uu.seUppsala University Publications
Change search
Link to record
Permanent link

Direct link
BETA
Klimek, Maciej
Publications (10 of 45) Show all publications
Klimek, M. (2019). Personal reflections on Jozef Siciak's mathematical journey. Annales Polonici Mathematici, 123(1), 1-7
Open this publication in new window or tab >>Personal reflections on Jozef Siciak's mathematical journey
2019 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 123, no 1, p. 1-7Article in journal (Refereed) Published
Abstract [en]

The recent passing of Professor Jozef Siciak inevitably brings about reflections on his legacy, not just in terms of mathematical results he had obtained or inspired, but also in terms of shaping the way mathematics is being developed internally and as a part of science in general. Based on several decades of close personal contacts, the author attempts to outline Professor Siciak's views concerning these matters.

Place, publisher, year, edition, pages
POLISH ACAD SCIENCES INST MATHEMATICS-IMPAN, 2019
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:uu:diva-397595 (URN)10.4064/ap4610-7-2018 (DOI)000493728300001 ()
Available from: 2019-11-22 Created: 2019-11-22 Last updated: 2019-11-22Bibliographically approved
Alghamdi, A., Klimek, M. & Kosek, M. (2018). Attractors of compactly generated semigroups of regular polynomial mappings.. Complexity, Article ID 5698021.
Open this publication in new window or tab >>Attractors of compactly generated semigroups of regular polynomial mappings.
2018 (English)In: Complexity, ISSN 1076-2787, E-ISSN 1099-0526, article id 5698021Article in journal (Refereed) Published
Abstract [en]

We investigate the metric space of pluriregular sets as well as the contractions on that space induced by infinite compact families of proper polynomial mappings of several complex variables. The topological semigroups generated by such families, with composition as the semigroup operation, lead to the constructions of a variety of Julia-type pluriregular sets. The generating families can also be viewed as infinite iterated function systems with compact attractors. We show that such attractors can be approximated both deterministically and probabilistically in a manner of the classic chaos game.

Keywords
Julia sets, pluricomplex Green function, iterated function systems
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:uu:diva-355806 (URN)10.1155/2018/5698021 (DOI)000450216100001 ()
Available from: 2018-07-05 Created: 2018-07-05 Last updated: 2018-12-19Bibliographically approved
Klimek, M. & Kosek, M. (2018). On the metric space of pluriregular sets. Dolomites Research Notes on Approximation, 11(Special issue), 51-61
Open this publication in new window or tab >>On the metric space of pluriregular sets
2018 (English)In: Dolomites Research Notes on Approximation, ISSN 2035-6803, Vol. 11, no Special issue, p. 51-61Article in journal (Refereed) Published
Abstract [en]

The metric space of pluriregular sets was introduced over two decades ago but to this day most of its topological properties remain a mystery. The purpose of this short survey is to present the current state of knowledge concerning this space.

Keywords
extremal plurisubharmonic functions, pluricomplex Green functions, iteration of polynomial mappings
National Category
Computer Sciences Mathematical Analysis
Identifiers
urn:nbn:se:uu:diva-397590 (URN)10.14658/pupj-drna-2018-4-5 (DOI)000494423400005 ()
Available from: 2019-11-22 Created: 2019-11-22 Last updated: 2019-12-03Bibliographically approved
Alghamdi, A. & Klimek, M. (2017). Probabilistic approximation of partly filled-in composite Julia sets. Annales Polonici Mathematici, 119(3), 203-220
Open this publication in new window or tab >>Probabilistic approximation of partly filled-in composite Julia sets
2017 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 119, no 3, p. 203-220Article in journal (Refereed) Published
Abstract [en]

We study properties of the metric space of pluriregular sets and of contractions on that space induced by finite families of proper polynomial mappings of several complex variables. In particular, we show that closed balls in the space of pluriregular sets do not have to be compact and we give a simple proof of applicability of the so-called chaos game in the case of composite Julia sets. Part of the construction of those sets also leads to a computationally viable approximation by simpler sets based on Monte-Carlo simulation.

