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um.vscht.cz

[google_search] => 001523547858480163194:u-cbn29rzve [social_fb_odkaz] => [social_tw_odkaz] => [social_yt_odkaz] => [intranet_odkaz] => [intranet_text] => [mobile_over_nadpis_menu] => Menu [mobile_over_nadpis_search] => Search [mobile_over_nadpis_jazyky] => Languages [mobile_over_nadpis_login] => Login [menu_home] => Homepage [aktualizovano] => Updated [autor] => Author [paticka_mapa_odkaz] => [paticka_budova_a_nadpis] => BUILDING A [paticka_budova_a_popis] => Rector, Department of Communications, Department of Education, FCT Dean’s Office, Centre for Information Services [paticka_budova_b_nadpis] => BUILDING B [paticka_budova_b_popis] => Department of R&D, Dean’s Offices: FET, FFBT, FCE, Computer Centre, Department of International Relations, Bursar [paticka_budova_c_nadpis] => BUILDING C [paticka_budova_c_popis] => Crèche Zkumavka, General Practitioner, Department of Economics and Management, Department of Mathematics [paticka_budova_1_nadpis] => NATIONAL LIBRARY OF TECHNOLOGY [paticka_budova_1_popis] => [paticka_budova_2_nadpis] => CAFÉ CARBON [paticka_budova_2_popis] => [paticka_adresa] => UCT Prague
Technická 5
166 28 Prague 6 – Dejvice
IČO: 60461373 / VAT: CZ60461373

Czech Post certified digital mail code: sp4j9ch

Copyright: UCT Prague 2015
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Department of mathematics has been an important part of the University of chemistry and technology since its foundation. It provides mathematical classes for the students of all the faculties and programs. 

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Department of Mathematics UTC Prague was transformed from the former Dpartment of Mathematics, School of Chemical Technology of Czech Technical university in Prague,  (1945 – 1952). 

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Head of the department

Doc. Ing. Jan Mareš, Ph.D.
22044 4172
Jan.Mares@vscht.cz
d A334A

 

Department administrator

RNDr. Lucie Borská, Ph.D.
22044 5035
Lucie.Borska@vscht.cz
d C208

Library

Mgr. Jana Šnupárková, Ph.D.
22044 5032
Jana.Snuparkova@vscht.cz
C202

Secretary

Ing. Pavlína Hanková
22044 3096
Pavlina.Hankova@vscht.cz
C207

Address

UCT Prague, building C
Studentská 6
166 28, Praha 6 Dejvice

Mailing address

Department of mathematics
UCT Prague
Technická 5
166 28, Praha 6 Dejvice

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Welcome to the Molecular Modeling and Simulation Group! We are a newly formed group at the Department of Mathematics at Faculty of Chemical Engineering, University of Chemistry in Prague.

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Our focus is molecular modeling and simulations of different systems, from physical chemistry of the simplest biological systems like water to various chemical processes in important biological systems, such as biological membranes and membrane proteins.

We are using different computational methods, including classical mathematical modeling, quantum chemical calculations to molecular dynamics simulations, always in combination with different experimental techniques, such as FT-IR, Raman, NMR and UV spectroscopy in collaboration with many experimental groups in Czechia and around the world.

Bachelor and master students are always welcome!

A couple of snapshots showing what we are doing:

Self-association of a highly charged arginine-rich cell-penetrating peptide

Positively charged particles are mutually repelled from each other according to the Coulomb law. However, in solvents with high dielectric constant (such as water), and in some special situations it is possible that repulsion counterintuitive converts to attraction between like-charged particles. Using molecular dynamics simulations and complementary SAXS and NMR experiments, we showed that two positively charged deca-arginines (R10) associate in water.

G. Tesei, M. Vazdar, M. Ringkjøbing Jensen, C. Cragnell, P. E. Mason, J. Heyda, M. Skepö, P. Jungwirth, M. Lund, Proceedings of the National Academy of Sciences of the United States of America, 114 (2017), 11428-11433

Arginine “Magic”: Guanidinium Like-Charge Ion Pairing from Aqueous Salts to Cell Penetrating Peptides

Guanidinium (Gdm+) cation is a pivotal moiety in arginine amino acid. Due to its structural and electronic properties, Gdm+ cations make like-charge pairs, which in turn has important consequences in numerous properties, ranging from formation of small Gdm+ clusters to cell penetration of arginine rich cell penetration peptides.

