Steven Duplij

About

CURRICULUM VITAE

Passport name: Stepan Douplii
Pen/scientific name: Steven Duplij
Cyrillic name: Степан Анатольевич Дуплий

Address:
Center of Information Technology (CIT)
University of Münster
48149 Münster Germany
E-mails:
douplii@uni-muenster.de sduplij@gmail.com duplij@gmx.de
Homepage:
https://www.uni-muenster.de/IT.StepanDouplii

RESEARCH AREAS

Quantum computing, mathematics, theoretical physics, cryptography, DNA.

PERSONAL INFORMATION

Date and place of birth: August 29, 1954, Chernyshevsk, Russia.
Citizenship: Ukraine. Nonsmoking.

Steven Duplij ON WEB

Science:
https://scholar.google.com/citations?hl=ru&user=BeLVm2QAAAAJ&view_op=list_works&sortby=pubdate
https://www.semanticscholar.org/author/S.-Duplij/6188960?sort=pub-date
https://arxiv.org/search/?searchtype=all&query=duplij
https://inspirehep.net/literature?sort=mostrecent&size=100&page=1&q=duplij
https://orcid.org/0000-0003-1184-6952
https://www.researchgate.net/profile/Steven_Duplij
http://www.scopus.com/authid/detail.url?authorId=6602814921
https://www.slideshare.net/duplij
https://zbmath.org/authors/duplij.steven
http://www.mathnet.ru/php/person.phtml?personid=17918&option_lang=eng
https://mathscinet.ams.org/mathscinet/publications-search?query=duplij&page=1&size=100&sort=newest
https://search.crossref.org/search/works?q=duplij&from_ui=yes&sort=year
https://www.webofscience.com/wos/author/record/NHQ-3965-2025
https://sciprofiles.com/profile/1350010
https://www.sciencegate.app/app/search#6a255698-1b10-436c-88e2-09f2745fe5d6/10/0
https://www.adscientificindex.com/citation-ranking.php?ft_search=Steven+Duplij+Stepan+Douplii&ft_search_type=name&ft_mode=all
https://www.youtube.com/watch?v=G6MfKFiplnI

Mixed:
https://www.linkedin.com/in/duplij
https://uk-m-wikipedia-org.translate.goog/wiki/%D0%94%D1%83%D0%BF%D0%BB%D1%96%D0%B9_%D0%A1%D1%82%D0%B5%D0%BF%D0%B0%D0%BD_%D0%90%D0%BD%D0%B0%D1%82%D0%BE%D0%BB%D1%96%D0%B9%D0%BE%D0%B2%D0%B8%D1%87?_x_tr_sl=uk&_x_tr_tl=en&_x_tr_hl=ru&_x_tr_pto=wapp
https://uk.wikipedia.org/wiki/%D0%94%D1%83%D0%BF%D0%BB%D1%96%D0%B9_%D0%A1%D1%82%D0%B5%D0%BF%D0%B0%D0%BD_%D0%90%D0%BD%D0%B0%D1%82%D0%BE%D0%BB%D1%96%D0%B9%D0%BE%D0%B2%D0%B8%D1%87
https://catalog.loc.gov/vwebv/search?searchArg=duplij&searchCode=GKEY%5E*&searchType=0&recCount=25&sk=en_US
https://stabikat.de/Search/Results?type=AllFields&limit=100&lng=en&lookfor=duplij&commit=Search
https://katalog.ub.uni-heidelberg.de/cgi-bin/search.cgi?sess=e4f226546d23c6e8aba1545ff4b39bed&start=1&pagesize=20&query=duplij&sort=1
https://bll01.primo.exlibrisgroup.com/discovery/search?query=any,contains,duplij&tab=LibraryCatalog&search_scope=Not_BL_Suppress&vid=44BL_INST:BLL01&lang=en&offset=0
https://search.rsl.ru/en/search#q=author%3A%20Steven%20Duplij
https://www.barnesandnoble.com/s/duplij
https://www.ebay.com/sch/i.html?_nkw=steven+duplij
https://www.amazon.de/s?k=duplij+-duplik&i=stripbooks
https://www.amazon.com/s?k=duplij&i=stripbooks
https://www.amazon.com/stores/Steven-Duplij/author/B0BGYQHR3D/allbooks
https://www.gettextbooks.com/author/Duplij_Steven
https://www.buecher.de/ni/search_search/quick_search/q/cXVlcnk9JTIyRHVwbGlqJTIyJnJlc3VsdHM9MTU=/receiver_object/shop_search_quicksearch/
https://www.youtube.com/playlist?list=PLqhewbQXhDcsAPEqZ7qO_je32tDFGXIBb
https://rutube.ru/plst/519860
https://bastyon.com/stepan_douplii
https://www.waterstones.com/books/search/term/steven+duplij

DEGREES

2002 The academic status of Senior Research Fellow is given by Higher Certifying Commission, Kiev, Ukraine
1999 Habilitation Thesis: "Semigroup Methods in Supersymmetric Theories of Elementary Particles", Bogolyubov Institute of Theoretical Physics, Kiev, Ukraine,
Doctor Habilitatus in Theoretical Physics (Doctor of Science in Physics and Mathematics)
1983 Ph.D. Thesis: "Theoretical Investigation of Hard Processes in QCD";
1978-1982 Post Graduate Course in Theoretical Physics, Kharkov State University;
PhD (Candidate of Science in Physics and Mathematics); adviser M.P. Rekalo EDUCATION
1994-1995 Special German Language Course, Goethe Institute, Mannheim, Germany;
Distinguished diploma
1974-1978 Department of Theoretical Physics, Kharkov State University;
The Distinguished Diploma in Theoretical Nuclear Physics - M.Sc.
1973-1976 Special English Language Course, Kharkov State University;
The Distinguished Diploma
1971-1973 Department of Theoretical Radiophysics, Kharkov State University