Keywords
composite Julia sets, pluricomplex Green functions, iterated function system, the chaos game, complex dynamics, Monte-Carlo simulation
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-339527 (URN)10.4064/ap4100-8-2017 (DOI)000417986400002 ()
Available from: 2018-01-22 Created: 2018-01-22 Last updated: 2018-07-06Bibliographically approved
Klimek, M. (2015). Stochastic characterization of plurisubharmonicity and convexity of functions. In: Leokadia Bialas-Ciez and Marta Kosek (Ed.), Constructive Approximation of Functions: (pp. 175-181). Warszawa: Institute of Mathematics, Polish Academy of Sciences
Open this publication in new window or tab >>Stochastic characterization of plurisubharmonicity and convexity of functions
2015 (English)In: Constructive Approximation of Functions / [ed] Leokadia Bialas-Ciez and Marta Kosek, Warszawa: Institute of Mathematics, Polish Academy of Sciences , 2015, p. 175-181Chapter in book (Refereed)
Abstract [en]

It is shown that both plurisubharmonicity and convexity of functions can be characterized in terms of Brownian motions with individually scaled components. Applications related to multivariable Jensen's inequality are also given.

Place, publisher, year, edition, pages
Warszawa: Institute of Mathematics, Polish Academy of Sciences, 2015
Series
Banach Center Publications, ISSN 0137-6934 ; Vol. 107
Keywords
plurisubharmonic functions, convex functions, Brownian motion
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-206703 (URN)978-83-86806-30-0 (ISBN)
Available from: 2013-09-03 Created: 2013-09-03 Last updated: 2016-05-12
Klimek, M. (2011). The price of a rose: How names influence pricing?. Charaktery - Magazyn Psychologiczny, May, 100-103
Open this publication in new window or tab >>The price of a rose: How names influence pricing?
2011 (Polish)In: Charaktery - Magazyn Psychologiczny, ISSN 1427-695X, Vol. May, p. 100-103Article, review/survey (Other (popular science, discussion, etc.)) Published
National Category
Mathematics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
urn:nbn:se:uu:diva-293136 (URN)
Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-12
Klimek, M. (2010). Reckoning with probability. Charaktery - Magazyn Psychologiczny, September, 76-79
Open this publication in new window or tab >>Reckoning with probability
2010 (Polish)In: Charaktery - Magazyn Psychologiczny, ISSN 1427-695X, Vol. September, p. 76-79Article, review/survey (Other (popular science, discussion, etc.)) Published
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-293135 (URN)
Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-12
Klimek, M. (2010). Tracking the invisible science: Why does mathematics stay in the shadow of other sciences?. Charaktery - Magazyn Psychologiczny, May, 80-82
Open this publication in new window or tab >>Tracking the invisible science: Why does mathematics stay in the shadow of other sciences?
2010 (Polish)In: Charaktery - Magazyn Psychologiczny, ISSN 1427-695X, Vol. May, p. 80-82Article, review/survey (Other (popular science, discussion, etc.)) Published
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-293134 (URN)
Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-12
Klimek, M. & Kosek, M. (2009). Generalized iterated function systems, multifunctions and Cantor sets. Annales Polonici Mathematici, 96(1), 25-41
Open this publication in new window or tab >>Generalized iterated function systems, multifunctions and Cantor sets
2009 (English)In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 96, no 1, p. 25-41Article in journal (Refereed) Published
Abstract [en]

Using a construction similar to an iterated function system, but withfunctions changing at each step of iteration, we provide a natural example of a continuous one-parameter family of holomorphic functions of infinitely many variables. This family is parametrized by the compact space of positive integer sequences of prescribed growth and hence it can also be viewed as a parametric description of a trivial analytic multifunction.

Place, publisher, year, edition, pages
Warsaw: IM PAN, 2009
Keywords
holomorphic mappings, analytic multifunctions, set-valued functions, affine contractions, iterations, generalized Cantor sets
National Category
Mathematics
Identifiers
urn:nbn:se:uu:diva-104373 (URN)10.4064/ap96-1-2 (DOI)000271321900002 ()
Available from: 2009-05-28 Created: 2009-05-28 Last updated: 2017-12-13
Klimek, M. (2008). Change of expected value under equivalent probability measures and use of surrogate assets.
Open this publication in new window or tab >>Change of expected value under equivalent probability measures and use of surrogate assets
2008 (English)Report (Other academic)
Publisher
p. 8
Series
U.U.D.M. report / Uppsala University, Department of Mathematics, ISSN 1101-3591 ; 2008:41
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-142978 (URN)
Available from: 2011-01-18 Created: 2011-01-18 Last updated: 2016-05-12
Organisations

Search in DiVA

Show all publications