M. Vazdar, J. Heyda, P. E. Mason, G. Tesei, C. Allolio, M. Lund, P. Jungwirth, Accounts of chemical research, 51 (2018), 1455-1464

Mechanism of Cell Penetration by Permeabilization of Late Endosomes: Interplay between a Multivalent TAT Peptide and Bis(monoacylglycero)phosphate

Arginine rich peptides are used frequently as compounds which penetrate through cell membranes and are often used for pharmaceutical purposes. In collaboration with cell biologists and with help of molecular dynamic simulations, we proposed the mechanism how cell penetrating peptides permeate across endosomes, in turn reaching cellular interior.

D. J. Brock, H. Kondow-McConaghy, J. Allen, Z. Brkljača, L. Kustigian, M. Jiang, J. Zhang, H. Rye, M. Vazdar, Jean-Philippe Pellois, Cell Chemical Biology, 27 (2020), 1296-1307

Contact persons:

Y Dr. Mario Vazdar
b Mario.Vazdar@vscht.cz
e 22044 3160

Y Dr. Jaroslav Schmidt
b Jaroslav.Schmidt@vscht.cz

Y Dr. Eliška Rezlerová
b Eliska.Rezlerova@vscht.cz

Collaborators:

  • Dr. Jan Heyda, UCT, Prague
  • Prof. Pavel Jungwirth, IOCB, Prague
  • Prof. Lukasz Cwiklik, Heyrovsky institute, Prague
  • Prof. Elena Pohl, University of Veterinary medicine, Vienna
  • Prof. Mikael Lund, Lund University, Sweden
  • Dr. Danijela Bakaric, Rudjer Boskovic Institute, Zagreb
  • Prof. Paul S. Cremer, Penn State University, USA
  • Prof. Jean-Phillipe Pellois, Texas A&M University, USA

Selected publications:

  • D. J. Brock, H. Kondow-McConaghy, J. Allen, Z. Brkljača, L. Kustigian, M. Jiang, J. Zhang, H. Rye, M. Vazdar, Jean-Philippe Pellois, Cell Chemical Biology, 27 (2020), 1296-1307 (journal impact factor = 7.739)
  • O. Jovanović, S. Škulj, E.E. Pohl, M. Vazdar, Free Radical Biology and Medicine, 143 (2019), 433-440 (journal impact factor = 5.657)
  • . Vazdar, J. Heyda, P. E. Mason, G. Tesei, C. Allolio, M. Lund, P. Jungwirth, Accounts of chemical research, 51 (2018), 1455-1464 (journal impact factor = 20.955)
  • G. Tesei, M. Vazdar, M. Ringkjøbing Jensen, C. Cragnell, P. E. Mason, J. Heyda, M. Skepö, P. Jungwirth, M. Lund, Proceedings of the National Academy of Sciences of the United States of America, 114 (2017), 11428-11433 (journal impact factor = 9.504)
  • L. Artiglia, J. Edebeli, F. Orlando, S. Chen, M.-T. Lee, P. Corral-Arroyo, A. Gilgen, T. Bartels-Rausch, A. Kleibert, M. Vazdar, M. Carignano, J. S. Francisco, P. B. Shepson, I. Gladich, M. Ammann, Nature Communications, 8 (2017), 700-1 (journal impact factor = ‎12.353)
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Our research group is mainly concerned with exploring open problems in combinatorics, discrete mathematics and graph theory.

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Research areas

Graph Theory

Over the past decades, graph theory has found many applications in various areas of human activity from network designing (electrical, water, social), allocation of mobile or broadcasting frequencies to various types of optimization (in traffic, searching, etc.). Our group focuses mainly on the study of a special class of graphs derived from partially ordered sets, so-called cover-incomparability graphs, their properties and the complexity of their recognition. Another area that is currently at the center of our interest is the study of equivalences on graphs defined by various graph operations, such as Seidel's switching.