WORK EXPERIENCE

2019-now Scientific Researcher at the Center of Information Technology (CIT), Universität Münster, Münster, Germany
2016 Lecturer in Mathematics, Bochum University of Applied Sciences, Germany
2014-2016 Scientific Researcher at the Mathematisches Institut, Universität Münster, Münster, Germany
2012 Lecturer in Mathematics, Rutgers University, Piscataway, USA
2011-2012 Visiting Fulbright Scholar, Rutgers University, USA
2000-2014 Lead Senior Staff Researcher at the Nuclear Physics Laboratory, Kharkov National University, Kharkov, Ukraine
2000-now CMS collaboration, CERN, Geneva
1997-2000 Senior Staff Researcher at the Nuclear Physics Laboratory, Kharkov National University, Kharkov, Ukraine
1983-1997 Staff Researcher at the Nuclear Physics Laboratory, Kharkov State University, Kharkov, Ukraine
1983-1992 Staff Researcher at the Nuclear Physics Laboratory, Kharkov State University, Kharkov, Ukraine
1978-1983 Half-time Researcher at the Radiophysics Laboratory, Kharkov State University, Kharkov, Ukraine

FELLOWSHIPS & GRANTS

2015-2016 European Research Council Grant at University of Münster (Host: J. Cuntz)
2010 Alexander von Humboldt Fellowship at University of Münster (Host: J. Cuntz)
2011-2012 Fulbright Scholar Program at the Rutgers University,
Piscataway, USA (Host: G. A. Goldin)
2010 Alexander von Humboldt Fellowship at University of Münster (Host: J. Cuntz)
2008 Alexander von Humboldt Fellowship at University of Köln (Host: M. Zirnbauer)
2007 American Physical Society Travel Grant at John Hopkins University (Host: J. Bagger)
2005-2006 Alexander von Humboldt Fellowship, University of Münster (Host: J. Cuntz)
2004 Simons Foundation Travel Grant (Stony Brook, USA)
2001 Alexander von Humboldt Fellowship at Max-Planck-Institute for Dynamics and Self-Organization, Göttingen (Host: F. Müller-Hoissen)
2001 National Natural Science Foundation of China Grant at Zhejiang University, Hangzhou (Host: Fang Li)
1994-1997 Alexander von Humboldt Fellowship at the Physics Department, University of Kaiserslautern, Kaiserslautern, Germany (Host: W. Rϋhl)

SCIENTIFIC PUBLICATIONS

In total: 207 publications, among them 9 books and 198 articles
https://www.uni-muenster.de/IT.StepanDouplii/Duplij_publications-(1980-2026)-full.pdf
including
Physical Review, Journal of Physics, Communications in Mathematical Physics, Journal of Mathematical Physics, Communications in Algebra, Semigroup Forum, Letters in Mathematical Physics, Theoretical and Mathematical Physics; Journal of Lie Theory, International Journal of Geometric Methods in Modern Physics, Linear Algebra and Applications, etc. Full lists are on the homepage.

SCIENTIFIC BOOKS (available on Amazon, Barnes&Noble, etc.):

S. Duplij, R. Vogl, “Innovative Quantum Computing”, IOP Publ., Bristol-London, 2023, 178 pp.
S. Duplij,“Polyadic Algebraic Structures”, IOP Publ., Bristol-London, 2022, 461 pp.
S. Duplij and M.L. Walker, eds, “Selected Topics in Gravity, Field Theory and Quantum Mechanics”,, MDPI Books, Basel, 2022, 348 pp.
S. Duplij, “Exotic Algebraic and Geometric Structures in Theoretical Physics”, Nova Publishers, New York, 2018, 410 pp.
S. Duplij, “Supersymmetry, Quantum Groups, Multigravity and Singulaer Theories”, Central West Publ., Australia, 2018, 254 pp.
S. Duplij, W. Siegel, and J. Bagger, eds., “Concise Encyclopedia of Supersymmetry And Noncommutative Structures In Mathematics And Physics”, Kluwer Academic Publishers, Dordrecht-Boston-London, 2004, 584 pp. (Second printing, Springer Science and Business Media, Berlin- New York-Heidelberg, 2005).
S. Duplij and J. Wess, eds., “Noncommutative Structures in Mathematics and Physics”, Kluwer, Dordrecht, 2001, 493 pp.
S. Duplij and V. G. Zima, eds., “Supersymmetric Structures in Mathematics and Physics”, UkrINTI, Kiev, 2000, 262 pp.
S. Duplij “Semisupermanifolds and Semigroups”, Kharkov: Krok, 2000, 220 pp. (Second Print by CreateSpace Publ.: Charleston, 2013).

COEDITORS (5): J. Bagger, W. Siegel, M.L. Walker, J. Wess, V. Zima
COAUTHORS (53): V.P. Akulov, A.Yu. Berezhnoy, A. Borowiec, A.J. Bruce, N. Chashchin, V.V. Chitov, M. Chursin, A. Frydryszak, O.M. Getmanetz, E. Di Grezia, W. Dudek, D.R. Duplij, N.V. Duplii, V.P. Duplij, G. Esposito, Moukun Fang, Na Fu, G.A. Goldin, Qiang Guo, Yanyong Hong, Shuai Huang, V.V. Kalashnikov, M. Kaliuzhnyi, O.I. Kotulska, A.T. Kotvytskiy, G.Ch. Kurinnoj, S.V. Landar, Fang Li, Li-Chao Liu, Y.G. Mashkarov, W. Marcinek, E.A. Maslov, N.M. Pelykhaty, V.M. Puzh, Liangang Qi, M.P. Rekalo, M.A. Rukavitsyn, A. Sadovnikov, Z.S. Sagan, S. Sinel'shchikov, I.I. Shapoval, V.M. Shtelen, D.V. Soroka, V.A. Soroka, S.A. Steshenko, Yuhang Tian, R. Vogl, M.L. Walker, Yani Wang, W. Werner, Tianfang Xu, I.I. Zalyubovsky, Wenjie Zhao

EDITOR EXPERIENCE

1999-2013 Editor of Kharkov National University Journal (Vestnik KSU), ser. Nuclei, Particles and Fields
2013-now Editor of East European Journal of Physics
2018 Invited Editor at World Scientific Publishing Co

Reviewing:
1998-now Zentralblatt Mathematik, Karlsruhe-Berlin, Germany 2005-now Journal of Zhejiang University. Science, Hangzhou, China 2007-now AIP, Melville, USA
2010-now Reports of Mathematical Physics, Warsaw, Poland 2012-now Advances in Mathematical Physics, New York, USA 2016-now Modern Physics Letters A, World Scientific, Singapore
2017-now International Journal of Modern Physics B, World Scientific, Singapore 2014-now Advances in Applied Clifford Algebras, Springer, Heidelberg, Germany 2015-now Hindawi Publishing Co., London, UK
2018-now Symmetry, Basel, Switzerland

