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Research Groups


Treść (rozbudowana)
Complex analysis

Investigation of the properties of holomorphic solutions of complex partial differential equations of many complex variables, of the Temljakov-Bavrin type. Application of the properties of the above PDE for the study of symmetric biholomorphic convex and starlike mappings in complex finite-dimensional space. Connecting the results to problems for non-commutative position and differential operators.


Team Members: Renata Długosz (CMF, Lodz University of Technology), Piotr Liczberski, Edyta Trybucka (University of Rzeszów).

Essential Publications

Renata Długosz, Piotr Liczberski, Some results of Fekete-Szego type for Bavrin's families of holomorphic functions in n, Annali di Matematica Pura ed Applicata 200 (4) (2021), 1841–1857.

Renata Długosz, Piotr Liczberski, Edyta Trybucka, Majorization of the Temljakov operators for the Bavrin families in n, Results in Mathematics 75 (2) (2020), nr art. 60.

Renata Długosz, Piotr Liczberski, Some results of Fekete-Szego type. Results for some holomorphic functions of several complex variables, Symmetry12 (2020), nr art. 1707, 10 pp.

Renata Długosz, Piotr Liczberski, An application of hypergeometric functions to a construction in several complex variables, Journal d'Analyse Mathématique 137 (2019), 707–721.

Renata Długosz, Piotr Liczberski, Relations among starlikeness, convexity and k-fold symmetry of locally biholomorphic mappings in n, Journal of Mathematical Analysis and Applications 450 (2017), 169–179.


Dynamics and control of systems arising in biomedical applications

The research activities of this group go in two directions. The first one is focused on the analysis of the dynamics and control of systems appearing in modeling of novel therapies for cancer, Newest methods of geometric optimal control are applied with the goal of constructing the so-called regular synthesis of optimal solutions in the sense of Boltyansky. These solutions are expected to provide benchmarks for constructing realizable treatment protocols.The second direction concerns the formulation of mathematical models describing the dynamics of the transmission of a parasite in the population of mosquitos and humans in the presence of drugs blocking transmission of the parasite or interrupting its life cycle. This analysis can be used in preparing and applying treatments in a way that they are the most effective in the control of malaria leading to its complete elimination.

Team Members: Jacek Banasiak, Urszula Ledzewicz, Heinz Schättler (Washington University, USA)

Essential Publications

H. Schättler and U. Ledzewicz, Optimal Control for Mathematical Models of Cancer Therapies – An Application of Geometric Methods, Springer, Interdisciplinary Applied Mathematics, vol. 42, October 2015, 496 pp.

U. Ledzewicz, H. Schaettler, On the Role of Pharmacometrics in Mathematical Models for Cancer Treatments, Discrete and Continuous Dynamical Systems, series B, vol. 26 (1), 2021, pp. 483–499.

G. A. Ngwa, J. Banasiak et al., On a three-stage structured model for the dynamics of malaria transmission with human treatment, adult vector demographics and one aquatic stage, Journal of Theoretical Biology 481 (21), pp. 202–222, 2019.

W. A. Woldegerima, R. Ouifki, J. Banasiak, Mathematical analysis of the impact of transmission-blocking drugs on the population dynamics of malaria, Applied Mathematics and Computation 400, 2021, article 126005.


Moment generating functions on hypergroups

The aim of the project is to study properties of (generalized) moment functions using methods of spectral analysis and spectra synthesis. The properties of exponential polynomials and their connections with moment generating functions are also considered.

Team Members: Żywilla Fechner; współpraca: Eszter Gselmann, László Székelyhidi (University of Debrecen)

Essential Publications

Żywilla Fechner, Eszter Gselmann, László Székelyhidi, Moment functions and exponential monomials on commutative hypergroups, Aequationes Mathematicae  95, 1281–1290 (2021).

Żywilla Fechner, Eszter Gselmann, László Székelyhidi, Moment Functions on Groups, Results in Mathematics 76 (4), art. 171 (2021).

László Székelyhidi, Żywilla Fechner, Finite dimensional varieties on hypergroups, Aequationes mathematicae 95 (3), 551–567 (2021).