Graph theory in Chemistry

In this area, we primarily focus on the study of so-called Wiener Index of molecular graphs. Harry Wiener introduced this index to determine the approximation formula of the boiling point of paraffin.
Since then, the Wiener Index has become one of the most commonly used molecular descriptors and it is currently used e.g. for pre-screening of drug molecules.
We are mainly interested in determining the extremal values of Wiener index for important graph classes.

Computational complexity

Asymptotic complexity is one of the essential tools to compare algorithm efficiency and speed. The particular problem is the determination of its time complexity with respect to the size of the input, which can be enormous for relatively simple tasks and relatively small inputs (e.g. hundreds of years). Finding the boundary for polynomial complexity for different tasks on graphs is at the center of our interest (see known problem P versus NP).

Groups of reflections and their applications

Group of reflections describe (among other things) natural symmetries of regular and semiregular n-dimensional object, e.g. Platonic solids. We study propertis of special functions related to reflection groups orbit functions. Corresponding symmetries are used in the study of generalized discrete fourier transforms.  

Presentation card

Contact persons:

Y RNDr. Jana Maxová, Ph.D. - team representative
b jana.maxova@vscht.cz
e 22044 5039

Y Ing. Lenka Háková, Ph.D.
b lenka.hakova@vscht.cz
e 22044 5035

Y Ing. Tomáš Hejda, Ph.D.
b tomas.hejda@vscht.cz
e 22044 4349

Y RNDr. Eva Jelínková, Ph.D
b eva.jelinkova@vscht.cz
e 22044 5030

Y Doc. RNDr. Daniel Turzík, CSc.
b daniel.turzik@vscht.cz
e 22044 5036

Recent papers

  • Bok, Jan & Maxová, Jana. (2018). Characterizing Subclasses of Cover-Incomparability Graphs by Forbidden Subposets. Order. 10.1007/s11083-018-9470-7.
  • Jelínek, V.; Jelínková, E.; Kratochvíl, J. On the hardness of switching to a small number of edges. Lecture Notes in Computer Science, Springer, 2016.
  • Háková L.; Tereszkiewicz A. On Generalization of Special Functions Related to Weyl Groups. Acta Polytechnica, Journal of Advanced Engineering 2016, 56 (6), 440–447
  • Háková L.; Hrivnák J.; Motlochová L. On cubature rules associated to weyl group orbit functions. Acta Polytechnica, Journal of Advanced Engineering 2016, 56 (3), 202–213
  • Hejda, T.; Pelantová, E. Spectral properties of cubic complex Pisot units Mathematics of Computatio. 2016.
  • Maxová, J.; Dubcová, M.; Pavlíková, P.; Turzík, D. Which k-trees are cover-incomparability graphs? Discrete Applied Mathematics, 2014.
  • Jelínková, E.; Kratochvíl, J. On Switching to H-Free Graphs. Journal of Graph Theory, 2014.
  • L.Háková, A. Tereszkiewicz, On immanant functions related to Weyl groups of A_n, J. Math. Phys., Vol.55, Issue 11, 2014
  • Maxová, J.; Turzík, D. Which distance-hereditary graphs are cover-incomparability graphs? Discrete Applied Mathematics, 2013.
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Research involving dynamical systems has a long tradition in our department. The first seminar devoted to the systems of differential equations and general theory of dynamical systems was established more than 30 years ago. We are currently investigating a large number of problems associated with dynamical systems, both at the theoretical and application levels.

[ikona] => mikroskop [obrazek] => [obsah] =>

Research areas

Qualitative theory of dynamical systems

Systems of ordinary differential equations are examined with respect to their geometrical and qualitative properties; they are studied within the framework of general qualitative theory of dynamical systems.

     

Discontinuity appears in many applications including chemical engineering, biology, control theory, etc. It can be an integral, natural feature of the system, or it can be caused for instance by external interference. Piecewise smooth dynamical systems possess a fascinating and complex dynamics. The techniques available for the continuous case enable us to investigate the phase portrait, stability, bifurcations and other local or global properties of discontinuous so-called Filippov systems.

