** Completed projects**

- "Nonlinear parameter dependent eigenproblem", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek) - Project coordinator: Ninoslav Truhar
**Summary:**This project is dedicated to the study of nonlinear parameter dependent eigenvalue problems, where the special emphasis is on the behavior of the eigenvalues and eigenvectors of the parameter dependent quadratic eigenvalue problems*(ʎ(p)²M(p)+ʎ(p)C(p)+K(p))x(p)=0*, where*M, C, K*Hermitian matrices,*ʎ*is eigenvalues,*x*is eigenvector and*p*is some parameter. Characteristics of the parameter dependent eigenvalues and eigenvectors will be used to derive perturbation bounds(absolute and relative type) for the case whan*M, C, K*are arbitrary Hermitian matrices. The new results are planned to be generalized to other parameter dependent eigenproblems, such as the rational and polynomial problem.**Programme:**Guest researcher (INGI-2015) Josip Juraj Strossmayer University of Osijek**Guest researcher:**Rafikul Alam**Project partners:**Department of Mathematics, Indian Institute of Technology Guwahati, India**Team members (UNIOS):**Ivana Kuzmanović, Suzana Miodragović, Zoran Tomljanović, Matea Puvača**Project duration:**10 June 2016 - 10 July 2016 - "Exploration of optimization and estimation properties of Generalized method of moments and Nonlinear least squares", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek) - Project coordinator: Mirta Benšić
**Summary:**The visitor and a group of researchers from the Department of Mathematics, University of Osijek, will explore clustering optimization problems focusing on the optimization of likelihood initialized with tensor-based moment methods. The team will also explore efficiency of nonlinear least squares fit of empirical distributions in certain parametric estimation problems.**Programme:**Guest researcher (INGI-2015) Josip Juraj Strossmayer University of Osijek**Guest researcher:**Andrew R. Barron**Project partners:**Department of Statistics, Yale University, USA**Team members (UNIOS):**Kristian Sabo; Danijel Grahovac; Ivan Papić**Project duration:**March 2016 - November 2016 - "The development of modern study programmes for the purpose of training informatics, engineering, biology, chemistry, physics and mathematics teachers at the foundation of the Croatian Qualifications Framework", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of Science, Education and Sports) - Project coordinator: Ljerka Jukić Matić
**Summary:**The overall objective of the project is to contribute to the further implementation of the Croatian Qualifications Framework in the field of teacher training and education. A draft proposal of occupational and qualification standards will be developed for informatics, engineering, biology, chemistry, physics and mathematics teachers, which should contribute to the modernisation of study programmes for training and educating teachers inthe aforementioned fields, and based upon the Croatian Qualifications Framework by developing learning outcomes.

Specific objectives of the project are to develop 6 occupational standards, 6 qualification standards and 10 study programmes/curricula based on learning outcomes.

In the first part of the implementation of project activities, strategic documents, sector profiles, as well as the demand and supply for these occupations, will be analysed and an occupational standard survey will be carried out.

In the second part, key jobs and competencies in these positions will be established through roundtables of working groups in each of these fields, as well as the sets of learning outcomes required to achieve these competencies.