Żywilla Fechner, László Székelyhidi, Functional equations for exponential polynomials, Aequationes Mathematicae 93 (3), 535–545 (2019).

Żywilla Fechner, László Székelyhidi, Moment Functions on Affine Groups, Results in Mathematics 74 (1), art. 5 (2019).


External research projects
Uogólnione funkcje tworzące momenty na hipergrupach (Generalized moment generating functions on hypergroups) financed by the National Science Centre, the NCN Miniatura 1 (grant no. DEC-2017/01/X/ST1/00916) – research visit in April 2018.

Awards and distinctions
Żywilla Fechner, March 2021, Award of the Polish Society of Women in Mathematics for 2020.

Iterated function systems and distance type functions

Description of the research topic: iterated function systems and their generalizations, algorithms generating images of attractors (e.g., deterministic chaos game), semiattractors, fuzzy attractors, invariant idempotent measures and idempotent Markov operators, semimetric spaces, transformations of functions of distance type, metric fixed point theory.


Team Members: Jacek Jachymski, Filip Strobin, Filip Turoboś


Essential Publications

R. D. da Cunha, E. R. Oliveira, Filip Strobin, A multiresolution algorithm to generate images of generalized fuzzy fractal attractors, Numer. Algorithms 86 (2021), 223-256

Filip Strobin, Contractive iterated function systems enriched with nonexpansive maps, Results Math. 76, art. nr 153 (2021), 30 pp.

K. Leśniak, N. Snigireva, F. Strobin, Weakly contractive iterated function systems and beyond: a manual, J. Differ. Equ. Appl., 26, art. nr 8 (2020), 1114–1173.

Jacek Jachymski, Filip Turoboś, On functions preserving regular semimetrics ​​​​and quasimetrics satisfying the relaxed polygonal inequality, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas RACSAM 114 (3), art. 159 (2020).

I. Akbarbaglu, S. Głąb, S. Maghsoudi, F. Strobin, Topological size of some subsets in certain Calderón-Lozanowskii spaces, Advances in Mathematics 312 (2017), 737(2021)763.


Qualitative theory of difference equations

Considering the problems of the theory of difference equations has two sources: on the one hand, some phenomena are discrete, and on the other hand, difference problems are obtained in the discretization of continuous processes described, among others, by differential equations. The research conducted in our group concerns the qualitative theory of difference equations with particular emphasis on asymptotic aspects and the problem of multiple solutions to boundary problems. In the considered problems, we focus on the issues of boundedness, non-oscillations, convergence of solutions to problems with non-linearity of various types. Moreover, we study the approximation of solutions to nonlinear equations by solutions of certain linear equations.

Team Members: Michał Bełdziński, Marek Galewski, Janusz Migda (Adam Mickiewicz University), Małgorzata Migda (Poznań University of Technology), Magdalena Nockowska-Rosiak, Filip Pietrusiak, Robert Stegliński


Essential Publications

J. Migda, M. Nockowska-Rosiak, Asymptotic properties of solutions to difference equations of Sturm-Liouville type, Applied Mathematics and Computation, 340 (2019), 126–137.

R. Stegliński, M. Nockowska-Rosiak, Sequences of positive homoclinic solutions to difference equations with variable exponent, Mathematica Slovaca, 70 (2) (2020), 417–430.

M. Bełdzinski, T. Gałaj, R. Bednarski, F. Pietrusiak, M. Galewski, A. Wojciechowski, On the Existence of Non-Spurious Solutions to Second Order Dirichlet Problem, Symmetry 13 (2), art. 231 (2021).

J. Migda, M. Nockowska-Rosiak, M. Migda, Properties of Solutions of Generalized Sturm–Liouville Discrete Equations, Bulletin of the Malaysian Mathematical Sciences Society, 44 (5) (2021), 3111–3127

M. Nockowska-Rosiak, The Solvability of the Discrete Boundary Value Problem on the Half-Line, Entropy 23 (11), art. 1526 (2021), pp.13.

R. Stegliński, Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115 (2021), no. 3, Paper No. 140, 12 pp.


The polynomial method for graph colouring

Research concerns on graph colourings, in particular on list colouring of planar graphs using graph polynomials and Alon’s Combinatorial Nullstellensatz.

