**Current projects**

- "Vibration Reduction in Mechanical Systems (VIMS)", (Department of Mathematics, J. J. Strossmayer University of Osijek - Croatian Science Foundation) - Project coordinator: Zoran Tomljanović
**Summary:**Vibration analysis and vibration reduction for mechanical systems are prominent problems in numerous research fields. Although the vibrations analysis is an intensively studied topic in recent decades, many problems still remain open. While the case without external excitation leads to the study of homogeneous systems, presence of an external forcing leads to the study of nonhomogeneous systems. Depending on the presence of an external excitation and applications, we will consider four different research themes. Within the first research theme, we will study theoretical results that are relevant for vibration reduction. We plan to develop theoretical results that characterize important properties of the quadratic eigenvalue problem (QEP) arising from vibration analysis of mechanical systems. Within the second research theme we develop new methods for frequency isolation and utilize methods which are based on algorithms for non-smooth optimization. For this case we will derive new algorithms that preserve the structure of the matrices and structural properties of the considered QEP. In the third research theme, we will consider vibration reduction based on criteria that use system norms (e.g. H2 and Hinf) for Multiple-Input Multiple-Output case. We will also study approaches for approximating the full-order model with a reduced-order model that retains the structure of parametric dependence. The new approaches will be well suited for computationally efficient parameter optimization and the study of important system properties. In the fourth research theme we will consider integrating research themes I-III and applications in real world examples. Moreover, we will apply obtained new approaches and algorithms in various academic examples, but also in real life examples that arise, e.g., in car industry (such as disc brake problem) and civil engineering (such as beams, civil buildings), etc. Therefore, the result from this project could have wide applications.**Programme:**Croatian Science Foundation**Project members:**Serkan Gugercin, Ivana Kuzmanović Ivičić, Suzana Miodragović**Project duration:**1 January 2020 - 31 December 2023 - "yyy"
**Summary:****Programme:**The program of scientific-technological cooperation between the Republic of Croatia and the Republic of Serbia, Ministry of Science, Education and Sports**Project members:**Nenad Šuvak, Jasmina Đorđević, Danijel Grahovac, Miljana Jovanović, Ivan Papić, Marija Milošević, Una Radojičić, Marija Krstić, Dušan Đorđević**Project duration:**1 January 2019 - 31 December 2020 - "Application of short-range dependent stohastic models", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of Science and Education ) - Project coordinator: Nenad Šuvak
**Summary:****Programme:**The program of scientific-technological cooperation between the Republic of Croatia and the Republic of Serbia, Ministry of Science, Education and Sports**Project members:**Nenad Šuvak, Jasmina Đorđević, Danijel Grahovac, Miljana Jovanović, Ivan Papić, Marija Milošević, Una Radojičić, Marija Krstić, Dušan Đorđević**Project duration:**1 January 2019 - 31 December 2020 - "Application of short-range dependent stohastic models", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of Science and Education ) - Project coordinator: Nenad Šuvak
**Summary:****Programme:**The program of scientific-technological cooperation between the Republic of Croatia and the Republic of Serbia, Ministry of Science, Education and Sports**Project members:**Nenad Šuvak, Jasmina Đorđević, Danijel Grahovac, Miljana Jovanović, Ivan Papić, Marija Milošević, Una Radojičić, Marija Krstić, Dušan Đorđević**Project duration:**1 January 2019 - 31 December 2020 - "Application of optimization methods in biomedicine", (Department of Mathematics, J. J. Strossmayer University of Osijek - Ministry of Science and Education ) - Project coordinator: Slobodan Jelić
**Summary:****Programme:**The program of scientific-technological cooperation between the Republic of Croatia and the Republic of Serbia, Ministry of Science, Education and Sports**Project members:**Slobodan Jelić, Dušan Jakovetić, Domagoj Ševerdija, Tatjana Davidović, Snježana Majstorović, Irena Jovanović, Luka Borozan, Nataša Krejić, Mateja Đumić, Nataša Krklec Jerinkić, Rebeka Čorić, Luka Matijević, Marija Mioč**Project duration:**1 January 2019 - 31 December 2020 - "Computer managed corpus linguistics - UNIOS - ZUP 2018 - Youth Research Projects", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek ) - Project coordinator: Domagoj Ševerdija
**Summary:**Corpus linguistics investigate languages by using samples from given real-world texts. As a digitalized data source, it brings great possibilities for computer processing of corpus data inorder to help making corpus-based judgments. Most digitalized corpora today usually encompass a framework where one can make a linguistic-specific analysis. In this project, a unique network as a web application will be realized which will enable linguistic researchers to form their own corpora having at its disposal a set of tools for corpora analytics. This framework will be used for several case studies which are mostly investigated by theoretical linguistics approach. Our approach will be based on corpus data classification with respect to morphological and semantic features using standard corpus-based classification methods and recursive/recurrent neural network deep learning methods.