In the final stage, roundtables will be held to harmonise the qualifying study programmes with occupational and qualification standards for informatics, engineering, biology, chemistry, physics and mathematics teachers developed previously, as well as workshops on curriculum development in line with the approach based on learning outcomes.**Programme:**Grant for projects financed by the European Social Fund as part of Human Resources Development 2007-2013**Project partners:**Faculty of Philosophy in Zagreb, Faculty of Philosophy in Rijeka, University of Rijeka, Josip Juraj Strossmayer University of Osijek, III High School in Split and the Education and Teacher Training Agency. The project will also include representatives of key stakeholders in the education of the aforementioned staff as a target group.**Team members (UNIOS):**Ljerka Jukić Matić (mathematics), Tomislav Marošević (mathematics), Darija Marković (mathematics), Domagoj Ševerdija (informatics), Domagoj Matijević (informatics)**Project duration:**18 July 2015 – 18 September 2016 - "Mixed integer nonlinear programming (MINLP) for damper optimization", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of Science, Education and Sports and Deutscher Akademischer Austauschdienst (DAAD)) - Project coordinator: Ninoslav Truhar
**Summary:**The problem we will consider is devoted to damping optimization, in particular, the problem is to determine dampers' position and viscosities for a vibrational system. A criterion in the optimization problem is to minimize the total energy for a vibrational system over all initital states of unit energy, and all dampers' position and its viscosities. In general this is a Mixed Integer Nonlinear Program (MINLP) as viscosities represent real numbers, while position are given as coordinates in the network, indexed by nonnegative integers.The main drawback in damping optimization is the combinatorial explosion of the total number of damping combinations. Therefore, we would like to use recent advances in MINLP.

Furthemore, we would like to address the linearization of the MINLP, which in this case is possible since the product of variables can be expressed as separable functions. Hence, we end up with an Integer Program (IP).

In this setting, we would like to discuss and compare the result from the MINLP and IP approaches with the prevously investigated and abovely mentioned discrete to continous approaches.

Furthemore, we would like to consider a new damping optimization problem when a mechanical system is excited by an external force. In this case we consider a new criterion which is based on the amplitude, such as average energy amplitude and average displacement amplitude criterion.

With the knowledge of damping based on total energy we will derive explicit formulas for particular case studies. In the general setting we will propose approaches in which the objectives functions can be efficiently calculated. Moreover, in this optimization problem we would like to employ MINLP as well in order to determine optimal damping efficiently.

**Programme:**The programme aimed at encouraging the exchange of project participants between the Ministry of Science, Education and Sports of the Republic of Croatia and the DAAD**Partners in the project:**Max Planck Institute for Dynamics of Complex Technical Systems (Peter Benner, Yao Yue, Xin Liang, Jonas Denissen, Manuela Hund)**Project members:**Ninoslav Truhar, Zoran Tomljanović, Suzana Miodragović**Project duration:**1 January 2015 – 31 December 2016 - "Composition series of the induced representations of classical p-adic groups", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek) - Project coordinator: Ivan Matić
**Summary:**The goal of this project is to investigate irreducible subquotients and to determine the composition series of induced representations which play an important role in the unitary and non-unitary duals of classical groups over non-Archimedean local fields. Mostly, we plan to study the composition series of certain generalized principal series, representation induced from those of segment type and representations induced from several irreducible essentially square integrable ones on the general linear part and strongly positive discrete series on the classical-group part. We plan to generalize applications of intertwining operator methods and Jacquet modules method, starting inductively from known descriptions of Jacquet modules.**Programme:**Internal project of J. J. Strossmayer University of Osijek**Project members:**Ivan Matić (coordinator), Ljerka Jukić Matić, Darija Brajković**Project duration:**2 May 2015 – 2 May 2016 - "Fractional Pearson Diffusions", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek ) - Project coordinator: Nenad Šuvak
**Summary:**The research will be focused on the fractional Pearson diffusion (FPD), more specifically on the study of the construction techniques and probabilistic properties of special types of this class of fractional diffusions: Ornstein-Uhlenbec and Cox-Ingersol-Ross fractional diffusion. We will focus on two main problems: 1. construction of the FPD 2. the analysis of the spectrum of the infinitesimal generator of the FPD and the use of the known structure of its spectrum and corresponding eigenfunctions for deriving the transition density functions of some special cases of FPD.For Ornstein-Uhlenbeck and Cox-Ingersol-Ross FPD studied in more details we will investigate theirphysical interpretation and possible applications in other sciences.