Team Members: Przemysław Gordinowicz, Paweł Twardowski

Recent Publications

P. Gordinowicz, P. Twardowski, The polynomial method for list-colouring extendability of outerplanar graphs, Ars Mathematica Contemporanea, 21 (2021), art. P2.08


Methods of nonlinear analysis

The application of fixed point, variational and monotonicity methods in investigating the solvability and multiplicity of solutions for boundary value problems driven by both ODE and PDE and systems of such equations is undertaken. Non-local problems and problems on graphs and fractal domains are also considered. Stability investigations and numerical approximations for chosen problems are also performed.


Team Members: Michał Bełdziński, Marek Galewski, Igor Kossowski, Magdalena Nockowska-Rosiak, Filip Pietrusiak, Robert Stegliński, Wojciech Kryszewski


Essential Publications

Wojciech Kryszewski, Jakub Siemianowski, Constrained semilinear elliptic systems on ℝN , Advances in Differential Equations 26 (9-10) (2021), 459–504

Marek Galewski, Basic Monotonicity Methods with Some Applications, Compact Textbooks in Mathematics; Birkhäuser: Basel, Switzerland; Springer Nature: Basingstoke, UK, ISBN: 978-3-030-75308-5, 2021

Robert Stegliński, Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115 (3), art. 140 (2021)

Magdalena Nockowska-Rosiak, Christian Pötzsche, Monotonicity and discretization of Urysohn integral operators, Applied Mathematics and Computation , 414, art. 126686 (2022)

Michał Bełdzinski, Marek Galewski, Igor Kossowski, Stability of Non-Linear Dirichlet Problems with ϕ-Laplacian, Entropy 23(6), 647 (2021), 10 pp.


Applications of graph theory to traffic flow modeling

The main goal of this research team is the analysis of particular geographical and sociological factors on formation of the traffic flow. Further plans involve introducing new macroscopic traffic flow models, enabling the prediction of traffic in both standard and crisis conditions

Team Members: Marta Borowska-Stefańska (Uniwersytet Łódzki), Michał Kowalski (Uniwersytet Łódzki), Filip Turoboś, Szymon Wiśniewski (Uniwersytet Łódzki)


Recent publications and conference presentations

M. Borowska-Stefańska, M. Kowalski, F. Turoboś, S. Wiśniewski, On determining the weight of edges in map-representing graphs – applications of heuristic methods in planning escape routes, “Journal of Traffic and Transportation Engineering (English Edition)”, 2021 (w druku).

M. Borowska-Stefańska, M. Kowalski, F. Turoboś, S. Wiśniewski, Madryt (online), 20 października 2020, 4th International Conference on SmartRail, Traffic and Transportation Engineering, On determining the weight of edges in map-representing graphs – applications of heuristic methods in planning escape routes (presenter M. Borowska-Stefańska)

M. Borowska-Stefańska, M. Kowalski, F. Turoboś, S. Wiśniewski, Optimisation patterns for the process of a planned evacuation in the event of a flood, “Environmental Hazards”, vol. 18, no. 4, Wyd. Taylor&Francis 2019, s. 335–360, ISSN: 1747-7891 [DOI: 10.1080/17477891.2019.1593816]


Nonlinear nonlocal boundary value problems for differential equations

The team's research goes in two directions. In the first, nonlocality occurs in boundary conditions and is of different types. In the second, the differential operators themselves are nonlocal. These are modifications of classical operators such as the Laplace operator using spectral theory. We are interested in the existence of solutions, their number, and their asymptotic behaviour. We use a wide range of methods of nonlinear analysis: fixed point theorems, Leray-Schauder degree theory, variational methods.

Team Members: Igor Kossowski, Jean Mawhin (Universite Catholique de Louvain, Belgium), Bogdan Przeradzki, Ewa Skrzypek, Katarzyna Szymańska-Dębowska

Essential Publications

Bogdan Przeradzki, Katarzyna Szymańska-Dębowska, Jean Mawhin, Second order systems with nonlinear nonlocal boundary conditions, Electronic Journal of Qualitative Theory of Differential Equations 56 (2018), 1–11.