LECTURE COURSES

Calculus
Elementary Particle Physics Quantum chromodynamics Unified theories
Supersymmetry and supergravity

SUPERVISION

5 students received Distinguished M.Sc. Degree in Theoretical Physics 4 PhD students

PROFESSIONAL MEMBERSHIPS

2014 RUSSIAN UNION OF WRITERS (Moscow, Russia)
2008 AMERICAN PHYSICAL SOCIETY (College Park, MD)
2002 ALEXANDER VON HUMBOLDT CLUB Ukraine
1995 AMERICAN MATHEMATICAL SOCIETY (Providence, RJ)
1994 INTERNATIONAL ASSOCIATION OF MATHEMATICAL PHYSICS
(Cambridge, MA)
1993 ENGLISH INTERNATIONAL ASSOCIATION (Lund, Sweden)
1993 AMERICAN ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE
(Washington, DC)
1992 EUROPEAN PHYSICAL SOCIETY (Geneva, Switzerland)
1999 INTERNATIONAL MATHEMATICAL UNION (IAS, Princeton)

LISTED

World Directory Of Mathematicians
Marques Who Is Who In America
Encyclopedia of Modern Ukraine
Mathematical Portal (Math-Net)
MathSciNet (American Mathematical Society)
Academic Genealogy of Theoretical Physicists
Mathematics Genealogy Project
Wikipedia (UA)
Google Scholar
Microsoft Academics
Scopus
Semantic Scholar
MathSciNet (Author)
MathNet
ZMath
ORCID
Scopus
SciProfiles

CONFERENCE ORGANIZING

2017 December Workshop Supergeometry And Applications (Luxembourg), as a member of Advisory Board
2005 June-International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, as a member of Advisory Board
2000 September-NATO Advanced Research Workshop “Noncommutative Structures in Mathematics and Physics”, as a Partner Country Co-Director
(NATO Co-Director: Julius Wess)

CONFERENCE PARTICIPATION

Participated at numerous international conferences, workshops, schools and seminars
in USA, Germany, France, UK, Poland, Spain, Czech Republic, Russia, China, Ukraine.
2017 December Workshop Supergeometry And Applications (Luxembourg)
2016 January Workshop Banach Methods In Noncommutative Geometry (Münster, Germany)
2015 April Workshop Structure And Classification Of C*-Algebras (Münster, Germany)
2015 April Workshop Structure And Classification Of C*-Algebras (Münster, Germany)
2014 May Workshop Quantum groups and operator algebras (Münster, Germany)
2011 August 3rd International Conference Quantum Electrodynamics And Statistical Physics (Kharkov, Ukraine)
2010 June 26th Workshop Foundations And Constructive Aspects Of QFT (Münster, Germany)
2010 May Analytic And Algebraic Methods In Physics VI (Prague, Czech Republic)
2009 October Algebra, Geometry, And Mathematical Physics (Bedlewo, Poland)
2009 September The Fourth International Conference On p-Adic Mathematical Physics
(Hrodna, Belarus)
2009 June Symmetry In Nonlinear Mathematical Physics (Kiev, Ukraine)
2009 May Analytic And Algebraic Methods V (Prague, Czech Republic)
2008 December 100th Statistical Mechanics Conference (Rutgers, USA)
2008 July Summer School And Conference On Modern Mathematical Physics (Belgrade, Serbia)
2007 May 97th Statistical Mechanics Conference (Rutgers, USA)
2004 July-August Simons Workshop In Mathematics And Physics (Stony Brook, USA) 2001 July XV Max Born Symposium Schroedinger Operators, Random Potentials And Singular Perturbations (Wroclaw, Poland)
2000 July International Conference On Supersymmetry And Quantum Field Theory 75th Birthday of D. V. Volkov (Kharkov, Ukraine)
1999 July International Conference On Supersymmetry And Quantum Symmetries in the memory of V. I. Ogievetsky (Dubna, Russia)
1999 July International Conference Strings-99 (Potsdam, Germany)
1999 August International Conference On Quantum Gravity And Superstrings (Dubna, Russia)
1998 August International Congress Of Mathematicians (Berlin, Germany)
1997 January International Seminar On Supersymmetry And Quantum Field Theory in memory of D. V. Volkov (Kharkov, Ukraine)
1996 June Supersymmetry-96 (College Park, MD, USA)
1996 June International Conference On Higher Homotopy Structures In Mathematical Physics (Poughkeepsie,NY)
1995 June Cracow School Of Theoretical Physics (Zakopane, Poland)
1995 July International Conference On Gauge Theories, Applied Supersymmetry And Quantum Gravity (Leuven, Belgium)
1995 July European School Of Group Theory (Valladolid, Spain)
1994 July International Congress On Mathematical Physics (Paris)
1993 June First Carribean Spring School Of Mathematics And Theoretical Physics (Saint- Francois, Guadeloupe)

SCIENTIFIC VISITS (names)

S. Adler, H. Arodz, M.A. Aukhadiev, J. Bagger, M. Bianchi, L. Bonora, B. Broda, C. Burdik, R. Casalbuoni, S. Catto, Jiejing Cheng, M. Ciric, A. Comtet, J. Cuntz, M. Dabrowski, C. Delizia, A. Douglas, B. Dragovich, W. Dudek, G. Esposito, P. Etingof, A.M. Gal'mak, D.V. Gal'tsov, G.A. Goldin, S.A. Grigoryan, H. Grosse, D. Grumiller, Qiang Guo, U. Günther, L. Kauffman, R. Kotiuga, M.I. Krivoruchenko, J. Kupsch, M. Lapidus, M.I. Levchuk, Fang Li, Kang Li, E. Lomon, J. Lukierski, L. Lusanna, W. Marcinek, A. Martsinkovsky, M. Mulase, F. Müller-Hoissen, Chi-Keung Ng, W. Von Oertzen, J. Okninski, N. Poncin, A.Ya. Radyno, M. Schlichenmaier, A. Schwarz, M. Shifman, W. Siegel, G.L. Stavraki, C. Ringel, V. Rittenberg, W. Rühl, J. Stasheff, X. Tata, M. Tonin, P. Urbanski, A. Vilenkin, K. Wali, J. Wess, G. Wolschin, S. Woronowicz, R. Wulkenhaar, Yun-Long Xu, Zheng Yu, C. Zachos, M. Zirnbauer, M. Znojil