**Programme:**Internal project of J. J. Strossmayer University of Osijek**Project members:**Nenad Šuvak (coordinator); Danijel Grahovac; Ivan Papić; Mirta Benšić (consultant)**Project duration:**2 May 2015 – 2 May 2016 - "Damping optimization in mechanical systems excited with external force", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek) - Project coordinator: Zoran Tomljanović
**Summary:**This project is devoted to damping optimization which is a very important issue since prevents undesirable effects in vibrations of systems.We consider the case when a system is excited by an external force which has an important influence on system behavior. Optimization procedure will be based on the minimization of the average displacement and the average energy amplitude.

Since the optimization process is a very demanding we will develop several methods and algorithms for the efficient damping optimization. In particular, we will consider models with internal damping, different dampers viscosities and the influence of various external functions on system behavior

**Programme:**Internal project of J. J. Strossmayer University of Osijek**Project members:**Zoran Tomljanović (coordinator), Ivana Vuksanović, Jelena Jankov**Project duration:**2 May 2015 – 1 May 2016 - "Optimal damping of vibrational systems", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of Science, Education and Sports and Deutscher Akademischer Austauschdienst(DAAD)) - Project coordinator: Ninoslav Truhar
**Summary:**In real physical systems which possess elasticity and mass, dangerous vibrations are a typical phenomenon which have been widely studied in the past. But also nowadays this is an intensively investigated phenomenon. For the majority of engineering applications, resonance and sustained oscillations can cause structural damage. The way to reduce dangerous vibrations is through damping.

Our goal is to develop efficient approaches for solving problems which appear in damping optimization but also in closely connected issues such as optimality of the solution of the linear systems, stability via Lyapunov and optimal control.

The usage of model order reduction approaches is investigated for this task and additionally, we will derive a theory which will describe the geometry of the corresponding eigenspaces as well as the relative perturbation bounds for corresponding eigenvalues.

