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Faculty of Applied Mathematics - Scientific research

 

The Departments of the Faculty of Applied Mathematics conduct research in the following fields of study:

 

The Department of Algebra

Group theory, linear algebra and their interactions with geometry, mathematical logic and topology.

 

The Department of Mathematical Analysis and Topology

Wide range of problems connected to the mathematical analysis and topology, more precisely, dynamic systems on torus, generalization of Lapunow's functions, mathematical problems in control theory, as well as geometry of various subclasses of geodesic spaces and the metric fixed point theory, functional equations and inequalities, stability of functional equations, ultrafilters, infinite dimensional topology, continuum theory, topological groups and metrizable groups, vector series, special functions.

 

The Department of Computational and Industrial Mathematics

Artificial intelligence and its application, analytical and approximate methods of solving technical problems (in particular, the direct and inverse heat conduction problems and problems connected to the solidification of metals and their alloys) based, among others, on the optimization algorithms inspired by nature. Algorithms of solving the direct and inverse heat conduction problems of fractional order. Application of wavelets in solving technical heat conduction problems. System dynamics. Safety analysis of water supply system.

Research projects implemented by the Department members:

  • "Application of biologically inspired algorithms in solving inverse problems of solidification of metals and their alloys", 2012-2015, financed by the National Science Centre;
  • "Application of genetic algorithms in solving the inverse Stefan problem", 2007-2009, financed by the Ministry of Science and Higher Education. 

 

The Department of Computer Science

Dynamics of nonlinear systems, chaos and fractals, discrete dynamical systems and their application in computer science, chaos-based cryptography, sorting large data sets in NoSQL databases, artificial intelligence and its application, modelling of the human-computer interaction, quality assessment for UX, rating and comparison of developed interaction quality, adaptable user interfaces. Queueing theory, in particular the queueing models with various limitations in access to the service station and periodical suspension of processing (single/multiple vacation, N-policy, setup/closedown times type mechanisms), queueing models with failures of service station, mechanisms of Active Queue Management (AQM), reliability theory, scheduling of tasks, boundary problems for processes of independent increments and random walks on the Markov chains. Broadly defined stochastic modelling and simulations. Application of statistical and probabilistic methods in medical, economical and technical sciences. Algebraic algorithms of computer tomography with incomplete data input.

Research projects implemented by the Department members:

  • "Stochastic characteristics of single-channel queueing systems with limited access to server", 2013-2015, financed by the National Science Centre;
  • "Construction of detectors of features and shapes on 2D images for use in decision support systems", 2016-2017, financed by the Ministry of Science and Higher Education;
  • "Two-dimensional image analysis and categorization of components using methods of artificial intelligence", 2016-2019, the Diamond Grant;
  • "Mathematical-simulative analysis of periodic and quasi-periodic oscillations and chaos in chemical tubular reactors and the catalyst grain", 1997-1999, financed by the State Committee for Scientific Research;
  • "Theoretical analysis of stability and dynamics of non-adiabatic heterogeneous tubular reactor with longitudinal dispersion and recirculation of mass", 2000-2003, financed by the State Committee for Scientific Research;
  • "IT system supporting the optimization and planning of production and distribution of water intended for human consumption in the sub-region of central and western province of Silesia”, co-financed by the European Union from the European Regional Development Fund, Sub-measure 1.3.1. "Development Projects".
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