SCIENTIFIC VISITS (cities and names)

2025
Yantai, China (Yantai Res. Inst. Harbin Eng. Univ.)-Qiang Guo
2019
Heidelberg, Germany (Inst. Theor. Phys.)-G. Wolschin Szczecin, Poland (Inst. Phys.)-M. Dabrowski
Wroclaw, Poland (Inst. Theor. Phys.)-B. Jancewicz
2018
Tianjin, China (Chern Inst. Math.)-Chi-Keung Ng
Harbin, China (Harbin Eng. Univ.)-Qiang Guo, Zheng Yu
2017
Luxembourg (Math. Research Unit)-N. Poncin
2016
Jena, Germany (Inst. Math.)-D. Lenz
2014
Münster, Germany (Inst. Math.)-J. Cuntz, W. Werner, R. Wulkenhaar
Salerno, Italy (Univ. Salerno, Math. Dept.)-C. Delizia
2012
Davis, USA (UC, Math. Dept.)-M. Mulase, A. Schwarz Riverside, USA (UC, Math. Dept.)-M.Lapidus
Honolulu, USA (Univ. Hawaii, Phys. Dept.)-X. Tata Syracuse, USA (Univ. Syracuse, Phys. Dept.)-K.Wali
Medford, USA (Tufts Univ., Inst. Cosmology)-A. Vilenkin
Boston, USA (Northeastern Univ., Math. Dept.)-A.Martsinkovsky
Hangzhou, China (Zheijang Univ., Math. Dept.)-Fang Li Nanchang, China (Nanchang Univ.)-Jiejing Cheng
2011
Chicago, USA (UIC, Math. Dept.)-L. Kauffman
Minneapolis, USA (Univ. Minnesota, Phys. Dept.)-M. Shifman
Philadelphia, USA (Univ. Penn., Math. Dept.)-J. Stasheff
Piscataway, USA (Rutgers Univ., Math. Dept.)-G.A. Goldin
Argonne, USA (ANL, HEP Division)-C. Zachos
New York, USA (CUNY Graduate Center, Math. Dept.)-A. Douglas
2010
Münster, Germany (WWU, Inst. Math.)-J. Cuntz, W. Werner,
Heidelberg, Germany (Inst. Theor. Phys.)-G. Wolschin, J. Kupsch,
Wien, Austria (ESI, Univ. Wien)-H. Grosse,
Prague, Czech. Rep. (Inst. Nucl. Phys.,Rez)-M. Znojil, Wien, Austria (TUW, Inst. Theor. Phys.)-D. Grumiller, Padova, Italy (Inst. Nucl. Phys.)-M. Tonin,
Naples, Italy (Inst. Phys.)-G. Esposito,
Florence, Italy (Inst. Nucl. Phys.)-R. Casalbuoni, L. Lusanna, Rome, Italy (Inst. Theor. Phys.)-M. Bianchi
2009
Warsaw, Poland (Inst. Math.)-S. Woronowicz, P. Urbanski,
Lodz, Poland (Univ. Lodz, Dept. Theor. Phys.)-B. Broda, Wroclaw, Poland (Inst. Theor. Phys.)-J. Lukierski,
Zielona Gora, Poland (Inst. Phys.)-M. Dudek, Szczecin, Poland (Inst. Phys.)-M. Dabrowski,
Krakow, Poland (Inst. Phys.)-H. Arodz,
Prague, Czech. Rep. (Inst. Math.)-B. Burgstaller
Potsdam, Germany (AEI)
Dresden, Germany (Forsch. Zentrum Dresden-Rossendorf)-U. Günther
2008
Piscataway, USA (Rutgers Univ., Math. Dept.)-G. Goldin,
Medford, USA (Tufts Univ., Inst. Cosmology)-A. Vilenkin,
Cambridge, USA (MIT)-E. Lomon,
New York, USA (CUNY)-S. Catto,
Köln, Germany (Inst. Theor. Phys.)-M. Zirnbauer, Belgrade, Serbia (Inst. Phys.)-B. Dragovich,
Nic, Serbia (Inst. Phys.)-M. Ciric,
Trieste,
Italy (SISSA)-L. Bonora,
Bielefeld, Germany (Univ. Bielefeld, Math. Dept.)-C. Ringel,
Bonn, Germany (Phys. Inst.)-V. Rittenberg
2007
Princeton, USA (Inst. Adv. Study)-S. Adler,
Chicago, USA (Univ. Illinois, Math. Dept.)-L. Kauffman, Medford, USA (Tufts Univ., Inst. Cosmology)-A. Vilenkin, Cambridge, USA (MIT)-E. Lomon,
Baltimore, USA (Johns Hopkins, Univ., Phys. Dept.)-J. Bagger, Philadelphia, USA (Univ. Penn., Math. Dept.)-J. Stasheff
2006
Münster, Germany (Inst. Math.)-J. Cuntz,
Bielefeld, Germany (Univ. Bielefeld, Math. Dept.)-C. Ringel
2004
Princeton, USA (Inst. Adv. Study)-S. Adler,
Baltimore, USA (Johns Hopkins, Univ., Phys. Dept.)-J. Bagger,
Stony Brook, USA (SUNY, Inst. Theor. Phys.)-W. Siegel,
Minneapolis, USA (Univ. Minnesota, Theor. Phys. Inst.)-M. Shifman, Krakow,
Poland (Jagellonian Univ.)
2003
Wroclaw, Poland (Inst. Theor. Phys.)-W. Marcinek, J. Lukierski
2001
Göttingen, Germany (ISF, Inst. Theor. Phys.)-F.Müller-Hoissen,
Hangzhou, China (Zhejiang Univ., Math. Dept.)-F. Li, Shanghai, China (Inst. Phys.)-Y.-L. Xu,
Wroclaw, Poland (Inst. Theor. Phys.)-W. Marcinek, , J. Lukierski
Prague, Czech. Rep. (CTU, Math. Dept.)-C. Burdik
Rez, Czech. Rep. (Inst. Nucl. Phys.)-M. Znojil,
Mannheim, Germany (Univ. Mannheim, Math. Dept.)-M.Schlichenmaier
2000
Warsaw, Poland (Inst. Math.)-J. Okninski,
Wroclaw, Poland (Inst. Theor. Phys.) -W. Marcinek, J. Lukierski
1999 Potsdam, Germany (AI)
1998 Berlin, Germany (Hahn-Meitner-Inst., HZ)-W. Von Oertzen,
Berlin, Germany (Tech. Univ.),
Krakow, Poland (Inst. Nucl. Phys.)
1994
St.Andrews, UK (Univ. St.Andrews, Math. Dept.)-J. Howie
Orsay, France (Inst. Nucl. Phys.)-A. Comtet
1993-1996
Kaiserslautern, Germany (Univ. Kaiserslautern, Phys. Dept.)-W.Rühl
1993
München, Germany (Max-Planck-Inst. Physik)-J.Wess, Lyon, France (Inst. Phys.)