Igor Kossowski, Bogdan Przeradzki, Nonlinear equations with a generalized fractional Laplacian, RACSAM 115 (2), art. 58 (2021).

Bogdan Przeradzki, Selected methods for nonlinear boundary value problems, Wydawnictwo Politechniki Łódzkiej, ISBN 978-83-66741-06-5,, Monografia 2021.

Jean Mawhin, Ewa Skrzypek, Katarzyna Szymańska-Dębowska, Du Bois–Reymond Type Lemma and its Application to Dirichlet Problem with the p(t)-Laplacian on a Bounded Time Scale, Entropy 23 (10), 1352 (2021), 21 pp. 


Functional inequalities and their applications

The team's research focuses on the theory of equations and functional inequalities and related issues and their applications. We study extensions of the concept of convexity to objects without linear structure (together with Zsolt Páles), problems of stochastic binary games with the use of functional inequalities (together with Maria Słomian) and operator equations on spaces of smooth functions (together with Aleksandra Świątczak).

Team Members: Włodzimierz Fechner, Maria Słomian (graduate at the Lodz University of Technology), Aleksandra Świątczak (PhD student at the Lodz University of Technology); współpraca: Zoltán Boros, Eszter Gselmann, Zsolt Páles, Árpád Száz (University of Debrecen)

Essential Publications

W. Fechner, Z. Páles, Convexity properties of functions defined on metric Abelian groups, Aequationes Mathematicae 95/3, 449–481 (2021).

A. Bartoszewicz, W. Fechner, A. Świątczak, A. Widz, On the c0-equivalence and permutations of series, Annals of Functional Analysis 12/2, art. 23 (2021).

W. Fechner, Z. Páles, Convexity of sets in metric Abelian groups, Forum Mathematicum 32/6, 1477–1486 (2020).

W. Fechner, Richard’s inequality, Cauchy-Schwarz’s inequality, and approximate solutions of Sincov’s equation, Proceedings of the American Mathematical Society 147/9, 3955–3960 (2020).

W. Fechner, Á. Száz, Composition iterates, Cauchy, translation, and Sincov inclusions, Acta Universitatis Sapientiae, Mathematica 12/1, 54–84 (2020).


Zewnętrzne projekty badawcze
Stipendium Hungaricum Tempus Public Foundation
Rodzaj projektu: polsko-węgierska wymiana bilateralna (NAWA)
Numer kontraktu: BE AK2018/285228 (21.09.2018–21.12.2018)

Nagrody i wyróżnienia
Maria Słomian jest zwyciężczynią konkursu im. Mariana Rejewskiego o nagrodę Dyrektora Instytutu Matematyki PŁ na najlepszą pracę magisterską napisaną na kierunku matematyka stosowana w roku akademickim 2020/2021.

Operators with respect to monotone measures and aggregation operators

The research team is concerned with the analysis of aggregation operators determined by non-additive measures. We introduce new types of operators that generalize Choquet-like operators, Sugeno-like operators, survival func¬tions, real- and interval-valued operators, scientometric indices, and order statistics (OWA-type operators). We give a characterization of monotone measures at which the studied operators satisfy certain inequalities and have properties such as subadditivity, superadditivity and comonotonicity.


Team Members: Michał Boczek, Ondrej Hutnik (Pavol Jozef Šafárik University in Kosice, Słowacja), LeSheng Jin (Business School, Nanjing Normal University, Nanjing, Chiny), Marek Kałuszka, Andrzej Okolewski

Essential Publications

M. Boczek, L. Jin, M. Kałuszka, Interval-valued seminormed fuzzy operators based on admissible orders, Information Sciences 574 (2021), 96–110.

M. Boczek, L. Halčinová, O. Hutník, M. Kaluszka, Novel survival functions based on conditional aggregation operators, Information Sciences 580 (2021), 705–719.

M. Boczek, A. Hovana, O. Hutník, M. Kaluszka, New monotone measure-based integrals inspired by scientific impact problem, European Journal of Operational Research 290 (2021), 346–357.

