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Klimek, Maciej

Open this publication in new window or tab >>Personal reflections on Jozef Siciak's mathematical journey### Klimek, Maciej

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##### Abstract [en]

##### 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 ()
#####

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Available from: 2019-11-22 Created: 2019-11-22 Last updated: 2019-11-22Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.

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.

Open this publication in new window or tab >>Attractors of compactly generated semigroups of regular polynomial mappings.### Alghamdi, Azza

### Klimek, Maciej

### Kosek, Marta

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_some",{id:"formSmash:j_idt191:1:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_1_j_idt195_otherAuthors",{id:"formSmash:j_idt191:1:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_1_j_idt195_otherAuthors",multiple:true}); 2018 (English)In: Complexity, ISSN 1076-2787, E-ISSN 1099-0526, article id 5698021Article in journal (Refereed) Published
##### Abstract [en]

##### 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 ()
#####

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Available from: 2018-07-05 Created: 2018-07-05 Last updated: 2018-12-19Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Department of Mathematics, Faculty of Science, Albaha University, Al Baha, Saudi Arabia.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.

Jagiellonian University, Faculty of Mathematics and Computer ScienceInstitute of Mathematics, Institute of Mathematics..

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.

Open this publication in new window or tab >>On the metric space of pluriregular sets### Klimek, Maciej

### Kosek, Marta

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_some",{id:"formSmash:j_idt191:2:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_2_j_idt195_otherAuthors",{id:"formSmash:j_idt191:2:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_2_j_idt195_otherAuthors",multiple:true}); 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]

##### 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 ()
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Available from: 2019-11-22 Created: 2019-11-22 Last updated: 2019-12-03Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.

Jagiellonian Univ, Fac Math & Comp Sci, Inst Math, Krakow, Poland.

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.

Open this publication in new window or tab >>Probabilistic approximation of partly filled-in composite Julia sets### Alghamdi, Azza

### Klimek, Maciej

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_some",{id:"formSmash:j_idt191:3:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_3_j_idt195_otherAuthors",{id:"formSmash:j_idt191:3:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_3_j_idt195_otherAuthors",multiple:true}); 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]

##### 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 ()
#####

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Available from: 2018-01-22 Created: 2018-01-22 Last updated: 2018-07-06Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Albaha University, Faculty of Science, Department of Mathematics.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.

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.

Open this publication in new window or tab >>Stochastic characterization of plurisubharmonicity and convexity of functions### Klimek, Maciej

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_some",{id:"formSmash:j_idt191:4:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_4_j_idt195_otherAuthors",{id:"formSmash:j_idt191:4:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_4_j_idt195_otherAuthors",multiple:true}); 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]

##### 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)
#####

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Available from: 2013-09-03 Created: 2013-09-03 Last updated: 2016-05-12

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.

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.

Open this publication in new window or tab >>The price of a rose: How names influence pricing?### Klimek, Maciej

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_5_j_idt195_some",{id:"formSmash:j_idt191:5:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_5_j_idt195_otherAuthors",{id:"formSmash:j_idt191:5:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_5_j_idt195_otherAuthors",multiple:true}); 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)
#####

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Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-12

Open this publication in new window or tab >>Reckoning with probability### Klimek, Maciej

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_some",{id:"formSmash:j_idt191:6:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_6_j_idt195_otherAuthors",{id:"formSmash:j_idt191:6:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_6_j_idt195_otherAuthors",multiple:true}); 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)
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Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-12

Open this publication in new window or tab >>Tracking the invisible science: Why does mathematics stay in the shadow of other sciences?### Klimek, Maciej

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_some",{id:"formSmash:j_idt191:7:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_7_j_idt195_otherAuthors",{id:"formSmash:j_idt191:7:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_7_j_idt195_otherAuthors",multiple:true}); 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)
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Available from: 2016-05-12 Created: 2016-05-12 Last updated: 2016-05-12

Open this publication in new window or tab >>Generalized iterated function systems, multifunctions and Cantor sets### Klimek, Maciej

### Kosek, Marta

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_some",{id:"formSmash:j_idt191:8:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_8_j_idt195_otherAuthors",{id:"formSmash:j_idt191:8:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_8_j_idt195_otherAuthors",multiple:true}); 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]

##### 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 ()
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Available from: 2009-05-28 Created: 2009-05-28 Last updated: 2017-12-13

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.

Department of Mathematics, Jagiellonian University, Krakow, Poland.

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.

Open this publication in new window or tab >>Change of expected value under equivalent probability measures and use of surrogate assets### Klimek, Maciej

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_9_j_idt195_some",{id:"formSmash:j_idt191:9:j_idt195:some",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt191_9_j_idt195_otherAuthors",{id:"formSmash:j_idt191:9:j_idt195:otherAuthors",widgetVar:"widget_formSmash_j_idt191_9_j_idt195_otherAuthors",multiple:true}); 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)
#####

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Available from: 2011-01-18 Created: 2011-01-18 Last updated: 2016-05-12

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.