Chování systému pavouků na vinici s balónovým efektem M. Biák: Po částech hladké dynamické systémy. Disertační práce, VŠCHT Praha, 2015

Dynamical system of spiders on the vineyard with the balloon effect.
M. Biák: Piecewise smooth dynamical systems. PhD Dissertation, UCT Prague, 2015

Reconstruction of the dynamics from time-series

The dynamics reconstruction is based on the time delay approach, relying on the Takens embedding theorem. The time-series data, i.e. the projection of the dynamical system to a real interval, describe the dynamical system only partially. The method is able to qualitatively reconstruct the behaviour of the whole dynamical system; it can be applied to the time-series data originated for instance from chemical or medical problems.

     

Solving differential equations

Concerning the numerical methods for ordinary and partial differential equations we are oriented on the method of finite elements and finite volumes, marginally also the method of finite differences. Regarding the analytical methods we focus primarily on the Laplace

transform, as an efficient tool to solve linear partial differential equations appearing in the technical practice.

Fluid mechanics and thermodynamics

In the field of computational fluid dynamics (CFD), we use software OpenFOAM to simulate multiphase flows, for example in separation columns. In theory, we study the mathematical analysis of equations describing the flows of compressible fluids, among others chemically reacting mixtures.

Chaos theory

The chaos theory deals with nonlinear dynamical systems, characterized by complex, bounded, undamped and nonperiodic behaviour, so called deterministic chaos. Although it is deterministic, the precise trajectories are unpredictable due to sensitive dependence on the initial conditions.

Thermodynamics of information

Information thermodynamics combines information theory with the concepts of classical thermodynamics. The theory meets applications in a lot of physical processes.

Optimization and control theory

In the control theory we investigate the models of biochemical processes and their properties such as controllability, observability and stability. Further we estimate the parameters of the model, or perform simulations. From the perspective of possible applications, we are interested in the problem of optimal control or possible dimension reductions of the models.

Mathematical finance

The parabolic partial differential equations describing the dynamics of financial markets are studied. We focus on numerical solution of special difusion equation following from the Black–Scholes model for financial derivatives pricing.

Numerical methods on Clifford algebras

Within a long-term cooperation with the University of Hamburg, we study the numerical linear algebra for quaternions, and other commutative or noncommutative algebras in R4. Quaternions play currently a key role in robotics and computational graphics development. Another non-commutative algebra in R4, so called coquaternions, finds its applications for instance in complex problems of quantum chemistry and physics.

Presentation card

Contact persons

Mgr. Šimon Axman, Ph.D. - team representative
b simon.axmann@vscht.cz
e 22044 5030

Y RNDr. Lenka Červená, Ph.D.
b lenka.cervena@vscht.cz
e 22044 5031

Y RNDr. Miroslava Dubcová, CSc.
b miroslava.dubcova@vscht.cz
e 22044 5031

Y Ing. Bohdan Hejna, Ph.D.
b bohdan.hejna@vscht.cz
e 22044 5037

Y Ing. Martin Isoz, Ph.D.
b martin.isoz@vscht.cz
e 22044 4349

Y Prof. RNDr. Drahoslava Janovská, CSc.
b drahoslava.janovska@vscht.cz
e 22044 5040