RESEARCH INTERESTS

Supersymmetry and semigroups; supermatrix models; superconformal symmetry; super Riemann surfaces; exotic supermanifolds; supersymmetric quantum mechanics. Quantum groups and supergroups; weak Hopf algebras and Yang-Baxter equation; representations of quantized algebras, new actions of quantum algebras on quantum spaces.
Quantum computing and quantum information.
Polyadic algebraic structures, algebras, groups, fields, and their representations. Nonlinear methods in (super)electrodynamics, Yang-Mills, gravity and multigravity. Constrained systems and gauge theories, quantum chromodynamics and gravity.
Exactly solvable quantum field theory models, matrix models, numerical methods.
Secondary:
Symmetries of genetic code and visualization of DNA sequences; Helicity formalism in quantum chromodynamics;
Polarization phenomena in low energy nuclear physics; Rutherford backscattering method in ion implantation; Nonstationary radio noise.

SCIENTIFIC RESULTS AND INNOVATIVE IDEAS
https://arxiv.org/search/?searchtype=all&query=duplij
https://orcid.org/my-orcid?orcid=0000-0003-1184-6952

https://www.researchgate.net/publication/385046446_Abstract_of_my_life
https://www.uni-muenster.de/IT.StepanDouplii/Duplij_SciRes2026.pdf
(with direct links to articles)

A new direction in supersymmetric models of elementary particles, based on the inclusion of semigroups is proposed (book, thesis). The concept of semisupermanifold having noninvertible transition functions (satisfying higher von Neumann regularity) is introduced, and its deviation from being an ordinary manifold is given by a newly defined variable, obstructedness. Based on this idea, the novel notions of category regularization, regular topos, regular functor, higher regular braiding, regular Yang-Baxter equation and regular module, regular algebra and coalgebra, regular graded algebras are presented, and their role in topological quantum field theory is outlined. Even- and odd-reduced supermatrices are introduced and considered on a par, being complementary in terms of the newely obtained Berezinian addition formula, and are unified into a kind of "sandwich" semigroup. A special subset of odd-reduced supermatrices represent higher order rectangular bands for which new generalized "fine" Green's relations and egg-box diagrams are constructed. One-parameter semigroups of idempotent odd-reduced supermatrices and corresponding superoperator semigroups are introduced and studied by the new semigroup × semigroup method. The linear idempotent superoperators and exponential superoperators are mutually dual in some sense, and the first gives rise to an additional noninvertible non-exponential solutions to the initial Cauchy problem. A novel permanent-determinant symmetry is found for even complex superplane. It is shown that the corresponding counterparts (per analogs) of the cross ratio, distance and harmonic set are invariant under the introduced per mapping, a special noninvertible subset of the fractional linear transformation. The per analogs of the Laguerre formula for distance and Schwarzian derivative are presented. An additional superextension of complex structure is uncovered, which is noninvertible and can correspond to another (odd) superanalog of Riemann surfaces and to the counterpart of superconformal-like transformations which twist the parity of tangent space and their nonlinear realization, which together with the ordinary ones form the superconformal semigroup having special unusual properties. A unique formula connecting berezinian, permanent and determinant is obtained. From a physical viewpoint, the above conceptions can lead to semistatistics, being von Neumann regular analog of the ordinary statistics.

Quantum groups: a generalization of the Hopf algebra is introduced by relaxing the requirement for inverses of the generators of the Cartan subalgebra, which leads to a regular quasi-R-matrix structure. The classification of 6-vertex constant solutions to Yang-Baxter equation over Grassmann algebra is presented, including noninvertible ones which correspond to von Neumann regular R-matrix. The actions of universal enveloping quantum algebras on quantum planes (also of arbitrary dimension) are found. A novel double-graded quantum superplane and corresponding double-graded Hopf algebra are presented.

Singular theories with degenerate Lagrangians are formulated without involving constraints using Clairaut equation theory and the corresponding generalized Clairaut duality. A new antisymmetric bracket (an analogue of the Poisson bracket) describing the time evolution of singular systems is built. A novel partial Hamiltonian formalism is constructed. It is shown that a singular theory can be interpreted as the multi-time dynamics.

Nonlinear gauge theories: a generalized approach to nonlinear classical electrodynamics and supersymmetric electrodynamics is suggested, which takes into account all possible types of media and nonlocal effects, and is described in both Lagrangian and non-Lagrangian theories. First steps in the formulation of a general nonlinear conformal-invariant electrodynamics based on nonlinear constitutive equations and conformal compactification were made.

Gravity: constitutive equations for nonlinear gravito-electromagnetism and an exact form of the Maxwell gravitational field equations are obtained. A general approach to describing the interaction of multi-gravity models in space-times of arbitrary dimension is formulated. The gauge gravity vacuum is investigated in the constraintless Clairaut-type formalism (as in QCD). A special fermionic lineal gravity model which differs from standard supersymmetry is presented.

Quantum computing (book IOP, FrontMatter): a novel conception of quantum computing which incorporates an additional kind of uncertainty, vagueness/fuzziness, by introducing a new "obscure" class of qudits/qubits, is announced. A superqubit theory in super-Hilbert space is reconsidered, and a new kind of superqubit carrying odd parity is introduced. A new kind of quantum gates, namely higher braiding gates, is suggested, which lead to a special type of multiqubit entanglement that can speed up key distribution and accelerate various algorithms. A novel visualization of quantum walks in terms of newly defined objects, polyanders, is also proposed.