We also consider the feedback stabilization we will also consider the case of active damping with direct velocity feedback, since one can obtain almost the same second order system as with passive damping.**Programme:**The programme aimed at encouraging the exchange of project participants between the Ministry of Science, Education and Sport of the Republic of Croatia and the DAAD.**Partners in the project:**Max Planck Institute for Dynamics of Complex Technical Systems (Peter Benner, Jonas Denissen, Patrick Kürschner, Matthias Voigt, Andre Schneider)**Project members:**Ninoslav Truhar, Zoran Tomljanović**Project duration:**1 January 2013 – 31 December 2014 - "Discrete series in generalised principal series", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek) - Project coordinator: Ivan Matić
**Summary:**Knowledge of composition series of induced representations of p-adic groups is one of the most interesting and most important unsolved problems in the whole representation theory. A particulary important case of induced represenations are the so-called generalised principal series, i.e., representations induced from maximal parabolic subgroups of a discrete series located on the classical part. Although reducibility points of generalized principal series were obtained and presented by Goran Muić, irreducible subquotients of such representations are known only in the case of induction of a strictly positive representation. The aim of this project is to expand knowledge to the generalised principal series induced from more general types of discrete series, where the emphasis is placed on the detection of necessary and sufficient conditions to have a generalized discrete series contain a subquotient in a discrete series. We also plan to prove that in this case the induced representation must also contain a subrepresentation in a discrete series.**Programme:**Internal project of J. J. Strossmayer University of Osijek**Project members:**Dr. Ljerka Jukić Matić, Darija Brajković MMath**Project duration:**25 September 2013 – 25 September 2014 - "Parameter estimation problem in some two-parameter monotonic mathematical models", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer Univeristy of Osijek) - Project coordinator: Darija Marković
**Summary:**The theoretical part of research deals with various aspects of the problem of parameter estimation in a special family of nonlinear two-parameter mathematical models. Emphasis is placed on the existence problems of optimal parameters in a predefined parameter space, the problem of choosing a numerical minimization method and the problem of determining a good initial approximation. The problems are formulated and solved in different l_p standards (1≤ p≤∞), and in addition to the classical methods of optimisation, numerical analysis and approximation theory, the classical Ordinary Least Squares Method is particulary used in the research. As part of research, special attention is given to all aforementioned aspects of the parameter estimation problem in some mathematical models which are widely used in applied research (agriculture, economics, electrical engineering, biology, biotechnology, medicine, such as a two-parameter exponential regression model, a two-parameter power regression model, Fox`s model, Cobb-Douglas model, Schumacher equation and others.**Programme:**Internal project of J. J. Strossmayer University of Osijek**Project members:**Darija Marković, Dragana Jankov Maširević, Dragan Jukić, Luka Borozan(student)**Project duration:**25 September 2013 - 24 September 2014 - "Parallel computing on the graphics chip in a discrete optimisation problem", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek) - Project coordinator: Domagoj Matijević
**Summary:**By designing fast parallel algorithms we want to approximately solve a (mixed) packing and covering problem. By modifying the existing algorithms and comparing their performance we want to determine the most appropriate algorithm for the parallel CUDA computing model. The project result will significantly contribute to approximate solution of many NP-hard combinatorial optimisation problems which have important applications in robotics and telecommunications. For example, the SIMPLEX method solves an LP problem with 5,000 variables and 5,000 conditions in two hours by using a computer with one modern CPU. The objective is to efficiently solve the problem with the number of variables and parameters up to 50,000 by using modern graphics NVIDIA chips.**Programme:**Internal project of J. J. Strossmayer University of Osijek**Project members:**Domagoj Matijević, Domagoj Ševerdija, Slobodan Jelić**Project duration:**1 October 2013 – 1 October 2014 - "Evolutionary Friedrichs systems", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek) - Project coordinator: Krešimir Burazin
**Summary:**Friedrichs systems are a broad class of linear PDEs which includes many seemingly significantly different equations in a unique enviroment. In the last ten years, significant progress was made in their development, new results were obtained that refer to well established tasks for stationary Friedrichs systems and new numerical schemes were developed, which has motivated their further study. In this project, we will study nonstationary, i.e., evolutionary Friedrichs systems (in which the time variable occurs), and their possible applications, which naturally imposes further development of some well-known methods used in the study of PDEs.More precisely, our goal is to study under which assumptions the initial-boundary task for the evolutionary Friedrichs system is well posed in the weak sense, to explore the possibility of practical applications, as well as the possible generalisations of the existing compactness theory by compensation in the L^p-L^q case.

Research will be carried out by using semigroup theory, Galerkin method, and the vanishing viscosity method, while compactness by compensation will be explored by using pseudodifferential operators.

**Programme:**Internal project of J. J. Strossmayer University of Osijek**Project members:**Krešimir Burazin, Marin Mišur, Ivana Vuksanović**Project duration:**25 September 2013 – 25 September 2014 - "Optimisation of semi-active damping in vibrating systems", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek) - Project coordinator: Zoran Tomljanović
**Summary:**In many physical and engineering models, dangerous vibrations can damage or even break the resonant system, therefore optimal systems control has a wide range of applications.Research into damping optimisation is a very challenging problem that often leads to problems for which the numerical solution takes a lot of time, mathematical operations and computer memory. Therefore, in this project, we want to develop optimisation approaches that will effectively count the approximation of the solution to the considered optimisation problem.

In this project, special emphasis will be placed on the problem of optimising semi-active damping. In the above system, the basic problem is to minimise the impact of input to output such that we optimise the coefficients in the damping matrix. The impact of input to output can be measured by impulse response energy. This criterion leads to the resolution of the corresponding Lyapunov equation.

The goal is also to theoretically justify approximation algorithms. In this sense, we want to develop and apply perturbation theory that studies the eigenvalue square problem corresponding to the resonant problem.

