Tomislav Marošević
Associate Professor Department of Mathematics Josip Juraj Strossmayer University of Osijek Trg Ljudevita Gaja 6 Osijek, HR31000, Croatia¸

Research Interests
 Numerical and applied mathematics
Degrees
1998 PhD in Mathematics, Department of Mathematics, University of Zagreb, Croatia
1994 MSc in Mathematics, Department of Mathematics, University of Zagreb
1987 BSc in Mathematics and Physics, University of Osijek, Croatia
Publications
 D. Jukić, T. Marošević, An existence level for the residual sum of squares of the powerlaw regression with an unknown location parameter, Mathematica Slovaca (2020), prihvaćen za objavljivanjeIn 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 powerlaw regression with an unknown location parameter, and so we obtained a necessary and sufficient condition which guarantee the existence of the least squares estimate.
 T. Marošević, I. Soldo, Modified indices of political power: a case study of a few parliaments, Central European Journal of Operations Research 26/3 (2018), 645657According to yes–no voting systems, players (e.g., parties in a parliament) have some inﬂuence on making some decisions. In formal voting situations, taking into account that a majority vote is needed for making a decision, the question of political power of parties can be considered. There are some wellknown indices of political power e.g., the Shapley–Shubik index, the Banzhaf index, the Johnston index, the Deegan–Packel index. In order to take into account different political nature of the parties, as the main factor for forming a winning coalition i.e., a parliamentary majority, we give a modiﬁcation of the power indices. For the purpose of comparison of these indices of political power from the empirical point of view, we consider the indices of power in some cases, i.e., in relation to a few parliaments.
 T. Marošević, The Hausdorff distance between some sets of points, Mathematical Communications 23 (2018), 247257Hausdorff distance can be used in various areas, where the problems of shape matching and comparison appear. We look at the Hausdorff distance between two hyperspheres in $mathbb{R}^n$. With respect to different geometric objects, the Hausdorff distance between a segment and a hypersphere in $mathbb{R}^n$ is given, too. Using the Mahalanobis distance, a modified Hausdorff distance between a segment and an ellipse in the plane, and generally between a segment and a hyperellipsoid in $mathbb{R}^n$ is adopted. Finally, the modified Hausdorff distance between ellipses is obtained.
 R. Scitovski, T. Marošević, Multiple circle detection based on centerbased clustering, Pattern Recognition Letters 52 (2015), 916The multiple circle detection problem has been considered in the paper on the basis of given data point set $mathcal{A}subset Rn$. It is supposed that all data points from the set $mathcal{A}$ come from $k$ circles that should be reconstructed or detected. The problem has been solved by the application of centerbased clustering of the set $mathcal{A}$, i.e. an optimal $k$partition is searched for, whose clusters are determined by corresponding circlecenters. Thereby, the algebraic distance from a point to the circle is used. First, an adaptation of the wellknown $k$means algorithm is given in the paper. Also, the incremental algorithm for searching for an approximate globally optimal $k$partition is proposed. The algorithm locates either a globally optimal $k$partition or a locally optimal kpartition close to the global one. Since optimal partitions with 2, 3, ... clusters are determined successively in the algorithm, several wellknown indexes for determining an appropriate number of clusters in a partition are adopted for this case. Thereby, the Hausdorff distance between two circles is used and adopted. The proposed method and algorithm are illustrated and tested on several numerical examples.
 T. Marošević, R. Scitovski, Multiple ellipse fitting by centerbased clustering, Croatian Operational Research Review 6/1 (2015), 4353This paper deals with the multiple ellipse fitting problem based on a given set of data points in a plane. The presumption is that all data points are derived from k ellipses that should be fitted. The problem is solved by means of centerbased clustering, where cluster centers are ellipses. If the Mahalanobis distancelike function is introduced in each cluster, then the cluster center is represented by the corresponding Mahalanobis circlecenter. The distance from a point a∈R^2 to the Mahalanobis circle is based on the algebraic criterion. The wellknown kmeans algorithm has been adapted to search for a locally optimal partition of the Mahalanobis circlecenters. Several numerical examples are used to illustrate the proposed algorithm.