Polyadic structures (book IOP, FrontMatter): polyadization, i.e. exchanging binary operations with higher arity ones, is proposed as a general new approach to the algebraic structures used in physics. A new form of the Hosszu-Gluskin theorem (giving the general shape of n-ary multiplication by the chain formula) in terms of polyadic powers is given, and its “q-deformed” generalization is found using the newly introduced quasi-endomorphism. A polyadic analog of homomorphism, or heteromorphism, a mapping between algebraic structures of different arities, is introduced, which leads to the definition of a new kind of n-ary group representation, multiplace representations, as well as multiactions and a polyadic direct product. The arity invariance principle, a manifest expression of algebraic structure in terms of operations independent of their arity shape, is claimed. The relations of the von Neumann regular semigroups and the Artin braid group were found, and a higher arity generalization gave the polyadic-binary correspondence, which allowed the definition of the following new structures: higher braid groups, higher degree analogs of Coxeter group and Artin braid group. The following were also uncovered: unusual polyadic rings and fields (which can, remarkably, be zeroless and nonunital) having addition and multiplication of different arities, polyadic integer numbers and p-adic integers, polyadic convolution products having multiplication and comultiplication of different arities and their corresponding polyadic Hopf algebra and n-ary R-matrix, polyadic multistar adjoints and polyadic operator C*-algebras and Cuntz algebras. The polyadic analogs of the Lander–Parkin–Selfridge conjecture and Fermat's Last Theorem were formulated. It is proposed that mediality as a principle is more natural, unique and universal than commutativity in generalizing the latter to n-ary algebras (in the binary case commutativity directly follows from mediality). This is called the commutativity-to-mediality ansatz, which is applied to obtain almost medial n-ary graded algebras, a new kind of tensor categories, polyadic nonunital "groupal" categories with "quertors" (analogs of querelements in n-ary groups), "medialed" tensor categories and querfunctors. A principally new mechanism of additional "continuous noncommutativity", governed by a special "membership deformation" of commutativity for algebras with the underlying set as obscure/fuzzy set, is introduced. Using the membership deformation factor together with the ordinary graded commutation factor, the almost commutative graded (n-ary) algebras and Lie algebras with double commutativity are obtained, and their projective representations are studied. As a first step towards a the polyadic algebraic K-theory, the Grothendieck construction of the completion group for a monoid is generalized to the case, where both are of different, higher arities. As opposed to the binary case, an identity is not necessary for the initial m-ary semigroup to obtain a class n-ary group, which in turn need not contain an identity. A new (infinite) class of division algebras, the hyperpolyadic algebras, which correspond to the (only 4) binary division algebras R, C, H, O (reals, complex numbers, quaternions, octonions) are defined. A polyadic analog of the Cayley-Dickson construction is proposed, and a new iterative process gives "half-quaternions" and "half-octonions". A novel polyadic product of vectors in any vector space is defined, which is consistent with the polyadization procedure using vectorization. Endowed with newly introduced product, the vector space becomes a polyadic algebra which is a division algebra. New polyadic algebras with higher brackets which have (as opposed to n-ary Lie algebras) different arity from the initial n-ary algebra multiplication, are introduced. The sigma matrices and the Pauli group are generalized to higher arities. Using them, a toy model of one-dimensional supersymmetric quantum mechanics was constructed, as a first example of polyadic supersymmetry, which is specially extended in a way different from the new multigraded SQM previously proposed. The fundamental notion of number theory, the positional numeral system, is generalized from binary integer number ring Z=Z2,2 to nonderived polyadic rings Zm,n whose addition takes m arguments and multiplication takes n. Our key contributions include: 1) Demonstrating that every commutative polyadic ring supports a place-value expansion that respects fixed operation patterns. 2) Establishing a lower bound on digit counts based on the arity of addition. 3) Identifying a representability gap where only a subset of elements have finite expansions, determined by structural invariants. These findings enable novel approaches to arithmetic, data encoding, and hardware design that extend beyond conventional binary logic. In this paper we introduce and systematically develop the theory of polyadic group rings, a higher arity generalization of classical group rings R[G]. We construct the fundamental operations of these structures, defining the m-ary addition and n-ary multiplication for a polyadic group ring Rm,n=Rm,nGng built from an (m,n)-ring and an ng-ary group. A central result is the derivation of the «quantization» conditions that interrelate these arities, governed by the arity freedom principle, which also extends to operations with higher polyadic powers. We establish key algebraic properties, including conditions for total associativity and the existence of a zero element and identity. The concepts of the polyadic augmentation map and augmentation ideal are generalized, providing a bridge to the classical theory. The framework is illustrated with explicit examples, solidifying the theoretical constructions. This work establishes a new foundation in ring theory with potential applications in cryptography and coding theory, as evidenced by recent schemes utilizing polyadic structures. This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. The notion of grading by multiary group is introduced, and various compatibility conditions between the arity of algebra operations and grading group operations are investigated. Key ressults include «quantization» rules connecting arities, classification of graded homomorphisms, and concrete examples including ternary superalgebras and polynomial algebras over n-ary matrices. The theory reveals fundamentally new phenomena not present in the binary case, such as the existence of higher power gradings and nontrivial constraints on arity compatibility.

