We give a method for solving the parameter identification problem for ordinary differential equations of the second order using a noninterpolated moving least squares method. The method is tested in two practical examples.
38. R. Scitovski, D. Jukić, Total least squares problem for exponential function, Inverse Problems 12/3 (1996), 341-349
    Abstract

    Given the data (p_i,t_i,f_i), , i = 1,...,m, we consider the existence problem for the optimal parameters for the exponential function approximating these data in the sense of total least squares. We give sufficient conditions which guarantee the existence of such optimal parameters.
39. B. Dukić, D. Francišković, D. Jukić, R. Scitovski, M. Benšić, Strategije otplate zajma, Financijska teorija i praksa (1994), 15-26

1. D. Jukić, T. Marošević, Least squares fitting problem for the power-law regression with a location parameter, 18th International Conference on Operational Research, KOI 2020, Šibenik, 2020
2. D. Jukić, K. Sabo, An existence criterion for the sum of squares, Symposium on Operational Research in Slovenia, SOR '19, Bled, 2019, 500-505
   Abstract

   In this paper, we give a necessary and sufficient criterion for the existence of the least squares estimate for the nonlinear sum of squares. Our criterion is based on the existence level that describes the behavior of the sum of squares as its argument approaches the extended boundary of the parameter space.
3. D. Marković, D. 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
4. D. Jukić, R. Scitovski, A. Baumgartner, K. Sabo, Localization of the least squares estimate for two-parametric regression models, 10th International Conference on Operational Research KOI 2004, Trogir, 2005, 165-174
5. D. Jukić, R. Scitovski, K. Sabo, Total least squares problem for the Hubbert function, Conference on Applied Mathematics and Scientific Computing, Brijuni, 2003, 217-234
6. R. Scitovski, G. Kralik, D. Jukić, R. 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
7. D. Jukić, K. Sabo, G. Bokun, Least squares problem for the Hubbert function, 9th International Conference on Operational Research KOI 2002, Trogir, 2002, 37-46
8. D. Jukić, D. Marković, M. Ribičić Penava, A. Krajina, On the choice of initial approximation of the least squares estimate in some growth models of exponential type, 9th International Conference on Operational Research KOI 2002, Trogir, 2002, 47-55
9. D. Jukić, R. Scitovski, Š. Ungar, The best total least squares line in R^3, 7th International Conference on Operational Research KOI 1998, Rovinj, 1998, 311-316
10. S. Tomas, D. Jukić, Estimation of humid air properties by moving total least squares method, 7th International Conference on Operational Research KOI 1998, Rovinj, 1998, 91-98
11. D. Jukić, M. Crnjac, R. Scitovski, Surfaces generated by the noninterpolating moving least squares method, 4th International Symposium on Operations Research in Slovenia SOR’97, Preddvor, 1997, 189-194
12. R. Scitovski, Š. Ungar, D. Jukić, M. Crnjac, Moving total least squares for parameter identification in mathematical model, Symposium on Operations Research SOR '95, Passau, 1996, 196-201
13. D. Jukić, R. Scitovski, The exponential growth model, 6th International Conference on Operational Research KOI 1996, Rovinj, 1996, 107-112
14. R. Scitovski, D. Jukić, I. Bašić, Application of the moving least squares method in surface generating, 17th Int. Conf. Information Technology Interfaces, Cavtat, 1995, 469-474
15. R. Scitovski, T. Marošević, D. Jukić, Estimation of the optimal initial conditions in mathematical model, 17th Int. Conf. Information Technology Interfaces, Cavtat, 1995, 475-480
16. D. Jukić, R. Scitovski, M. Crnjac, Primjena metode potpunih najmanjih kvadrata za procjenu parametara u matematičkom modelu, 5th Conference on Operational Research KOI 1995, Rab, 1995, 99-110
17. R. Galić, R. Scitovski, T. Marošević, D. Jukić, Problem optimalnih početnih uvjeta u matematičkom modelu, 5th Conference on Operational Research KOI 1995, Rab, 1995, 62-71
18. R. Scitovski, R. Galić, I. Kolund, I. Bašić, D. Jukić, Procjena rasprostiranja slojeva po dubini sondažnog profila, 5th Conference on Operational Research KOI 1995, Rab, 1995, 111-120
19. M. Crnjac, D. Jukić, R. Scitovski, Nove strategije otplate zajma, 4th Conference on Operational Research KOI 1994, Rab, 1994, 147-154