Y Prof. RNDr. Milan Kubíček, CSc.
b milan.kubicek@vscht.cz
e 22044 3095

Y Mgr. Jana Němcová, Ph.D.
b jana.nemcova@vscht.cz
e 22044 5038

Y RNDr. Pavel Pokorný, CSc.
b pavel.pokorny@vscht.cz
e 22044 5033

Doc. RNDr. Carmen Simerská, CSc.
b carmen.simerska@vscht.cz
e 22044 5040

obr

Recent publications

  • Janovska, Drahoslava; Opfer, Gerhard: The Relation Between the Companion Matrix and the Companion Polynomial in R-4 Algebras, ADVANCES IN APPLIED CLIFFORD ALGEBRAS, Volume: 28, Issue: 4, Article Number: UNSP 76, Published: SEP 2018
  • Isoz M., Haidl J.: CFD analysis of gas flow through corrugated sheet structured packing: Effects of packing geometry. Industrial & Engineering Chemistry Research, 57(34), 11785–11796, 2018.
  • van Schuppen J., Xi K., Němcová J.: A Subalgebraic Procedure for System Identification of a Continuous-Time Polynomial System. IFAC-PapersOnLine, 51, 395-400, 2018. 
  • Hejna B.: Information Transfer and Thermodynamic Point of View on Goedel Proof, in Ontology in Information Science, 280-300, 2018.
  • Axmann Š., Mucha P.B., Pokorný M.: Steady solutions to the Navier-Stokes-Fourier system for dense compressible fluid. Topol. Methods Nonlinear Anal., 52, 2018.
  • Hejna B.: Informační termodynamika IV. ; Goedelovy věty, přenos informace, termodynamika a Caratheodoryho věty, VŠCHT Praha, 2017.
  • Kočí P., Isoz M. et.al. 3D reconstruction and pore-scale modeling of coated catalytic filters for automotive exhaust gas aftertreatment. Catalysis Today, 2017.
  • Janovská D., Opfer G.: The number of zeros of unilateral polynomials over coquaternions and related algebras. Electronic Transaction on Numerical Analysis, 46, 55-70, 2017.
  • Němcová J., van Schuppen J.: Checking Algebraic Reachability of Polynomial and Rational Systems, IFAC-PapersOnLine, 50 (1), 12119-12124, 2017.
  • Axmann Š., Mucha P.B., Pokorný M.: Steady solutions to viscous shallow water equations. The case of heavy water. Communications in Mathematical Sciences, 15 (5), 1385-1402, 2017.
  • Malijevský A., Pokorný P.: Průvodce matematickými metodami, VŠCHT Praha, 2017.
  • Axmann Š., Mucha P.B.: Decently regular steady solutions to the compressible NSAC system. Topological Methods in Nonlinear Analysis, 48 (1),1-27, 2016. 
  • Janovská D., Opfer G. : Matrices Over Nondivision Algebras Without Eigenvalues. Advances in Applied Clifford Algebras 26, 591-612, 2016.
  • Bonnard B., Henninger H. C., Němcová J., Pomet J.-B.: Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer Towards Circular Orbits. Acta Applicandae Mathematicae, 135 (1), 47-80, 2015.
  • Němcová J., Petreczky M., van Schuppen J.: An Algorithm for System Identification of a Discrete-Time Polynomial System without Inputs, IFAC-PapersOnLine, 48 (28), 166-171, 2015.
  • Axmann Š., Pokorný M.:Time-periodic solutions to the full Navier–Stokes–Fourier system with radiation on the boundary, Journal of Mathematical Analysis and Applications, 428 (1), 414-444, 2015.
  • Janovská D., Opfer G.: Zeros and singular points for one-sided coquaternionic polynomials with an extension to other R4 algebras. Electronic Transaction on Numerical Analysis, 41, 133-158, 2014. 
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Research areas

The research activities of our group cover the following areas

Stochastic (partial) differential equations 

These equations are used for modelling various dynamical phenomenons (physical, chemical, biological, economic etc.) significantly affected by random effects (random noise). We study equations with random effects, which can be correlated in time (so called fractional noise), with focus on parameter estimation and asymptotic behavior of these models.

OU process

 Stochastic geometry and spatial statistics

This field of probability theory has many applications in image analysis and material science. We focus on spatial and spatio-temporal models of unions of interacting particles.

 Metadynamics and molecular simulations

We study mathematical properties (mainly convergence and its speed) of enhanced sampling techniques for molecular simulations, with focus on techniques based on additional (artificial) potential (such as metadynamics, „flying gaussians“ etc.)

molekulární statistika

Statistical analysis support

We provide support with statistical analysis and modelling to other cooperating departments. We participated on:

  • Modelling gass permeation through grafen-oxid membranes
  • Quality assessment of the distillation column models
  • Analysis of  exhaust emissions measurement

kostky

Presentation card

Contact persons:

Y RNDr. Leszek Szala, Ph.D. - team representative
b leszek.szala@vscht.cz
e 220445030