 T. Marošević, Data clustering for circle detection, Croatian Operational Research Review 5/1 (2014), 1524This paper considers multiplecircle detection problem on the basis of given data. The problem is being solved by application of centerbased clustering method. For the purpose of searching a locally optimal partition, modeled on a wellknown $k$means algorithm, $k$closest circles algorithm has been constructed. The method has been illustrated with several numerical examples.
 T. Marošević, K. Sabo, P. Taler, A mathematical model for uniform distribution voters per constituencies, Croatian Operational Research Review 4 (2013), 6364This paper presents two different approaches on the basis of which it is possible to generate constituencies. The first one is based on cluster analysis by means of which one can get compact constituencies having an approximately equal number of voters. An optimal number of constituencies can be obtained by using this method. The second approach is based on partitioning the country to several areas with respect to territorial integrity of bigger administrative units. Natural units obtained in this way will represent constituencies which do not necessarily have to have an approximately equal number of voters. Each constituency is associated with a number of representatives that is proportional to its number of voters, so the problem is reduced to the integer approximation problem. Finally, these two approaches are combined and applied on the Republic of Croatia.
 T. Marošević, R. Scitovski, An application of a few inequalities among sequences in electoral systems, Applied mathematics and computation 194 (2007), 480485We look at the concept of ‘favouring large states’ for divisor methods in proportional electoral systems, which is based on the comparison of the ratios of divisors. We show that it is possible in the ordered way to insert new divisor methods between any two divisor methods which have the property that one ‘favours large states’ over the other. It follows from a few sequences’ inequalities of the harmonic, geometric, arithmetic and quadratic means.
 T. Marošević, Over and Underrepresentation in Proportional Electoral Systems  an Empirical Study, Mathematical Communications  Supplement 1 (2001), 3341
 D. Jukić, T. Marošević, R. Scitovski, Discrete total lpnorm approximation problem for the exponential function, Applied mathematics and computation 94/23 (1998), 137143In this paper we consider the total lpnorm (p > 0) approximation problem for the exponential function. We give sufficient conditions which guarantee the existence of such optimal parameters.
 T. Marošević, D. Jukić, Least orthogonal absolute deviations problem for exponential function, Student 2/2 (1997), 131138We 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.
 T. Marošević, Least orthogonal absolute deviations problem for generalized logistic function, Mathematical Communications 2 (1997), 135141
 D. Jukić, T. Marošević, Least squares fitting problem for the powerlaw regression with a location parameter, 18th International Conference on Operational Research, KOI 2020, Šibenik, 2020
 T. Marošević, J. Miletić, M. Miloloža Pandur, Use of several inequalities in the comparison of proportional electoral methods, Book of Abstracts 17th International Conference on Operational Research, KOI 2018, Zadar, Croatia, 2018
 T. Marošević, On directional bias of the Lpnorm, Conference on Applied Mathematics and Scientific Computing 2001, Dubrovnik, 2003, 229235
 T. Marošević, D. Šterc, On estimating distances by means of Lpnorms, 9th International Conference on Operational Research KOI 2002, Trogir, 2002, 195199
 T. Marošević, Estimation of optimal parameters of generalized logistic modelfunction in the discrete Lp norm, 7th International Conference on Operational Research KOI 1998, Rovinj, 1999, 247256
