Instytut Informatyki - Zakład Fizyki Komputerowej i Informatyki Kwantowej

The Pedagogical University of Cracow

The Institute of Computer Science - Laboratory of Computer Physics

Dr Łukasz T. Stępień e-mail:

1. "Perturbations of planar interfaces in Ginzburg-Landau models" , (Co-Authors: Henryk Arodz and Robert Pelka): H. Arodz, R. Pelka and L. Stepien

2. "The Bogomolny decomposition for systems of two generalized nonlinear partial differential equations of the second order", (Co-Authors: Danuta Sokalska and Krzysztof Sokalski): L. Stepien, D. Sokalska and K. Sokalski,

3. "Some decomposition method for analytic solving of certain nonlinear partial differential equations in physics with applications" : L. T. Stepien,

4. L. T. Stepien, "Selected methods of software engineering in teaching of some school subjects" , in the book "Information technologies in teacher's methods" (Editors: Jacek Migdalek and Wojciech Folta), KSIEGARNIA AKADEMICKA, Krakow 2010 (in Polish).

5. "On the consistency of Peano's Arithmetic System" , (Co-Author: Teodor Stepien): T. J. Stepien and L. T. Stepien,

This above link leads to the Proceedings of the Conference "2009 European Summer Meeting of Association for Symbolic Logic, Logic Colloquium'09" (July 31 - August 5, 2009, Sofia, Bulgaria) . There, on the page 132, is published the abstract of the talk "On consistency of Peano's Arithmetic System", delivered by me, commonly with Dr Teodor Stepien, at "Logic Colloquium 2009" (July 31 - August 5, 2009, Sofia, Bulgaria). During this talk, we presented a sketch of the proof of the consistency of Peano's Arithmetic System (of course, the FULL proof was constructed by us before the mentioned Conference "Logic Colloquium 2009").

the consistency of Peano's Arithmetic System is provable within Peano's Arithmetic System.

6. "Atomic entailment and classical entailment" , (Co-Author: Teodor Stepien): T. J. Stepien and L. T. Stepien,

This above link leads to the Proceedings of the Conference "2010 European Summer Meeting of Association for Symbolic Logic, Logic Colloquium 2010" (July 25 - 31, 2010, Paris, France). There on the pages 317-318 is published the abstract of the talk "Atomic entailment and classical entailment".

In the next full paper, entitled "The Formalization of The Arithmetic System on The Ground of The Atomic Logic" and published in Journal of Mathematics and System Science (T. J. Stepien and L. T. Stepien,

7. "On Bogomolny Decompositions for the Baby Skyrme Models" , L. T. Stepien in: Geometric Methods in Physics, XXXI Workshop, Białowieża, Poland, June 2430, 2012, Series: Trends in Mathematics, Kielanowski, P.; Ali, S.T.; Odesskii, A.; Odzijewicz, A.; Schlichenmaier, M.; Voronov, T. (Eds.), pp. 229 - 237, Birkhäuser Basel 2013.

This paper was based on a talk, delivered at "XXXI Workshop on Geometric Methods in Physics" (24-30.06.2012, Białowieża, Poland). In this paper, the so-called Bogomolny decompositions (the keywords: Bogomolny equation, Bogomol'nyi equation, Bogomolny equations, Bogomol'nyi equations, Bogomolny argument, Bogomol'nyi argument) for baby Skyrme models: restricted and full one, in (2+0)-dimensions, have been derived.

The baby Skyrme model is some analogon of the Skyrme model. This last one can be considered as some generalization of the nonlinear "sigma" model ("O(3) model"): in order to avoid the consequences of Derrick-Hobart theorem (the keywords: Derrick theorem, Derrick-Hobart theorem, Derrick argument, Derrick's argument, (Derrick) scale argument), there in the lagrangian, beside the nonlinear "sigma" term, the so called "Skyrme term" appears.

8. "The Scope of the Structural Completeness in the Class of all Over-Systems of the Classical Functional Calculus with Identity" , (Co-Author: Teodor Stepien): T. J. Stepien and L. T. Stepien,

In this paper, the scope of the structural completeness in the class of all over-systems of the classical functional calculus with identity, was established.

9. Press information, among others, about the talk "On consistency of Peano's Arithmetic System", delivered by Dr Teodor J. Stepien and me, on 9th January 2013 , in Chair of Computer Science and Computational Methods (The Pedagogical University of Cracow)

The feuilleton "On the consistency of mathematics" (in Polish) of Professor Ryszard Tadeusiewicz (AGH University of Science and Technology), published in "Gazeta Krakowska" ("Cracow Newspaper") (9th January 2013), accessible on http://www.gazetakrakowska.pl/artykul/735525,o-niesprzecznosci-matematyki,id,t.html?cookie=1. This feuilleton was published also on http://www.agh.edu.pl/aktualnosci/info/article/o-niesprzecznosci-matematyki-felieton/

(Dr Teodor J. Stepien and me, thank very much to Professor Ryszard Tadeusiewicz, for writing this feuilleton).

10. "The Existence of Bogomolny Decompositions for Gauged O(3) Nonlinear "Sigma" Model and for Gauged Baby Skyrme Models" , L. T. Stepien,

11. "Bogomolny equation for the BPS Skyrme model from the strong necessary conditions" , L. T. Stepien,

The branch of physics, in which I am engaged (in Polish): theoretical physics, especially nonlinear field theory (among others, exact solutions as instantons, solitons etc.)

