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  • 1.
    Alghamdi, Azza
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Approximation of pluricomplex Green functions based on Monte Carlo integrationManuscript (preprint) (Other academic)
  • 2.
    Alghamdi, Azza
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. Albaha University, Faculty of Science, Department of Mathematics.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Probabilistic approximation of partly filled-in composite Julia sets2017In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 119, no 3, p. 203-220Article in journal (Refereed)
    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.

  • 3.
    Alghamdi, Azza
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Kosek, Marta
    Jagiellonian University, Faculty of Mathematics and Computer ScienceInstitute of Mathematics, Institute of Mathematics..
    Attractors of compactly generated semigroups of regular polynomial mappings.Manuscript (preprint) (Other academic)
  • 4.
    Alghamdi, Azza
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Kosek, Marta
    Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Mathematics..
    Bergman Functions and Nearly Orthonormal PolynomialsManuscript (preprint) (Other academic)
  • 5.
    Aron, R.M.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Klimek, Maciej
    Supremum norms for quadratic polynomials2001In: ARCHIV DER MATHEMATIK, ISSN 0003-889X, Vol. 76, no 1, p. 73-80Article in journal (Refereed)
    Abstract [en]

    We define two norms on R-3 as follows. For (a, b,c) is an element of R-3, we let parallel to (a, b, c)parallel to (R) = sup {/ax(2) + bx + c/ : x is an element of [-1, 1]} and parallel to (a, b, c)parallel to (C) = sup "/az(2) +bz +c/ : z is an element of

  • 6.
    Klimek, Grazyna
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Klimek, Maciej
    Discovering curves and surfaces with Maple1997Book (Refereed)
  • 7.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    A criterion of analyticity for set valued functions1986In: Mathematical Proceedings of the Royal Irish Academy, ISSN 1393-7197, E-ISSN 2009-0021, Vol. 86A, p. 1-4Article in journal (Refereed)
  • 8.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    A note on the L-regularity of compact sets in Cn1981In: Bulletin de l'Académie Polonaise des Sciences, Série des Sciences Mathématiques, Vol. 29, p. 449-451Article in journal (Refereed)
  • 9.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Change of expected value under equivalent probability measures and use of surrogate assets2008Report (Other academic)
  • 10.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Complex foliations generated by (1,1)-forms1984In: Proceedings of the American Mathematical Society, Vol. 91, p. 601-606Article in journal (Refereed)
  • 11.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Degenerate non-stationary flows and finite block frames2006Report (Other academic)
  • 12.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Extremal plurisubharmonic functions and invariant pseudodistances1985In: Bulletin de la Société Mathématique de France, Vol. 113, p. 231-240Article in journal (Refereed)
  • 13.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Extremal plurisubharmonic functions and L-regular sets in Cn1982In: Proceedings of the Royal Irish Academy, Vol. 82A, no 217, article id 230Article in journal (Refereed)
  • 14.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Infinitesimal pseudometrics and the Schwarz lemma1989In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 105, p. 134-140Article in journal (Refereed)
  • 15.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Invariant pluricomplex Green functions1995In: Topics in Complex Analysis / [ed] P. Jakobczak and W. Plesniak, Warsaw: Polish Academy of Sciences , 1995, p. 207-226Chapter in book (Refereed)
  • 16.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Inverse iteration systems in C^n1999In: Acta Univ. Upsaliensis: Skr. Uppsala Univ. C Organ Hist, Vol. 64, p. 206-214Article in journal (Refereed)
    Abstract
  • 17.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Iteration of analytic multifunctions2001In: NAGOYA MATHEMATICAL JOURNAL, ISSN 0027-7630, Vol. 162, p. 19-40Article in journal (Refereed)
    Abstract [en]

    It is shown that iteration of analytic set-valued functions can be used to generate composite Julia sets in C-N. Then it is shown that the composite Julia sets generated by a finite family of regular polynomial mappings of degree at least 2 in C-N, depend

  • 18.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Joint spectra and analytic set valued functions1986In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 294, p. 187-196Article in journal (Refereed)
  • 19.
    Klimek, Maciej
    Uppsala University.
    Metrics associated with extremal plurisubharmonic functions1995In: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 123, no 9, p. 2763-2770Article in journal (Other academic)
    Abstract [en]

    A natural metric is introduced on the family of all polynomially convex compact L-regular sets in C-n, thus turning this family into a complete metric space. An application in complex dynamics is described.