**Programme:**UNIOS - ZUP 2018 - Youth Research Projects**Project members:**dr. sc. Ana Mikić Čolić, Assistant Professor (Faculty of Philosophy, Josip Juraj Strossmayer University of Osijek) i dr. sc. Mario Essert, Full Professor (Faculty of Mechanical Engineering and Naval Arcitecture of the University of Zagreb)**Project duration:**18 month - "Isolation of the unwanted part of the spectrum in the quadratic eigenvalue problem - UNIOS - ZUP 2018 - Youth Research Projects", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek ) - Project coordinator: Suzana Miodragović
**Summary:**Some important properties of vibrational systems can be described by the corresponding quadratic eigenvalue problem. In the case when the eigenvalues of the mechanical system are close to the frequency of the external force this system undergo large oscillations. This is the phenomenon of so-called resonance. This acting of the system can be avoid by isolating the part of the eigenvalues in corresponding quadratic eigenvalue problem. If we define so-called resonance band in which we do not want eigenvalues, then the idea is to slightly modify damping matrix in order to obtain a new system whose eigenvalues are outside the resonance band. This problem will be obtained for the hyperbolic and also for gyroscopic quadratic eigenvalue problems.**Programme:**UNIOS - ZUP 2018 - Youth Research Projects**Project members:**Ninoslav Truhar (Department of Mathematics, J. J. Strossmayer University of Osijek), Zoran Tomljanović (Department of Mathematics, J. J. Strossmayer University of Osijek), Matea Puvača (Department of Mathematics, J. J. Strossmayer University of Osijek), Fernando de Teran (Universidad Carlos III de Madrid, Math. Department)**Project duration:**18 months - "Limiting behavior of intermittent processes and diffusions - UNIOS - ZUP 2018 - Youth Research Projects", (Department of Mathematics, J. J. Strossmayer University of Osijek - J. J. Strossmayer University of Osijek ) - Project coordinator: Danijel Grahovac
**Summary:**The inference in statistics and probability theory is largely based on limiting results that describe the stochastic properties of different models when time tends to infinity. For example, the central limit theorem guarantees that under some conditions the arithmetic mean has approximately a normal Gaussian distribution. Today it is quite clear that such results cannot describe the complexity of natural phenomena. Among other things, it is not possible to explain the fact that some phenomena show different behavior in small and large time scales (e.g. turbulent fluid flow, value of the financial asset, etc.). In this project the limiting properties of stochastic models will be studied. Emphasis will be placed on models that have the property of intermittency and on the implications that this property has on the stochastic nature of the model. In addition, the class of diffusion models will be studied, the limiting behavior of estimators of unknown parameters in these models, and the approximation of their transition density functions.**Programme:**UNIOS - ZUP 2018 - Youth Research Projects**Project members:**Nenad Šuvak (Department of Mathematics, J. J. Strossmayer University of Osijek), Ivan Papić (Department of Mathematics, J. J. Strossmayer University of Osijek), Nikolai N. Leonenko (School of Mathematics, Cardiff University), Murad S. Taqqu (Department of Mathematics and Statistics, Boston University), Una Radojčić (Department of Mathematics, J. J. Strossmayer University of Osijek) i Mirta Benšić (Department of Mathematics, J. J. Strossmayer University of Osijek)**Project duration:**18 months - "The optimization and statistical models and methods in recognizing properties of data sets measured with errors- Young Researchers' Career Development Project - Training of Doctoral Students", (Department of Mathematics, J. J. Strossmayer University of Osijek - Croatian Science Foundation) - Project coordinator: Mirta Benšić
**Summary:**The PhD student will deal with the methods of nonlinear regression and classification. Emphasis is placed on understanding, developing and applying nonparametric methods including neural networks. The specific purpose of this PhD education programme is to contribute to mathematical understanding of statistical and algorithmic properties of multilayer neural networks and related methods with a tendency to find expressions for the approximation of errors, complexity, statistical risk and time of calculation. Theoretically the results will be supported by simulations and applied to real problems. The PhD student is planned to enrol in the Joint Postgraduate Doctoral Study Programme in Mathematics of the universities of Osijek, Rijeka, Split and Zagreb, to specialise in the field of probability and mathematical ststistics and to further educate and train at the University of Yale (led by Prof. Andrew Barron).**Programme:**Young Researchers' Career Development Project - Training of Doctoral Students**Mentor's name and surname:**Mirta Benšić**PhD name and surname:**Una Radojičić**Project duration:**1 March 2017 - 28 February 2021 - "Optimization of parameter dependent mechanical systems - Young Researchers' Career Development Project - Training of Doctoral Students", (Department of Mathematics, J. J. Strossmayer University of Osijek - Croatian Science Foundation) - Project coordinator: Ninoslav Truhar
**Summary:**The doctoral student will deal with the optimization of active and passive damping of mechanical systems with and without external force. For this purpose, it will be necessary to develop a general theoretical framework that describes many important system properties and to construct adequate numerical algorithms for calculating the desired sizes. The doctoral candidate is planned to enroll in the Joint university postgraduate doctoral study program in mathematics at the universities of Osijek,Rijeka, Split and Zagreb and specialize in the field of control and optimization theory, i.e. ordinary differential equations and dynamic systems.