Tzw. solitony, bardzo ciekawe rozwiązania nieliniowych równań ewolucji czasowej.

I found these two below figures of solitons on Prof. Alex Kasman's soliton page:

http://math.cofc.edu/faculty/kasman/SOLITONPICS/index.html

and I placed it here ( with Prof. Kasman's consent ):

Tak się zderzaja tzw. solitony równania KdV.

A oto rownanie KdV:

| (1) |

File translated from T

On 09 Feb 2009, 01:12.

Inne rownanie solitonowe, to rownanie sinus-Gordona:

| (1) |

File translated from T

On 09 Feb 2009, 19:07.

Dla przyzwyczajonych do standardowych oznaczen pochodnych czastkowych, to samo rownanie sinus-Gordona (czasem nazywane rowniez rownaniem "sine-Gordona"), co powyzej, zapisane wlasnie w tradycyjnych oznaczeniach pochodnych czastkowych:

Jak widac, jednak troszke sie rozni od tej pierwszej wersji: lewa strona ma znak przeciwny do lewej strony tamtego rownania. Bierze sie to stad, ze w pierwszym rownaniu uzywamy metryki z tzw. sygnatura (+,-) ,a w drugim - ze sygnatura (-,+). W kazdym razie konsekwencja uzycia takich metryk (w obu przypadkach mamy tzw. przestrzen Minkowskiego) jest to, iz kwadrat czasu wchodzi do wyrazenia na interwal czasoprzestrzenny ze znakiem przeciwnym, niz kwadrat odleglosci przestrzennej (w tym przypadku "x").

Aktualizacja: 10.10.2013

Tematy prac dyplomowych - studia niestacjonarne, r. akademicki 2013/2014:

Some links :

Katedra Informatyki i Metod Komputerowych Uniwersytetu Pedagogicznego w Krakowie

Instytut Fizyki Uniwersytetu Pedagogicznego w Krakowie

Wydział Matematyczno-Fizyczno-Techniczny Uniwersytetu Pedagogicznego w Krakowie

Oddzial Krakowski Polskiego Towarzystwa Fizycznego

Strona o Wystawie "Fizyka blizej nas" - Krakow, Planty (ul. Golebia - sw. Anny), 10 maja - 31 lipca 2011 r. (tak sie sklada, ze bralem udzial w przygotowaniu tej Wystawy)

Association for Symbolic Logic ASL

9th International ISAAC Congress

Instytut Fizyki Uniwersytetu Jagiellońskiego

Wydzial Fizyki, Astronomii i Informatyki Stosowanej Uniwersytetu Jagiellońskiego

baza preprintow arXiv

COMS: Conference Management System - the advertisements on the conferences

the informational service "UK Nonlinear News" with news concerning "nonlinear" branches of sciences: the advertisements on the scientific events, the offers of jobs in "nonlinear" branches of sciences, some important publications etc.

Wydział Fizyki Uniwersytetu Warszawskiego

Polskie Towarzystwo Fizyczne (Polish Physical Society)

Physics World

metody numeryczne

kurs jezyka C++

: UTC + 1

(on the basis of:

the website on Jan Czochralski's life and works, developed by Czochralski's Family

another website on Jan Czochralski's life and works )

a broadcast on Jan Czochralski in Channel 1 of Polish Radio - 2nd June 2013 (in Polish)

(on the basis of:

the website on outstanding Polish physicists (among others on Władysław Natanson) (in Polish)

an article of Prof. Józef Spałek (Marian Smoluchowski Institute of Physics of Jagiellonian University in Kraków), on Wladyslaw Natanson's discovery of (Natanson-)Bose-Einstein statistics (in Polish)

the article "WLADYSLAW NATANSON (1864-1937) For the 110th anniversary of formulation of the thermodynamics of irreversible processes and the 95th anniversary of formulation of quantum statistics" of Prof. Bronislaw Sredniawa (Marian Smoluchowski Institute of Physics of Jagiellonian University in Kraków), published in: "The Old and New Concepts of Physics", vol. IV, No 4, 705 (2007) (IN ENGLISH) )

Another article, including a comparison of Natanson's results and Bose's and Einstein's results (The Author has showed that the mode of calculating the distribution of indistinguishable particles, explained by Natanson, is the same as the statistics published 13 years later by Bose.):

Bogdan Lange, "Natanson's Statistics versus Bose-Einstein Statistics as the Basis For Theory-Cognitive Quantum Mechanics". Physics Essays: September 1997, Vol. 10, No. 3, pp. 524-527. DOI: http://dx.doi.org/10.4006/1.3036440

Other article, where one of Natanson's papers is cited:

C. Feiler, M. Buser, E. Kajari, W.P. Schleich, E.M. Rasel, R.F. OConnell, "New Frontiers at the Interface of General Relativity and Quantum Optics", Space Sci. Rev. (2009) 148: 123147; DOI 10.1007/s11214-009-9613-7

(on the basis of:

the website, which includes links to many articles on Rudolf Weigl's life and works (mainly in Polish, some of them are written in English, German, Russian or Ukrainian) )

(on the basis of: the article on Vitelo's life and works (in Polish) )

termin: czwartek, godz. 13:00 - 15:30 lub ewentualnie, do uzgodnienia via e-mail

pokoj 411N, tel. +48 12 662-78-54,

(ewentualnie, proszę pytać w pokoju 402N, tel. +48 12 662-78-43, +48 12 662-78-44),

adresy e-mail (prosze w pierwszej kolejnosci pisac na pierwszy adres e-mail):

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