**Programme:**Internal project of J. J. Strossmayer University of Osijek**Project members:**Zoran Tomljanović, Suzana Miodragović**Project duration:**1 January 2014 – 31 December 2014 - “Some applications of geometric representations of graphs”, within the framework of the collaborative project “Geometric representations and symmetries of graphs and other discrete structures and applications in science” (Department of Mathematics, J.J. Strossmayer University of Osijek - Croatian Science Foundation and European Science Foundation) – coordinator of the individual project: Antoaneta Klobučar, coordinator of the collaborative project: Tomaž Pisanski
**Summary:**Geometric and other representations of graphs or graph-based structures have important applications in mathematics, computer science, social networks, chemistry, bioinformatics, etc. The main goal of the project is to develop a coherent theory of graph representations, mostly of symmetric or almost symmetric structures and products. The knowledge acquired by the researches will be applied to geometrically interesting combinatorial structures like configurations, maps and polytopes, as well as to large partially symmetric networks. The project will consist of the following parts:

1. representation and enumeration of highly symmetric graphs;

2. almost symmetric graph structures;

3. representation of large networks;

4. representations and configurations of symmetric maps and polytopes;

5. graph representations in mathematical chemistry and bioinformatics.

The individual goal of the project is to apply graph theory in the fields of chemistry, bioinformatics, sociological research and graph products.**Partners in the project:**

Faculty of Mathematics and Physics, Koper, Slovenia,

Faculty of Mathematics and Physics, Ljubljana, Slovenia,

Faculty of Arts and Sciences, Istanbul, Turkey,

Faculty of Mathematics, Natural Sciences and Information Technologies, Koper, Slovenia,

Faculty of Mathematics, Physics and Informatics, Bratislava, Slovakia,

Faculty of Mathematics and Computer Science, Leipzig, Germany,

Montanuniversitaet Leoben, Leoben, Austria

Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek**Programme:**EUROCORES “Graphs in Geometry and Algorithms (Euro GIGA)” European Science Foundation**Project members:**: Snježana Majstorović (J.J. Strossmayer University of Osijek, Department of Mathematics), Damir Vukičević, Jelena Sedlar, Tanja Vojković (University of Split, Faculty of Science)**Project duration:**1 May 2011 – 30 April 2014 - “Fast and efficient kinetic spanners” (J.J. Strossmayer University of Osijek, Department of Mathematics - Ministry of Science, Education and Sports - Deutscher Akademischer Austauschdienst (DAAD)) – Project coordinator: Domagoj Matijević
- 2007 - 2013 “Nonlinear parameter estimation problems in mathematical models” (235-2352818-1034) (J.J. Strossmayer University of Osijek, Department of Mathematics - Ministry of Science, Education and Sports) – Project coordinator: Dragan Jukić
- 2007 - 2013 “Statistical aspects of estimation problem in nonlinear parametric models” (235-2352818-1039) (J.J. Strossmayer University of Osijek, Department of Mathematics - Ministry of Science, Education and Sports) - Project coordinator: Mirta Benšić
- 2007 - 2013 “Passive control of mechanical models” (235-2352818-1039)" (J.J. Strossmayer University of Osijek, Department of Mathematics - Ministry of Science, Education and Sports) - Project coordinator: Ninoslav Truhar
- 2001 - 2006 “Parameter estimation in mathematical models” (0235001)" (J.J. Strossmayer University of Osijek, Department of Mathematics - Ministry of Science and Technology) – Principal investigator: Rudolf Scitovski
- 2001 - 2006 “Statistical aspects of parameter estimators in mathematical models” (0235002)" (J.J. Strossmayer University of Osijek, Department of Mathematics - Ministry of Science and Technology) - Principal investigator: Mirta Benšić
- 1• 1996 - 2000 “Parameter identification problems in mathematical models” (165021)"(J.J. Strossmayer University of Osijek, Department of Mathematics - Ministry of Science and Technology) - Principal investigator: Rudolf Scitovski
- • 1991 - 1995 “Application of numerical and finite mathematics” (1-01-129)" (J.J. Strossmayer University of Osijek, Faculty of Electrical Engineering - Ministry of Science and Technology) - Principal investigator: Rudolf Scitovski