**Programme:**Young Researchers' Career Development Project - Training of Doctoral Students**Mentor's name and surname:**Ninoslav Truhar**PhD name and surname:**Matea Puvača**Project duration:**20 September 2016 - 20 September 2020 - "Real-time measurements and forecasting for successful prevention and management of seasonal allergies in Croatia-Serbia cross-border region", (Department of Mathematics, J. J. Strossmayer University of Osijek - Interreg IPA CBC Croatia - Serbia 2014-2020) - Project coordinator: Kristian Sabo
**Summary:**Allergen avoidance is important for managing allergy. Knowledge about when certain pollen types are likely to be in the air helps allergy sufferers to plan activities and medication use. Since airborne pollen is transported by air masses it can easily cross the border resulting an increased risk for allergy symptoms in sensitive population. Airborne allergens are routinely monitored in cross-border area. However, applied methodology is time consuming and results are disseminated to end users with a delay which limits the impact of collected data in every day health management. The project will modernize public health service and notably enhance the quality and applicative value of the information they provide in cross-border area: by introducing real time monitoring of airborne allergens, by developing models for prediction exposure and by creating a joint platform for instantaneous dissemination of these information. In addition the project will make an effort to educate end users on the benefits from using information for prevention and management of allergy symptoms coming from the information public health services will provide following the implementation of this project. The project will focus on three major pollen allergens (i.e. Birch, Grass, Ambrosia) and thus, having in mind overall prevalence of seasonal allergies in the Croatia-Serbia cross-border region, its results will enhance public health services needed for 15-30% of the population. Particular attention will be given to introduction of developed services to vulnerable groups i.e. children and elderly people for which it can help to plan travelling, outdoor activities, start of the therapy, self assessment of the therapy effectiveness etc. Joint approach for dissemination of measurements and forecasts will improve information flow for people travelling from one side of the border to another but also for visitors coming from other regions.**Programme:**Interreg IPA Cross-border Cooperation Programme Croatia - Serbia 2014-2020**Project partners:**Institut BioSens - Istraživačko razvojni institut za informacione tehnologije biosistema (Lead Beneficiary), Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu and Grad Osijek**Project members:**Kristian Sabo, Krešimir Burazin, Nenad Šuvak and Slobodan Jelić**Project duration:**15 July 2017 - 14 January 2020 - "The optimization and statistical models and methods in recognizing properties of data sets measured with errors", (Department of Mathematics, J. J. Strossmayer University of Osijek - Croatian Science Foundation) - Project coordinator: Rudolf Scitovski
**Summary:**As a part of an attractive and active area of research known as big data analysis, optimization and statistical aspects of recognizing data sets properties will be analyzed. Research will be focused on clustering problems, deconvolution models and applications. The assumption is that the observed data sets represent the measured values of the variables to be analyzed but also that they contain a measurement error. In large data sets it is often appropriate to cluster data sets on the basis of certain characteristics and then apply models for each group that can describe variable properties such as relationship among them, possibility of separation, edges, specific form of the set of values, dimensions (length, surface or volume) of the set of values or general parameter vector which determines them. The problem in many practical situations can be formulated as an optimization problem for which the objective functions is generally neither differentiable nor convex. In order to solve such problems effectively, rapid and accurate numerical procedures will be developed. Also, due to errors in the data,in order to understand and correctly interpret the results, statistical models will be used and important statistical properties will be characterized.**Programme:**Croatian Science Foundation (IP-06-2016)**Team members (UNIOS):**Andrew Barron (Yale University, USA), Mirta Benšić (Department of Mathematics, University of Osijek, Croatia), Dragan Jukić (Department of Mathematics, University of Osijek, Croatia), Karlo Emmanuel Nyarko (Faculty of Electrical Engineering, Computer Science and Information Technology Osijek, University of Osijek, Croatia), Safet Hamedović (Faculty of Metallurgy and Materials, University of Zenica, BiH), Kristian Sabo (Department of Mathematics, University of Osijek, Croatia), Petar Taler (Department of Mathematics, University of Osijek, Croatia)**Project duration:**1 March 2017 - 28 February 2021