Cryptography: We present a novel encryption and decryption method that combines polyadic algebraic structures with signal processing techniques. The approach begins by encoding information into signals with integer amplitudes which are then transformed into structured integer sequences using polyadic operations. Decryption involves applying tailored rules and solving dedicated systems of equations to accurately reconstruct the original message. The foundation of our approach is the construction of polyadic integers - congruence classes of ordinary integers endowed with such m-ary and n-ary operations. A key innovation is the parameter-to-arity mapping Ф(a,b)=(m,n), which links the parameters (a,b) defining a congruence class to the specific arities required for algebraic closure. This mapping is mathematically intricate: it is non-injective, non-surjective, and often multivalued, meaning a single (a,b) can correspond to multiple arity pairs (m,n), and vice versa. This complex, non-unique relationship forms the core of the proposed cryptosystem's security. We then present two concrete encryption procedures that leverage this structure by encoding plaintext within the parameters of polyadic rings and transmitting information via polyadically quantized analog signals. In one method, plaintext is linked to the additive arity mi and secured using the summation of such signals; in the other, it is linked to a ring parameter ai and secured using their multiplication. In both cases, the «quantized» nature of polyadic operations - where only specific numbers of elements can be combined---generates systems of equations that are straightforward for a legitimate recipient with the correct key (knowledge of the specific polyadic powers and functional dependencies used during encoding) but exceptionally difficult for an attacker without it. The resulting framework promises a substantial increase in cryptographic security. The complexity of the Ф-mapping, combined with the flexibility in choosing polyadic powers and representative functions, creates a vast and intricate key space. This makes brute-force attacks computationally infeasible and complicates algebraic cryptanalysis, as the underlying nonderived polyadic structures defy the linear properties and homomorphisms exploitable in conventional binary algebraic systems. This work establishes the theoretical foundation for this new class of encryption schemes, demonstrates their feasibility through detailed examples, and highlights their potential for constructing robust, next-generation cryptographic protocols.

DNA theory: a new characteristic of nucleotides, the determinative degree, which is proportional to the dipole moment and the weight of hydration site, is unveiled. The physical characteristics of nucleotides such as dipole moment, heat of formation and energy of the most stable formation are newly computed by advanced methods. The concept of a triander is set up, which leads to a new method of visual sequence analysis and identification using DNA walk diagrams.

SCIENTIFIC PUBLICATIONS Recent 2018-2026
https://www.uni-muenster.de/IT.StepanDouplii
with direct clickable links to the full text of articles and the front matter and first chapter of books
(all 207 are here https://www.uni-muenster.de/IT.StepanDouplii/Duplij_publications-(1980-2026)-full.pdf)

2026
• S. Duplij, Multiary gradings, preprint arXiv: 2601.11738 [math.RA] (PDF), 16 pages, 2026.
2025
• S. Duplij, N. Fu and Q. Guo, Cryptographic transformations over polyadic rings, preprint arXiv: 2512.12580 [cs.CR] (PDF), 21 pages, 2025.
• S. Duplij, Higher power polyadic group rings, preprint arXiv: 2510.14029 [math.RA] (PDF), 18 pages, 2025.
• S. Duplij and Q. Guo, Polyadic encryption, Axioms 2025, 14 (11), 835 (Special issue Computational Algebra, Coding Theory and Cryptography: Theory and Applications, 2nd Edition).
• S. Duplij, Positional numeral systems over polyadic rings, preprint arXiv: 2506.12930 [math.NT] (PDF), 13 pages, 2025.
• S. Duplij, Polyadic supersymmerty, Universe 11 (4), 125 (2025).
• S. Duplij, Supergravity was discovered by D.V. Volkov and V.A. Soroka in 1973, In The Supersymmetric World: The Beginnings of the Theory. 2nd Edition", 2025, Edited by G. Kane and M. Shifman, World Scientific: Singapore, p. 371-373.
• Q. Guo, M. Fang, S. Douplii, and Y. Wang, Pattern synthesis of sparse linear arrays based on the atomic norm minimization and alternating direction method of multipliers approach, Digital Signal Process. 162 (2025), 105160.
• Y. Tian, Q. Guo, L. Liu, and S. Douplii, A SAR RFI suppression method based on low-rank guided CUR decomposition in complex electromagnetic environment, 26th International Radar Symposium (IRS) (2025), p. 1-6.
• Q. Guo, S. Huang, L. Liu, M. Kaliuzhnyi, and S. Douplii, A radar signal deinterleaving method based on enhanced sparse subspace clustering, IEEE Trans. Aerosp. Electron. Syst. 61 (2025), 2956-2972.
• S. Huang, T. Xu, Q. Guo, and S. Douplii, A radar signal sorting method based on the graph neural network combined with GCN and GAT, 26th International Radar Symposium (IRS) (2025), p. 7-12.
• Q. Guo, B. Na, S. Douplii, An HF channel parameter estimation method based on HR-IPFrFT, Adv. Space Research, 75, n. 10, 2025, 7624-7644.
2024
• S. Duplij, Polyadic sigma matrices, J. Math. Phys. 65 (2024), 083509 , listed in Editor's Picks, preprint arXiv:2403.19361 (PDF) [math.GT], 19 pages, 2024.
• S. Duplij, Hyperpolyadic structures, Mathematics 12 2378, (2024), 29 pages.
S. Duplij, Polyadic supersymmerty, preprint arXiv:2406.02188 [hep-th], 14 pages, 2024.
• V.P. Duplij, N.V. Duplii, S. Duplij, DNA walk diagram in Triander and jsTriander applications, Plant Phys. Genet. (Fiziol. rast. genet.) 56 (2024), no. 4, 353-361.
• Q. Guo, W. Zhao, L. Qi, Y. Wang, M. Kaliuzhnyi, S. Duplii, Method for DOA estimation of coprime arrays through joint auxiliary arrays with atomic norm minimization in the presence of gain-phase errors, Circuits Systems Signal Process. 43 (2024), 6637-6660.
2023
Books
• S. Duplij, R. Vogl, Innovative Quantum Computing, IOP Publishing (Bristol-London) 2023, 178 pages.
Articles
• S. Duplij, Hyperpolyadic structures, preprint arXiv:2312.01366 [math.RA], 29 pages, 2023.
• S. Duplij, R. Vogl, Polyander visualization of quantum walks, preprint arXiv:2311.00409 [quant-ph], 12 pages, 2023.
• S. Duplij, R. Vogl, On superqubits, preprint arXiv:2310.09635 [quant-ph], 14 pages, 2023.
2022
Books
• S. Duplij, Polyadic Algebraic Structures, IOP Publishing (Bristol-London) 2022, 461 pages.
• Selected Topics in Gravity, Field Theory and Quantum Mechanics, S. Duplij and M.L. Walker, Editors, MDPI Books, Basel, 2022, 348 pages. https://www.mdpi.com/books/book/6455.
Articles
• S. Duplij, Polyadic analogs of direct product, Universe 8 (2022), 230.
• S. Duplij, Polyadic rings of p-adic integers, Symmetry 14 (2022), 2591.
• S. Duplij, Polyadization of algebraic structures, Symmetry 14 (2022), 1782.
• M.L. Walker and S. Duplij, Gauge gravity vacuum in constraintless Clairaut-type formalism, Universe 8 (2022), 176.
• S. Duplij and W. Werner, Extensions of special 3-fields, preprint arXiv:2212.08606 [math.RA], 22 pages, 2022.
2021
Articles
• S. Duplij and W. Werner, Structure of unital 3-fields, Math. Semesterber. 68 (2021), 27–53.
• S. Duplij, Polyadic Hopf algebras and quantum groups, East European J. Phys. 2 (2021), 5–50 (arXiv:1811.02712).
• S. Duplij, Higher braid groups and regular semigroups from polyadic-binary correspondence, Mathematics 9 (2021), 972.
• S. Duplij, Graded medial n-ary algebras and polyadic tensor categories, Symmetry 13 (2021), 1038.
• M.L. Walker and S. Duplij, Gauge gravity vacuum in constraintless Clairaut-type formalism, preprint arXiv: 2106.07723, 23 pages, 2021.
• S. Duplij and R. Vogl, Polyadic braid operators and higher braiding gates, Universe 7 (2021), 301.
• S. Duplij and R. Vogl, Obscure qubits and membership amplitudes, in Topics on Quantum Information Science, S. Curilef and A. R. Plastino, eds., IntechOpen, London, 2021, 20 pp.
• S. Duplij, Membership deformation of commutativity and obscure n-ary algebras, J. Math. Physics, Analysis, Geometry 17 (2021), 441–462 (arXiv:2006.07865).
• A.J. Bruce and S. Duplij, Double-graded quantum superplane, Rep. Math. Phys. 86 (2020), 383–400 (arXiv:1910.12950).
• A.J. Bruce and S. Duplij, Double-graded supersymmetric quantum mechanics, J. Math. Phys. 61 (2020), 063503, 13 ( arXiv:1904.06975).
2019
Articles
• S. Duplij, Supergravity Was Discovered by D.V. Volkov and V.A. Soroka in 1973, Wasn’t it? East European J. Phys. (2019), 3, 81-82 (arXiv:1910.03259).
• S. Duplij, Arity shape of polyadic algebraic structures, J. Math. Physics, Analysis, Geometry 15 (2019), 3–56 (arXiv:1703.10132).
• A.J. Bruce and S. Duplij, Double-graded quantum superplane, Univ. Luxembourg, preprint arXiv:1910.12950, 2019.
2018
Books
• S. Duplij, Exotic Algebraic and Geometric Structures in Theoretical Physics, Nova Publishers, New York, 2018, 410 pp.
Articles
• G.A. Goldin, V.M. Shtelen, and S. Duplij, Conformal symmetry transformations and nonlinear Maxwell equations, in Mathematical Structures and Applications, T. Diagana and B. Toni, eds., Springer, Berlin, 2018, pp. 211–224.
• S. Duplij, Polyadic Hopf algebras and quantum groups, preprint arXiv:math.RA/1811.02712, 57 pages, 2018.

