## Division of Mathematical Analysis

**Head of the Division:**

Assist. Prof. Danijel Krizmanić

**Members of the Division:**

Assist. Prof. Bojan Crnković

Assist. Prof. Davor Dragičević

Assist. Prof. Danijel Krizmanić

Assist. Prof. Ivana Slamić

Assist. Prof. Milena Sošić

Lecturer Ines Radošević Medvidović

**Aims and organization of the Division**

Activities of the Division include:

- gathering staff members that work in similar, same or compatible scientific areas based on Mathematical Analysis

- professional, technological and innovation activities

- taking care of teaching

- continuous work on the improvement of educational process as well as on the increase of scientific production

Division for Mathematical Analysis was formed in 2009. It gathers staff members whose scientific 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

Division consists of six members, five of which hold a PhD degree while one member holds a master’s degree. Five members hold a tenure track position, while one holds position of a lecturer.

**Scientific work**

In their scientific work, members of the Division collaborate with mathematicians from different countries, participate and present their scientific 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 scientific projects:

- Nonautonomous dynamical systems:hyperbolicity and statistical properties (leader: Davor Dragičević), initial research support by University of Rijeka for junior researchers
- Modelling and control of dynamical systems with applications (leader: Bojan Crnković), initial research support by University of Rijeka for junior researchers
- Geometric, ergodic and topological analysis of low dimensional dynamical systems, (leader: Siniša Slijepčević, PMF, Zagreb), financed by Croatian science foundation

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 (leader: Zoran Vondraček, PMF, Zagreb), 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 (leader: Neven Grbac), research support by University of Rijeka

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

List of selected scientific papers:

• 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, Nelida, 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. Krizmanić: Weak convergence of multivariate partial maxima processes, Journal of multivariate analysis 155 (2017), 1-11.

• D. Krizmanić: Functional weak convergence of partial maxima processes, Extremes 19 (2016), 7-23.

• B. Basrak, D. Krizmanić: A Multivariate Functional Limit Theorem in Weak M1 Topology, Journal of theoretical probability 28 (2015), 119-136.

• D. Krizmanić: J1 convergence for partial sum processes with a reduced number of jumps, Probability and Mathematical Statistics 35 (2015), 107-128.

• 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.

• L. Barreira, D. Dragičević, C. Valls: Tempered exponential dichotomies and Lyapunov exponents for perturbations, Communications in contemporary mathematics 18 (2016), 1-16.

• L. Bareira, D. Dragičević, C. Valls: Admissibility for exponential dichotomies in average, Stochastics and dynamics 15 (2015), 1-16.

• L. Barreira, D. Dragičević, C. Valls: From one-sided dichotomies to two-sided dichotomies, Discrete and continuous dynamical systems 35 (2015), 2817-2844.

• D. Dragičević: Admissibility, a general type of Lipschitz shadowing and structural stability, Communications on pure and applied analysis 14 (2015), 861-880.

• L. Bareira, D. Dragičević, C. Valls: Characterization of strong exponential dichotomies, Bulletin of the Brazilian mathematical society 46 (2015), 81-103.

• L. Bareira, D. Dragičević, C. Valls: Admissibility and nonuniform exponential trichotomies, Regular & chaotic dynamics 20 (2015), 49-62.

• L. Bareira, D. Dragičević, C. Valls: Nonuniform hyperbolicity and admissibility, Advanced nonlinear studies 14 (2014), 791-811.

• I. Slamić: l^p -linear independence of the system of integer translates, The 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**

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 Biotechnology and on Faculties of Humanities and Social Sciences, Civil Engineering and Engineering.

For their courses, most staff members have formed corresponding e-courses on systems Mudri and 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).

Through their teaching activities, members of the Division support professional activities of students which resulted with a series of papers produced in a collaboration between staff members and their students. Some of the most recent ones are:

• D. Čudina, I. Slamić: Some applications of the properties of convexity and concavity in economics, Croatian mathematical electronic journal math.e 31 (2017).

• D. Krizmanić, V. Skobljanec: Some dilemmas, paradoxes and delusions in probability, Mathematics and School 18 (2017), 123-127.

**Professional activities**

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. In a collaboration with the Agency for upbringing and education, in 2015 and 2018 the Division has organized Rijeka mathematical meetings with the purpose of professional development of elementary and high school teachers and popularization of Mathematics among high school students.