M. Boczek, M. Kaluszka, Sharp bounds of Jensen type for the generalized Sugeno integral, Information Sciences 481 (2019), 463–473.

A. Okolewski, Estrem properties of order statistic distributions for dependent samples with partially known multidimensional marginals, Journal of Multivariate Analysis 160 (2017), 1–9.

Projekty badawcze
Wymiana Bilateralna Naukowców (NAWA) pomiędzy Polską i Słowacją, PPN/BIL/2018/1/00049/U/00001 (2019–2021).

Combinatorial optimization on metric-like structures

The aim of the research group is to develop and verify the effectiveness of novel approximation techniques for the Traveling Salesperson Problem. In the long term, the team intends to expand their works on metric and semimetric variants of other NP-hard problems (e.g. vehicle routing problem, quadratic assignment problem).

Team Members: Mateusz Krukowski, Filip Turoboś 

Recent Publications

M. Krukowski, F. Turoboś (2021). Comparison of approximation algorithms for the travelling salesperson problem on semimetric graphs. arXiv preprint arXiv:2108.13070.

M. Krukowski, F. Turoboś (2021). Approximate solutions to the Travelling Salesperson Problem on semimetric graphs. arXiv preprint arXiv:2105.07275.


Algebraic structures in analysis and topology

We are interested in Fraisse limit theory and in lineability theory. Fraisse limits are used to find universal objects for classes of algebraic or algebraic-topological structures. Lineability is about finding large algebraic structures within non-linear sets.


Team Members: Agnieszka Widz (PhD student in Lodz University of Technology), Artur Bartoszewicz (currently University of Lodz), Szymon Głąb , Przemysław Gordinowicz, Filip Strobin, Małgorzata Terepeta (CMF, Lodz University of Technology); cooperation: Małgorzata Filipczak (University of Lodz)


Essential Publications

Artur Bartoszewicz, Szymon Głąb, Agnieszka Widz, Olivier’s theorem: ideal convergence, algebrability and Borel classification, RACSAM 115, art. 200 (2021).

Szymon Głąb, Przemysław Gordinowicz, Filip Strobin, Dense free subgroups of automorphism groups of homogeneous partially ordered sets, Forum Mathematicum 31 (1), 215–240 (2019).

Artur Bartoszewicz, Marek Bienias, Szymon Głąb, Lineability within Peano Curves, Martingales, and Integral Theory, Journal of Function Spaces, art ID 9762491, 8 pp. (2018).

Artur Bartoszewicz, Małgorzata Filipczak, Małgorzata Terepeta, Continuous functions in Hashimoto topologies and their algebraic properties. Results Math. 76, no. 4, Paper No. 203, 18 pp. (2021).

Artur Bartoszewicz, Małgorzata Filipczak, Małgorzata Terepeta,  Lineability of linearly sensitive functions. Results Math. 75, no. 2, Paper No. 64, 14 pp. (2020).


Dynamical systems and optimal control in life and medical sciences

The team carries out qualitative and quantitative analysis of finite and infinite dimensional dynamical systems that model processes occurring in nature as well as appearing in medical applications. The main research topics are multiscale epidemiological and ecological models and their asymptotic analysis, nonlocal and nonlinear integro-differential equations of fragmentation-coagulation theory, and dynamical systems on networks. We also develop methods of functional analysis and, in particular, the theory of operator semigroups, applicable to the analysis of infinite dimensional systems.


Team Members: Jacek Banasiak, Adam Błoch, Wilson Lamb (University of Strathclyde), ‪Sergey Shindin (University of KwaZulu-Natal), Katarzyna Szymańska-Dębowska


Essential Publications

J. Banasiak, W. Lambem, P. Laurençot, Analytic Methods for Coagulation-Fragmentation Models, series Chapman & Hall/CRC Monographs and Research Notes in Mathematics, CRC Press (Taylor &Francis Group), 2019.

J. Banasiak, W. Lambem, Growth-fragmentation-coagulation equations with unbounded coagulation kernels, Phil. Trans. R. Soc. A 378: 2019.0612.

J. Banasiak, M.S. Seuneu Tchamga, K. Szymańska-Dębowska, Canard solutions in equations with backward bifurcations of the quasi-steady state manifold, Journal of Mathematical Analysis and Applications, 2019, 471 (1–2), pp. 776–795.