SPECIAL SKILLS

Languages: English (perfect), German (speaking), Russian (native), Ukrainian (native), Italian (basic).
Programming: Perl, Mathematica, Maple, LaTeX, BibTeX, HTML. PC platforms: MS-DOS, Windows, Unix, Linux.
PC software: Scientific Work Place, dBase, Adobe products, Microsoft Excel, Word, Photoshop, Dreamweaver, PowerPoint.

MASS MEDIA & SOCIAL LIFE

TV programs and interviews at the Kharkov TV studios:
https://www.uni-muenster.de/IT.StepanDouplii/old/TV-RADIO
Scientific program “Logos” (interviews at the Central Kharkov radio station).
Articles about S. Duplij: in USA (SCOOP USA, Gazette, Library of Congress); in Germany, in Ukrainian press.
Alexander von Humboldt Fellows meetings/workshops.

LITERARY & MUSICAL ACTIVITY

Writing poetry and short stories

More than 200 publications in USA/UK professional literary magazines in English, German, French, Spanish, etc. (the full list is on homepage).
https://www.uni-muenster.de/IT.StepanDouplii/old/pub-lit.htm

Poetry readings with own composed and arranged songs to guitar:
https://www.uni-muenster.de/IT.StepanDouplii/old/readings.htm
https://www.uni-muenster.de/IT.StepanDouplii/old/duplij-presentations.htm

Literary books (available on Amazon, Barnes&Noble, etc.):

S. Duplij, “Poephysics of Spirit” (prose, bilingual English/Russian), 2024 Woodbridge Press, Toronto, 372 pp.
S. Duplij, “Poetification of the Soul” (poems in English), 2024 Woodbridge Press, Toronto, 168 pp.
S. Duplij, “Poephysik der Seele” (prose in German), 2023 Woodbridge Press, Toronto, 268 pp.
S. Duplij, “Symmetry of Passion" (U.S. Edition, full collection of poems and translations, in Russian) 2022, Cross-Cultural Communications, New York, 500 pp.
S. Duplij, “Bosonization of Feelings” (poems and prose in Russian), 2019 Central West Publ., Australia, 232 pp.
S. Duplij, “Supermanifold of Life" (poems and prose in 9 languages), 2014 Trilingual Press, Cambridge, USA, 222 pp.
S. Duplij, “Dash-Dotted” (poems, bilingual English/Russian), 2014 Trilingual Press, Cambridge, USA, 356 pp.
S. Duplij, “In Cry” (poems, bilingual English/Russian), 1999 Mitez, Kharkov, Ukraine, 72 pp.
S. Duplij, “Angel” (poems in English), 1997 JVC Books, Arcadia FL, USA, 125 pp.

Playing guitar and composing songs

CD audio albums of songs
for mp3’s see Music Site:

https://www.uni-muenster.de/IT.StepanDouplii/old/music

“Blitz” (Heidelberg, 1995)
“Motifs of years” (Heidelberg, 1996)
“Supermanifold of life” (Houston, 2007)
MC audio album of songs:
“Blitz” (GEMA, Berlin, 1996)

My homepage with downloadable publications, clickable detailed scientific directions and general information is here:
https://www.uni-muenster.de/IT.StepanDouplii