Division of Mathematical Analysis

Division for Mathematical Analysis

 
Head of the Division:

Assoc. Prof.  Davor Dragičević

Members of the Division:

• Assoc. Prof. Bojan Crnković
• Assoc. Prof. Davor Dragičević
• Assoc. Prof. Danijel Krizmanić
• Assist. Prof. Ivana Slamić
• Assist. Prof. Milena Sošić
• Sen. Lecturer Ines Radošević Medvidović
• Emma Šepić

 
Division for Mathematical Analysis was formed in 2009. It gathers staff members whose research activities and interests are related to the following fields of Mathematics:

• Functional Analysis
• Numerical Analysis and Applications
• Dynamical Systems
• Probability Theory and Statistics
• Differential Geometry

 
The Division has seven members, five of which are holding tenure track positions, one senior lecturer and one teaching assistant.

 
Science

Members of the Division collaborate with mathematicians from different countries, participate and present their research achievements on international scientific conferences and seminars, visit international institutions, review papers for relevant databases of mathematical literature and referee papers submitted for publication to international journals.

Members of the Division actively participate in the realization of the following research projects:

• Transfer operators, statistical laws and infinite dimensional dynamical systems (principal investigator: Davor Dragičević), financed by the Croatian Science Foundation
• Methods of mathematical analysis in theoretical and applied mathematics (principal investigator: Davor Dragičević), UNIRI project, University of Rijeka
• Smart cities in function of national economy development (principal investigator: Saša Drezgić), UNIRI project, University of Rijeka
• Stochastic methods in mathematical analysis (principal investigator: Danijel Krizmanić), UNIRI-plus project, University of Rijeka

 
Finished research projects in which members of the Division participated:

• Mathematical and numerical modeling of the compressible micropolar fluid (principal investigator: Nermina Mujaković), research support by University of Rijeka
• Stochastic methods in analytic and applied problems (principal investigator: Zoran Vondraček), financed by Croatian science foundation
• Discovery and tracking of coherent structures in geophysical flows (leaders: M. Dellnitz, G. Froyland, O. Junge i A. Quas), financed by Australian Research Council
• Algebraic and analytic methods in number theory (principal investigator: Neven Grbac), research support by University of Rijeka    
• On A Data-Driven, Operator-Theoretic Framework for Space-Time Analysis of Process Dynamics (leader: Maria Fonoberova), financed by Defense Advanced Research Projects Agency (USA)
• Geometric, ergodic and topological analysis of low dimensional dynamical systems, (principal investigator: Siniša Slijepčević), financed by Croatian science foundation
• Modeling anomalous diffusion by generalized Langeven, Fokker-Planck equations and fractional diffusion-wave equations (Anomalous diffusion) (leader: Živorad Tomovski), NEWFELPRO project
• Modelling  and control of  dynamical  systems with  applications (leader: Bojan Crnković), initial research support by University of Rijeka for junior researchers
• Nonautonomous dynamical systems: hyperbolicity and statistical properties (leader: Davor Dragičević), initial research support by University of Rijeka for junior researchers

 
Members of the Division regularly publish considerable number of research papers both individually and in a collaboration with researchers from other scientific institutions. Large number of those papers is published in highly prestigious international journals.


List of selected research papers:

