Hypercomplex Seminar 2009:
From Schauder Basis to Hypercomplex, Randers-Ingarden
and Fractal Structures, and Nanostructures

24 – 31 July, 2009
The Mathematical Research and Conference Center, Będlewo, Poland

PRELIMINARY PROGRAMME
(updated July 22)

Friday, July 24

14.30Lunch
17.30-18.30Registration
19.00Dinner
21.00-22.00Registration

Saturday, July 25

08.00 Breakfast
09.00 Opening of the Seminar - Bogdan Bojarski (Warszawa), László Kozma (Debrecen), Julian Ławrynowicz (Łódź), Yaroslav G. Prytula (Lviv)
Initial lecture. Chairperson: Bogdan Bojarski (Warszawa)
09.15 Yaroslav G. Prytula (Lviv): Juliusz Paweł Schauder (1899-1943) - Lvov mathematician
Session I. Chairperson: Lajos Tamássy (Debrecen)
10.10 Józef Zając (Chełm / Lublin): Influence of Professor Ławrynowicz and his Lublin colleagues during 20 years of Polish-Mexican collaboration in complex analysis. I
11.05 László Kozma (Debrecen): Sub-Finslerian Geometry
12.00 Tea / Coffee break
Session II. Chairperson: László Kozma (Debrecen)
12.30 Lajos Tamássy (Debrecen): Projective flat Finsler spaces
13.10 Roman Stanisław Ingarden (Toruń): Randers antisymmetrical metric
13.50 R.S. Ingarden and Julian Ławrynowicz (Łódź): Finsler geometry and physics. Mathematical overview
14.30 Lunch
15.30 Walk to Lake Dymaczewskie (with a possibility of swimming)
19.00 Dinner

Sunday, July 26

08.00 Breakfast
09.30 Walk to Łódź and neighbouring lakes (possibility of the Mass attendance in a XIIIth-century church and of swimming in a lake)
14.00 Lunch
Session III. Chairperson: Leszek Wojtczak (Łódź)
15.05 Józef Zając (Chełm / Lublin): Influence of Professor Ławrynowicz and his Lublin colleagues during 20 years of collaboration in complex analysis. II
16.00 Roman Stanisław Ingarden (Toruń) and Julian Ławrynowicz (Łódź): Randers geometry and gauge the- ories. I. Solitons and complex gauge theories
16.40 R.S. Ingarden and J. Ławrynowicz: Randers geometry and gauge theories. II. Randers and Kałuża-Klein gauge theories, self-duality and homogeneity
17.20 Tea / Coffee break
Session IV. Chairperson: Osamu Suzuki (Tokyo)
17.50 Andrzej Michalski (Lublin): Harmonic mappings generated by convex conformal mappings
18.30 Valentin Ibáñez Fernández (Madrid / Kyiv): On special relativity theory
19.00 Dinner

Monday, July 27

08.00 Breakfast
Session V. Chairperson: Józef Zając (Chełm / Lublin)
09.00 Claude Surry (Font-Romeu, Pyrénées-Orientales): The problem of Coulomb friction in contact melting of thin lead films between two elastic solids
09.55 Osamu Suzuki (Tokyo): Repertory of certain non-associative algebras on stick-broken models and their application to Jordan algebra
10.50 O. Suzuki: Differential and integral calculus for Schauder basis on a fractal set (II)
11.45 Tea / Coffee break
Session VI. Chairperson: Yuri Zelinskiĭ (Kyiv)
12.15 Jerzy Grzybowski (Poznań): The Minkowski-Radstrm-Hrmander spaces applied to a crystal growth description
13.10 Julian Ławrynowicz (Łódź): Randers and Ingarden spaces with thermodynamical applications
13.50 R.S. Ingarden and J. Ławrynowicz: Model of magnetic electron microscope including the scanning microscope
14.30 Lunch
15.30 Free discussions
19.00 Dinner

