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Division of Molecular Photophysics and Didactics of Physics |
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Methods of physics education which induce dynamic participation, commitment, activeness and initiative of students (the so-called heuristicm techniques, exploiting, among others, teaching based on finding answers to questions);
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Issues concerning substantial correctness of physical content being taught (textbooks on physics, in that academic ones, scientific publications and papers for general public);
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Application of micro-computers for automation of measurement processes, in particular, in case of problems concerning interfacing and probes design, providing relevant operating system level software as well as dedicated applications utilizing integrated micro-controllers;
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Application of micro-computers in education of physics in a range of physical experiments.
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Division of Acoustics and Nuclear Physics |
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Ultrasonic spectroscopy (frequency dependence of the absorption and the velocity propagation of ultrasound in fluids)
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Photo-acoustics spectroscopy (PAS -- investigation of non-radiative processes)
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Acoustical modal analysis of instruments, room acoustics, noise control, acoustic isolation problems
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Surface reology of composite organic matter films present as pollutants at air/water interfaces of atmospheric, fresh and marine waters
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Surface tensometry studies of drug-preservative lecithin pharmaceutical formulations
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Wettability energetics parameters of natural and artificial solid substrata submerged in natural water bodies as indicators of pollution state level. Wettability characterization of different solid/liquid systems of concern in technology and medicine with a contact angle hysteresis methodology
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Division of Algebra |
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Mapping class groups and their properties
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Symmetries of Riemann and Klein surfaces
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Automorphism groups of Klein surfaces
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Division of Applied Mathematics and Probability |
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Markov processes and their stability
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Random dynamical systems
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Limits theorems – Central Limit Theorem and Law of Large Numbers
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Fractal sets
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Stochastic differential equations in infinite dimensions
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Division of Applied Physics |
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High resolution spectroscopy of atomic systems
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Precision spectroscopy of atoms in an external fields
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Magnetic resonance imaging and spectroscopy of cardiac and skeletal muscles
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Synthesis and characterization of new hydrogel nanocomposite polymers containing clay nanoparticles by means of physical methods and NMR spectroscopy to their application in pharmacy and medicine
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Division of Artificial Intelligence |
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Multi-Agents Systems
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Software Agents
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Petri hypernets
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3D Graphics
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Digital image processing
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Nature inspired algorithms
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Division of Atomic and Molecular Spectroscopy and Astrophysics |
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Interaction of strong coherent light beams with atomic medium
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Propagation of light pulse in atomic medium in presence of collisional relaxation, magnetic field and strong electromagnetic field
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Theoretical calculations of potential energies for heavy two-atomic molecules
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”Ab-initio” calculations of electronic structure of ionic crystals
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Theoretical studies of pressure influence on luminescence spectra
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Investigation of physical conditions in interstellar matter by means of ultraviolet satellite spectra
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Division of Biomaterials and Medical Physics |
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Optical hybrid organic-inorganic materials, thin luminescent films, organic luminescent materials
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Surface plasmon resonance and surface plasmon coupled emission. Experimental techniques and biomedical applications
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Energy transfer and trapping in polymers, glasses, gels, biological membranes, proteins, solutions and low dimensional systems molecular aggregation
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Enhanced energy transfer
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Spectroscopic properties of biologically and medically active species
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Time-resolved and steady state luminescence spectroscopy
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Monte-Carlo simulations and meta dynamics
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Division of Combinatorial Optimization |
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Ramsey numbers – classical, three color, on-line
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Graph coloring
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Discrete and computational geometry
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Bio-inspired and on-line algorithms in data mining
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Statistical methods in data mining
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Division of Condensed Matter Spectroscopy |
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Spectroscopic investigation of optoelectronic materials doped with transition metals and rare earth ions
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Spectroscopic analysis of the lattice dopand systems under high hydrostatic pressure
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Analysis and modeling of relaxation and energy transfer process in solids
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Numerical calculations of energy structure and relaxation process for transition metal rare earth ions in lattices
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Division of Didactics of Mathematics |
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Teaching of gifted students
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Transition from basic to middle level in teaching of mathematics
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Computers in teaching of mathematics
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Division of Formal Languages |
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Mathematical linguistics
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Combinatorics
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Mathematical libraries
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Space complexity
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Concurrency
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Division of Geometry |
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Knot theory and its generalization
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Flat manifolds, crystallographic groups
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Calabi-Yau manifolds
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Skein modules of 3-dimensional manifolds
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Topology of wild spaces
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Division of Mathematical Analysis |
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Approximation of nonlinear boundary problems
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Nonlinear spectral problems in finite dimension
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Mathematical structures of quantum mechanics
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Iterative methods in solving Darboux problem with function dependence
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Basic problems for functional-differential equations
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Division of Mathematical Methods of Physics |
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Quantum theory of open systems
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Quantum probability
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Noncommutative Orlicz spaces and their applications
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Modeling of synchronization in physiological systems
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Analysis of physiological signals via computer techniques
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Quantum thermodynamics
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Division of Quantum Optics and Information |
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Theory of quantum correlations
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Thermodynamics as a resources theory
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Theory of quantum resources: entanglement and non-classicality
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Experimental realizations of quantum information schemes (in collaboration with experimental groups)
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Quantum interferometry
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Quantum communication
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Division of Real Functions |
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Ideal convergence of sequences of functions
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Hamel bases and Hamel-like functions
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Omega-limits of one dimensional dynamical systems
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Lineability and algebrability of real functions
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Ideal types of ‘equal’-convergence for sequences of functions
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Division of Set Theory |
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Isomorphisms of Ellentuck and Hechler topology
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Ideal convergence of series
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Axial continuous functions
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Ideals and sigma ideals defined by density topology
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Division of Topology |
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Polynomial mappings into Stiefel manifolds
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Homotopy classes of Stiefel-Whitney manifolds
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Real curve singularities
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Polynomials mappings from the plane into the plane
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Real algebraic geometry and singularity theory
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Institute of Informatics |
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Mathematical linguistics
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Space complexity
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Algorithms in data mining
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Combinatorics, Ramsey numbers
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Multi-Agents Systems, Software agents
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Graph coloring
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Petri hypernets
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