• S. Ivić, B. Crnković, H. Arbabi, S. Loire, P. Clary, I. Mezić: Search strategy in a complex and dynamic environment: the MH370 case, Scientific Reports 10, 19640 (2020)
• T. Bosner, B. Crnković, J. Škifić: Application of CCC–Schoenberg operators on image resampling. BIT 60 (2020), 129–155.
• B. Crnković, T. Sandev, Ž. Tomovski: Generalized distributed order diffusion equations with composite time fractional derivative, Computers & Mathematics with Applications 73 (2017), 1028-1040.
• B. Crnković, N. Črnjarić-Žic, L. Kranjčević: Improvements of semi-implicit schemes for hyperbolic balance laws applies on open channel flow equations, Computers & Mathematics with Applications 58 (2009), 292-309.
• D. Dragičević, Y. Hafouta: Limit Theorems for Random Expanding or Anosov Dynamical Systems and Vector-Valued Observables, Ann. Henri Poincaré 21 (2020), 3869–3917.
• D. Dragičević, W. Zhang, W. Zhang: Smooth linearization of nonautonomous differential equations with a nonuniform dichotomy, Proceedings of the London Mathematical Society 121 (2020), 32-50.
• D. Dragičević, A. L. Sasu, B. Sasu: On the asymptotic behavior of discrete dynamical systems—an ergodic theory approach, Journal of Differential Equations 268 (2020), 4786–4829.
• D. Dragičević, G. Froyland, C. Gonzalez-Tokman, S. Vaienti: A spectral approach for quenched limit theorems for random hyperbolic dynamical systems, Transactions of the American Mathematical Society 373 (2020), 629--664.
• D. Dragičević, W. Zhang, W. Zhang: Smooth Linearization of Nonautonomous Difference Equations with a Nonuniform Dichotomy, Mathematische Zeitschrift 292 (2019), 1175-1193.
• D. Dragičević: A note on the nonuniform exponential stability and dichotomy for nonautonomous difference equations, Linear algebra and its applications 552 (2018), 105-126.
• D. Dragičević, G. Froyland, C. Gonzalez-Tokman, S. Vaienti: A spectral approach for quenched limit theorems for random expanding dynamical systems, Communications in mathematical physics 360 (2018), 1121-1187.
• D. Dragičević, G. Froyland, C. Gonzalez-Tokman, S. Vaienti: Almost sure invariance principle for random piecewise expanding maps, Nonlinearity 31 (2018) 2252-2280.
• D. Krizmanić: On joint weak convergence of partial sum and maxima processes, Stochastics 92 (2020), 876-899.
• D. Krizmanić: Functional convergence for moving averages with heavy tails and random coefficients, ALEA-Latin American Journal of Probability and Mathematical Statistics 16 (2019), 729-757.
• D. Krizmanić: Joint functional convergence of partial sums and maxima for linear processes, Lithuanian Mathematical Journal 58 (2018), 457-479.
• D. Krizmanić: Weak convergence of multivariate partial maxima processes, Journal of multivariate analysis 155 (2017), 1-11.
• B. Basrak, D. Krizmanić, J. Segers: A functional limit theorem for partial sums of dependent random variables with infinite variance, Annals of probability 40 (2012), 2008-2033.
• I. Slamić: l^p(G)-linear independence and p-zero divisors, Mediterranean Journal of Mathematics 15 (2018), 1-19.
• I. Slamić: l^p -linear independence of the system of integer translates, Journal of Fourier analysis and applications 20 (2014), 766-783.
• M. Sošić: Some factorization in the twisted group algebra of symmetric groups, Glasnik matematički 51 (2016), 1-15.

 
We point out here that a member of the Division, Davor Dragičević is the co-author (together with Luis Barreira and Claudia Valls) of the book Admissibility & Hyperbolicity, published in 2018 by the prestigious publisher Springer.
 

Teaching and professional activities

Members of the Division participate in teaching of courses on both undergraduate and graduate study programme in Mathematics and they run courses on Department of Physics, Department of Informatics, Department of Polytechnics and on Faculties of Civil Engineering and Engineering.

For their courses, most staff members have formed corresponding e-courses on systems Merlin, thus implementing the most advanced didactic accomplishments in the educational process. Furthermore, due to the specificity of courses thought by the members of the Division (like Numerical Mathematics or Mathematical Statistics), we regularly follow trends in the IT technology so that the students can work in recent and widely accepted software packages and programming languages (like Phyton, C++ or R).

Besides activities related to research and teaching, members of the Division are involved in professional activities in the areas of Mathematics, Applied Mathematics and Engineering, Mathematics Education and popularization of science.