J. Banasiak, L. O. Joel, S. Shindin, Discrete growth-decay-fragmentation equation:well-posedness and long term dynamics, Journal of Evolution Equations, 2019, 19, 771–802.

External research projects 
Grant NCN MINIATURA 2, 2018/02/X/ST1/02082, dr hab. Katarzyna Szymańska-Dębowska (2018–2019) 

Multiagent random walks

Research concerns on analysis of multiagent random walks, as well in probabilistic way (via Markov chains) as by simulations.

Team Members: Grzegorz Andrzejczak, Szymon Głąb, Przemysław Gordinowicz, Mateusz Krukowski, Filip Turoboś

Recent Publications

Sz. Głąb, P. Gordinowicz, S. Sobór, F. Turoboś, P. Twardowski, Broadcasting on grids, w przygotowaniu.


Methods of data analysis in social science

The aim of the research team is to analyze the influence of various sociological factors on certain social behaviors. The team deals with the issues of suicides and suicide attempts in Poland and the world, as well as research on the dynamics of depressive disorders depending on the occurrence of unusual social phenomena.

The Project Manager: dr Jacek Stańdo, prof. PŁ (CMF, Lodz University of Technology)

The Project Members:
Karl Andriessen (Melbourne School of Population and Global Health, The University of Melbourne)
Adam Czabański (The Jacob of Paradies University, Gorzów Wielkopolski)
Żywilla Fechner (Institute of Mathematics, Lodz University of Technology)
Włodzimierz Fechner (Institute of Mathematics, Lodz University of Technology)
Karolina Krysińska (Melbourne School of Population and Global Health, The University of Melbourne)
Jacek Stańdo (The Centre of Mathematics and Physics of the Lodz University of Technology)

Essential Publications

Jacek Stańdo, Adam Czabański, Żywilla Fechner, Ewa Baum, Karl Andriessen, Karolina Krysińska, Suicide and attempted suicide in Poland before and during the Covid-19 pandemic between 2019 and 2021, International Journal of Environmental Research and Public Health 19 (2022), no. 15: 8968.

Jacek Stańdo, Gabriela Piechnik-Czyż, Andrzej Adamski, Żywilla Fechner The COVID-19 Pandemic and the Interest in Prayer and Spirituality in Poland According to Google Trends Data in the Context of the Mediatisation of Religion Processes, Religions 13 (2022), no. 7: 655.

Jacek Stańdo, Żywilla Fechner, Agnieszka Gmitrowicz, Karl Andriessen, Karolina Krysinska, Adam Czabański, Increase in Search Interest for “Suicide” and “Depression” for Particular Days of the Week and Times of Day: Analysis Based on Google Trends, Journal of Clinical Medicine 12 (2023), no. 1: 191.

Jacek Stańdo, Przemysław Żebrok, Żywilla Fechner, Tomasz Kopiczko, John Paul II and the Family—The Role of Authority Figures in the Lives of Young Poles, Religions 14 (2023), no. 1: 55.


Insurer’s solvency and incomplete financial markets

Research is carried out in three directions. The first concerns modeling of insurer’s solvency with switching models, evaluation of ruin probability, time to ruin, deficit size, etc., and estimation of model’s parameters. The second direction is related to interest rate risk in long-term insurance, methods of pricing and hedging against this risk. The third direction concerns optimal risk transfers in the insurance market.

Team Members: Lesław Gajek, Marcin Rudź

Essential Publications

Lesław Gajek, Marcin Rudź, General methods for bounding multidimensional ruin probabilities in regime-switching models, Stochastics: An International Journal of Probability and Stochastic Processes 93 (5) (2021), 764–77.

Lesław Gajek, Marcin Rudź, Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model, Methodology and Computing in Applied Probability 22 (2020), 1507–1528.

Lesław Gajek, Marcin Rudź, Banach Contraction Principle and ruin probabilities in regime-switching models, Insurance: Mathematics & Economics 80 (2018), 45–53.