Y Mgr. Jana Šnupárková, Ph.D.
b jana.snuparkova@vscht.cz
e 220445032

Y Mgr. Zuzana Vlasáková
b Zuzana.Vlasakova@vscht.cz
e 22044 5036

Y Mgr. Markéta Zikmundová, Ph.D.
b marketa.zikmundova@vscht.cz
e 220445032

brownův pohyb

 

Recent publications

  • Kříž P.: A space-consistent version of the minimum-contrast estimator for linear stochastic evolution equations,  Stochastics and Dynamics, DOI: 2050019. 10.1142/S0219493720500197, 2019
  • Natov P.; Nuhlíček O.; Dvořák J.; Szala L. M.; Syrovátková H.: Analysis of volume differences occuring during timber scaling on different production locations ,Zprávy lesnického výzkumu (Reports of Forestry Research), 64, 1, 45-50, 2019
  • Jankovský M.; Natov P.; Dvořák J.; Szala L. M.: Norway spruce bark thickness models based on log midspan diameter for use in mechanized forest harvesting in Czechia, Scandinavian Journal of Forest Research, 34, 7, 617-626, 2019
  • Čoupek P., Maslowski B., Šnupárková J.: SPDEs with Volterra Noise, kapitola v knize Stochastic Partial Differential Equations and Related Fields, In Honor of Michael Roeckner SPDERF, Bielefeld, Germany, October 10 -14, 2016, 147 - 158, 2018.
  • Maslowski B., Šnupárková J.: Stochastic Affine Evolution Equations with Multiplicative Fractional Noise, Appl. Math., 63(1), 7 - 35, 2018.
  • Kříž P., Maslowski B.: Central Limit Theorems and Minimum-Contrast Estimators for Linear Stochastic Evolution Equations,  Stochastics 91, 1-32, DOI: 10.1080/17442508.2019.1576688., 2019
  • Kříž P., Šućur Z., Spiwok V.: Free Energy Surface Prediction by Flying Gaussian Method: Multi-System Representation, Journal of Physical Chemistry B 121(46) 10479-10483, 2017.
  • Hošek P., Kříž P., Toulcová D., Spiwok V.: Multisystem altruistic metadynamics—Well-tempered variant, The Journal of Chemical Physics 146, 125103, 2017.
  • Garrido–Atienza, M.; Maslowski, B.; Šnupárková,J.: Semilinear stochastic equations with bilinear fractional noise, Discrete Contin. Dyn. Syst. Ser. B, 21(9), 3075 - 3094, 2016.
  • Szala L.: Chaotic behaviour of uniformly convergent nonautonomous systems with randomly perturbed trajectories. J. Differ. Equ. Appl., 21, 592-605, 2015.
  • Zikmundová M., Staňková Helisová K., Beneš V.: On the use of particle Markov chain Monte Carlo in parameter estimation of space-time interacting discs,  Methodology And Computing in Applied Probability, 16(2), 451-463, 2014.
  • Beneš V., Zikmundová M.: Functionals of spatial point process having density with respect to the Poisson process, Kybernetika 49, 896-913, 2014.
  • Szala L.: Recurrence in systems with randomly perturbed trajectories on the n-dimensional cube. Internat. J. Bifur. Chaos Appl. Sci. Engrg., 24, 1450137, 2014.
  • Gosiewski T., Szala L., Pietrzyk A., Brzychczy-Wloch M., Heczko P., Bulanda M.: Comparison of Methods for Isolation of Bacterial and Fungal DNA from Human Blood. Current Microbiology, 68, 149-155, 2014.
  •  
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List of conferences and worshops which were organised or co-organised by the department.

[ikona] => [obrazek] => [obsah] =>

Noncommutative Algebras and Aplications

Goslar, 14 - 16 June 2015

  • Department of mathematics (prof. Janovská) co-organised a conference on numerical solutions of problems related to non-commutative algebras.
  • Webpage

4th Scientific Colloquium

Praha,  24 - 26 June  2014

  • The colloquium was organised by the Department of mathematics, FEE CTU Prague and FMP CU Prague, in honor of prof. Klíč and prof. Kubíček
  • Webpage.

3th Scientific Colloquium 

Praha, 26 - 28 June 2001

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