 T. Marošević, I. Bašić, Primjena dviju inačica metode najmanjih kvadrata u ispitivanju električnih strojeva, 6th International Conference on Operational Research KOI 1996, Rovinj, 1996, 6974
 R. Scitovski, T. Marošević, D. Jukić, Estimation of the optimal initial conditions in mathematical model, 17th Int. Conf. Information Technology Interfaces, Cavtat, 1995, 475480
 R. Galić, R. Scitovski, T. Marošević, D. Jukić, Problem optimalnih početnih uvjeta u matematičkom modelu, 5th Conference on Operational Research KOI 1995, Rab, 1995, 6271
 R. Galić, R. Scitovski, T. Marošević, Primjena pomične metode najmanjih kvadrata za rješavanje problema identifikacije parametara u matematičkom modelu, 4th Conference on Operational Research KOI 1994, Rab, 1994, 181191
 D. Sobol, T. Marošević, Procjena nula u dijagramu zračenja adaptivnih antenskih sustava, 33. Simpozij ETAN u pomorstvu, Zadar, 1991, 283286
 T. Marošević, M. Šarić, O indeksima snage u sustavima glasovanja dane, Math.e : hrvatski matematički elektronski časopis 36/1 (2019), 112U sustavima glasovanja dane, ”igrači” (primjerice, stranke u parlamentu) imaju određeni utjecaj na donošenje nekih odluka. U tim situacijama glasovanja, kod kojih je potrebna većina glasova za prihvaćanje odluke, može se razmatrati pitanje snage pojedinih stranaka (odnosno ”igrača”). Postoji više različitih indeksa snage, od kojih nekoliko poznatih opisujemo u ovom članku, primjerice ShapleyShubik indeks, Banzhaf indeks, Johnston indeks, DeeganPackel indeks. Radi ilustracije, promatramo te indekse snage u nekoliko primjera i u slučaju Europskog parlamenta.
 T. Marošević, I. Soldo, Kako se mjeri snaga stranaka u parlamentu (2016)U članku su prikazani neki kvantitativni (brojčani) pokazatelji političke snage u sustavu glasovanja DANE : ShapleyShubik indeks, Banzhaf indeks i DeeganPackel indeks. Za ilustraciju tih indeksa navedeno je nekoliko primjera. Web strana: www.glasslavonije.hr/sglasnik/sveucilisniglasnik18.pdf
 T. Marošević, O metodama raspodjele mjesta u razmjernim izbornim sustavima, Osječki matematički list 1 (2001), 2933
 T. Marošević, A choice of norm in discrete approximation, Mathematical Communications 1 (1996), 147152
 T. Marošević, Nonparametric Regression  Some Approaches, Mathematical Communications 1 (1996), 4350
 T. Marošević, Verižni razlomci i fizika, Matka 5 (1996), 711
 T. Marošević, O metodama za rješavanje rijetkih nelinearnih sustava jednadžbi, Tehnički vjesnik 2/34 (1995), 3340
 T. Marošević, Verižni razlomci, Matka 4 (1995), 127132
Projects

Nonlinear parameter estimation problems in mathematical models (23523528181034)
Project leader: prof.dr.sc. Dragan Jukić, Dept. of Mathematics, University of Osijek ((Ministry of Science, Education and Sport of the Republic of Croatia, 20072013), investigator

Parameter estimation in mathematical models (0235001) Project leader: prof.dr.sc. Rudolf Scitovski, Dept. of Mathematics, University of Osijek (Ministry of Science, Education and Sport of the Republic of Croatia, 20022006), investigator
 Parameter identification problems in mathematical models (165021) (Department of Mathematics, University of Osijek;  Ministry of Science and Technology), investigator

Application of numerical and finite mathematics (101129) (Faculty of Electrical Engineering, University of Osijek;  Ministry of Science, Technology and Computing), investigator
Professional Activities
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Teaching
Konzultacije (Office Hours): petak (Fri) u 11:00. Također, konzultacije su moguće i po dogovoru.
Teme diplomskih radova: pdf
Nastava u akad.god. 2020./2021.:
Matematički aspekti izbornih sustava
Matematika 3  funkcije više varijabli (Odjel za fiziku u Osijeku)
Matematika III (Fakultet elektrotehnike, računarstva i informacijskih tehnologija u Osijeku)
Matematika II (Prehrambenotehnološki fakultet u Osijeku)
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