1. D. Jukić, K. Sabo, Najbolja aproksimacija rezultata eksperimentalnih mjerenja, Osječki matematički list 10 (1997)
2. D. Jukić, The matrix of a linear operator in a pair of ordered bases, Mathematical Communications 2/1 (1997), 77-82
   Abstract

   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. D. Jukić, Djeljivost cijelih brojeva, Osječki matematički list (1996), 41-45
4. D. Jukić, The existence theorem for the solution of a nonlinear least squares problems, Mathematical Communications 1/1 (1996), 61-66
   Abstract

   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. D. Jukić, The problem of the initial approximation for a special nonlinear least squares problems, Mathematical Communications 1/1 (1996), 25-32
   Abstract

   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.
6. D. Jukić, Rekurzivne relacije i potencije kvadratnih matrica , Ekonomski vjesnik 6/1 (1992), 133-136
7. D. Jukić, Rekurzivne relacije i potencije kvadratnih matrica, Ekonomski vjesnik 2 (1992), 133-136
8. D. Jukić, Uvod u LaTeX, Ekonomski vjesnik 1 (1989), 169-178

1. D. Jukić, Konveksni skupovi, Sveučilište Josipa Jurja Strossmayera u Osijeku, Odjel za matematiku, Osijek, 2021.
2. D. Jukić, Realna analiza, Sveucilište Josipa Jurja Strossmayera u Osijeku, Odjel za matematiku, Osijek, 2020.
   Abstract

   Ovaj udžbenik namijenjen je u prvom redu studentima Odjela za matematiku Sveučilišta u Osijeku za potrebe kolegija Realna analiza. Materija je podijeljena u devet poglavlja: Topologija na euklidskom prostoru $mathbb{R}^n$, Konvergencija nizova, Konvergencija nizova funkcija, Potpuni metrički prostori, Kompaktnost, Neprekidna preslikavanja, Banachov teorem o fiksnoj točki, Povezani prostori i povezanost putevima te Limes funkcije. Na kraju udžbenika nalaze se popis literature i kazalo pojmova. U svim poglavljima teorijski dio ilustriran je mnoštvom primjera. Na kraju svakog poglavlja dani su zadaci za utvrđivanje izloženog gradiva i proširivanje znanja. Za većinu tih zadataka dane su detaljne upute. U svakom su poglavlju redom numerirane definicije, teoremi, korolari, leme, propozicije i primjeri. Na kraju, zahvaljujem svima koji su izravno ili na drugi način pomogli da se ovaj udžbenik tiska i bude što bolji. Posebno zahvaljujem recenzentima prof. dr. sc. Krešimiru Burazinu i prof. dr. sc. Tiboru Pogany koji su pažljivo proćitali rukopis i svojim primjedbama i sugestijama utjecali na mnoge dijelove teksta. Unaprijed zahvaljujem svima koji mi ukažu na neku pogrešku ili propust i predlože ispravak ili poboljšanje.
3. D. Jukić, R. Scitovski, Matematika I, Sveučilište Josipa Jurja Strossmayera u Osijeku, Odjel za matematiku, Osijek, 2017.
4. D. Jukić, Mjera i integral, Odjel za matematiku, Sveučilište J. J. Strossmayera, Osijek, 2012.
5. D. Jukić, Uvod u teoriju mjere i integracije-I dio, Odjel za matematiku, Osijek, 2008.
6. M. Crnjac, D. Jukić, R. Scitovski, Matematika, Sveučilište Josipa Jurja Strossmayera u Osijeku, Ekonomski fakultet u Osijeku, Osijek, 1994.

Projects

Professional Activities

• Mathematical Communications, Editor-in-Chief

• Journal of  Classical Analysis

• Croatian Operational Research Review

• Osječki matematički list

• 10^th   International Conference on Operational Research (Trogir, Croatia, 2004), Editor

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

• Member of the  Scientific Committee of the 5^th 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 4^th 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, 2005-2021.

• Mathematical Communications 

• Journal of  Classical Analysis

• Osječki matematički list

• AMS Mathematical Review

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

• 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, 2005-2021

Teaching

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

Konveksni skupovi

Matematički modeli

Mjera i integral

Realna analiza

Uvod u teoriju mjere

Uvod u teoriju integracije

Matematika 1 (Odjel za kemiju)

Matematika 2 (Odjel za kemiju)

Popis tema završnih i diplomskih radova u akademskoj 2018./2019. godini

Personal

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