Tuesday, July 28

08.00 Breakfast
09.00 Coach excursion to lakes and forests of the Wielkopolski National Park area including Jeziory, Szrenia- wa, Konarzewo, and Puszczykowo
14.45 Lunch
Session VII. Chairperson: Dariusz Partyka (Lublin)
15.45 Roman Stanisław Ingarden (Toruń) and Julian Ławrynowicz (Łódź): Finsler-geometrical model of quantum electrodynamics
16.25 R.S. Ingarden and J. Ławrynowicz: Finsler geometry and physics. Physical overview
17.05 Tea / Coffee break
Session VIII. Chairpersons and panel coordinators: Roman Stanisław Ingarden (Toruń), László Kozma (Debrecen), Julian Ławrynowicz (Łódź), Lajos Tamássy (Debrecen)
17.35 Round table discussion on Finsler geometry and physics From algebraic foundations to applications
19.00 Banquet

Wednesday, June 29

08.00 Breakfast
Session IX. Chairperson: Claude Surry (Font-Romeu, Pyrénées-Orientales)
09.00 Bogdan Bojarski (Warszawa): Beltrami equation and Hilbert transform on Riemann surfaces
09.55 Hariton Polatoglou (Thessaloniki): Finite element analysis of the electronic properties of quantum dots. I (Erasmus / Socrates programme lecture)
10.50 Paweł Domański (Poznań): Why has the space of real analytic functions no Schauder basis?
11.45 Tea / Coffee break
Session X. Chairperson: Paweł Domański (Poznań)
12.15 H. Polatoglou: Finite element analysis of the electronic properties of quantum dots. II (E / S progr. lect.)
13.10 Oleg Gerus (Zhytomyr): On the spectra of some integral operators related to the potential theory
13.50 Małgorzata Nowak-Kępczyk (Radom): Binary alloys with arbitrary atom concentrations and vacancies
14.45 Lunch
Session XI. Chairperson: Hariton Polatoglou (Thessaloniki)
15.45 Tatyana Osipchuk (Kyiv): A criterion of linear convexity of the complete Hartogs domains in H²
16.15 Agnieszka Niemczynowicz (Olsztyn): An analogue of Zwanzig's approach in the quantum spin-waves resonance theory
17.10 Tea / Coffee break
17.40 Dmytro Mierzejewski (Zhytomyr): Solutions of quaternionic polynomial equations: what is known up to now
Session XII. Chairpersons and panel coordinators: Kazimierz Jezuita (Warszawa), Hariton Polatoglou (Thessaloniki), Jerzy Rutkowski (Łódź), Dana Simian (Sibiu), Claude Surry (Font-Romeu, France), Leszek Wojtczak (Łódź)
18.30 Round table discussion on fractal analysis and finite element analysis in nanophysics
19.45 Dinner and bonfire

Thursday, July 30

08.00 Breakfast
Session XIII. Chairperson: Maciej Skwarczyński (Warszawa)
09.00 Dariusz Partyka (Lublin): Generalized problem of regression (I)
09.55 Yuri Zelinskii (Kyiv): Integral complex geometry
10.50 Yuuishi Uetani (Tokyo): Knot theory and formal languages
11.30 Tea / Coffee break
Session XIV. Chairperson: Dana Simian (Sibiu)
12.00 Maciej Skwarczyński (Warszawa): On the Bieberbach problem and Clausen identity
12.55 D. Partyka: Generalized problem of regression (II)
13.50 Vitalii Shpakivs'kyi (Zhytomyr): Integral theorems and Cauchy integral formula in a commutative three-dimensional harmonic algebra
14.45 Lunch
Session XV. Chairperson: Oleg Gerus (Zhytomyr)
15.45 Kazimierz Jezuita (Warszawa): Remarks on octonion wave equations
16.35 K. Jezuita: Geometric algebra on elementary level. Matrix representations of oriented objects and geometrical operations
17.25 Tea / Coffee break
Session XVI. Chairpersons and panel coordinators: Paweł Domański (Poznań), Oleg Gerus (Zhytomyr), Kazimierz Jezuita (Warszawa), Yaroslav G. Prytula (Lviv)
17.55 Round table discussion on Schauder bases in hypercomplex analysis and fractal analysis
18.50 Closing of the Seminar
19.00 Dinner

Friday, July 31

08.00 Breakfast
13.00 Lunch