Lesław Gajek, Elżbieta Krajewska, Balance-sheet interest rate risk: a weighted Lp approach, Journal of Risk 21 (1) (2018), 91–104.

Lesław Gajek, Łukasz Kuciński, Complete discounted cash flow valuation, Insurance: Mathematics & Economics 73 (2017), 1–19.

Research projects

Grant NCN OPUS 7, UMO-2014/13/B/HS4/03222, Lesław Gajek (2015–2017)

Grant NCN MINIATURA 4, 2020/04/X/HS4/00961, Marcin Rudź (od 2020)


Precrash vehicle velocity determinantion

The aim of the research group is determining the precrash vehicle velocity. To this end we employ the tensor products of Legendre polynomials as well as B-splines. The newest trend in our research focuses on the application of artificial neural network.

Team Members: Jacek Gralewski (Faculty of Management and Production Engineering, Lodz University of Technology), Paulina Mierzejewska (Faculty of Mechanical Engineering, Lodz University of Technology), Adam Mrowicki (Faculty of Mechanical Engineering, Lodz University of Technology), Mateusz Krukowski, Przemysław Kubiak (Faculty of Mechanical Engineering, Lodz University of Technology), Krzysztof Siczek (Faculty of Mechanical Engineering, Lodz University of Technology), Filip Turoboś

Essential Publications

Mateusz Krukowski, Przemysław Kubiak, Adam Mrowicki, Filip Turoboś, Determining vehicle pre-crash speed in frontal barrier crashes using artificial neural network for Intermediate car class, Forensic Science International, (2020).

Mateusz Krukowski, Przemysław Kubiak, Paulina Mierzejewska, Nonlinear methods of vehicle velocity determination based on inverse systems and tensor products of Legendre polynomials, Forensic Science International 295 (2019), 19–29.

Jacek Gralewski, Mateusz Krukowski, Przemysław Kubiak, Adam Mrowicki, Krzysztof Siczek, Non-linear method of determining vehicle pre-crash speed based on tensor B-spline products with probabilistic weights — Intermediate car class, Forensic Science International 293 (2018), 7–16.


Small sets, set theoretical methods and its applications

Investigations deal with families of small sets in Euclidean spaces, and, more generally, in Polish metric spaces, and their applications in problems of real analysis. A class of generalized Haar null sets has been investigated. A series of publications is devoted to generalized convergence of sequences and series generated by ideals of subsets of natural numbers. Generalized Cantor sets on the real line are studied in the aspect of their classification, algebraic properties and porosity. Set-theoretical methods are used in the problem of existence of liftings and lower density operators, in problems of functional analysis and classical real analysis (feebly continuous functions of two variables, characterizations of Baire 1 functions and equi-Baire 1 functions).


Team Members: Marek Balcerzak, Tomasz Filipczak, Szymon Głąb, dr Jarosław Swaczyna, Małgorzata Terepeta (CMF, Lodz University of Technology), cooperation: Paolo Leonetti (Milano, Italy), Piotr Nowakowski (University of Lodz), Michał Popławski (University of Kielce)


Essential Publications

Tomasz Kania, Jarosław Swaczyna, Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces, Bull. London Math. Soc. 53 (2021), 231–239.

Taras Banakh, Szymon Głąb, Eliza Jabłońska, Jarosław Swaczyna, Haar-I sets: looking at small sets in Polish groups through compact glasses, Dissertationes Math. 564 (2021), 1-105.

Marek Balcerzak, Tomasz Natkaniec, Małgorzata Terepeta, Families of feebly continuous functions and their properties, Topology Appl. 272 (2020), 107077.

Marek Balcerzak, Paolo Leonetti, The Baire Category of Subsequences and Permutations which preserve Limit Points, Results Math. 75 (2020), art. 171.

Marek Balcerzak, Szymon Głąb, A Lower Density Operator for the Borel Algebra, Results Math. 75 (2020), art.50.

External research projects
Jarosław Swaczyna, a contractor employed 50% of the time in the grant „Linear-analysis techniques in operator algebras and vice versa”, GACR projekt 19–07129Y; RVO 67985840, Institute of Mathematics of the Czech Academy of Sciences, 02.2020–12.2021.