  • 20.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Modeling discrete time stochastic processes with block frames.Manuscript (preprint) (Other academic)
  • 21.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. MATHEMATICS I-V.
    On perturbations of pluriregular sets generated by sequences of polynomial maps2003In: Annales Polonici Mathematici, Vol. 80, p. 171-184Article in journal (Refereed)
    Abstract
  • 22.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    On the invariance of the L-regularity under holomorphic mappings1982In: Universitatis Iagellonicae Acta Mathematica, Vol. 23, p. 27-38Article in journal (Refereed)
  • 23. Klimek, Maciej
    Pluripotential Theory1991Book (Refereed)
  • 24.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Rational valuation systems and compatibility of information2005Report (Other academic)
  • 25. Klimek, Maciej
    Reckoning with probability2010In: Charaktery - Magazyn Psychologiczny, ISSN 1427-695X, Vol. September, p. 76-79Article, review/survey (Other (popular science, discussion, etc.))
  • 26.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Remarks on derivations on normed algebras1979In: Universitatis Iagellonicae Acta Mathematica, Vol. 20, p. 161-166Article in journal (Refereed)
  • 27.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Stochastic characterization of plurisubharmonicity and convexity of functions2015In: 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.

  • 28.
    Klimek, Maciej
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Teaching differentiation in normed spaces1993In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 25, no 5, p. 679-683Article in journal (Refereed)
  • 29. Klimek, Maciej
    The price of a rose: How names influence pricing?2011In: Charaktery - Magazyn Psychologiczny, ISSN 1427-695X, Vol. May, p. 100-103Article, review/survey (Other (popular science, discussion, etc.))
  • 30. Klimek, Maciej
    Tracking the invisible science: Why does mathematics stay in the shadow of other sciences?2010In: Charaktery - Magazyn Psychologiczny, ISSN 1427-695X, Vol. May, p. 80-82Article, review/survey (Other (popular science, discussion, etc.))
  • 31.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Cegla, Wojciech
    Dublin Institute for Advanced Studies.
    Criterion for the large deviation principle1990In: Mathematical Proceedings of the Royal Irish Academy, ISSN 1393-7197, E-ISSN 2009-0021, Vol. 90A, p. 5-10Article in journal (Refereed)
  • 32.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Dineen, Sean
    University College Dublin.
    Timoney, Richard
    Trinity College Dublin.
    Biholomorphic mappings and Banach function modules1988In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 387, p. 122-147Article in journal (Refereed)
  • 33.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Gardiner, Stephen
    University College Dublin, Dublin, Ireland.
    Convexity and subsolutions of partial differential equations1886In: Bulletin of the London Mathematical Society, Vol. 18, p. 41-43Article in journal (Refereed)
  • 34.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Karlsson, Erlendur
    Matsuura, Masaya
    Okabe, Yasunori
    A geometric proof of the fluctuation-dissipation theorem for the KM2O-Langevin equation2002In: Hokkaido Mathematical Journal, Vol. XXXI, no 3, p. 615-628Article in journal (Refereed)
  • 35.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Klimek, Grazyna
    Mathematical Visualization2005In: Newsletter of the European Mathematical Society, no 55, p. 17-22Article in journal (Refereed)
  • 36.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Klimek, Grazyna
    Mathematical Visualization [Polish]2000In: Mathematics as a force of cultural evolution . (Ed. A. Pelczar), PAU, Kraków , 2000, p. 53-66Chapter in book (Refereed)
  • 37.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics. MATHEMATICS I-V.
    Kosek, M.
    Composite Julia sets generated by infinite polynomial arrays2003In: Bulletin des Sciences Matematiques, Vol. 127, p. 885-897Article in journal (Refereed)
  • 38.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
    Kosek, Marta
    Department of Mathematics, Jagiellonian University, Krakow, Poland.
    Generalized iterated function systems, multifunctions and Cantor sets2009In: Annales Polonici Mathematici, ISSN 0066-2216, E-ISSN 1730-6272, Vol. 96, no 1, p. 25-41Article in journal (Refereed)
    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.

  • 39.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Mathematics I -V.
    Kosek, Marta
    Strong Analyticity of Partly Filled-in Composite Julia Sets2006In: Set-Valued Analysis, Vol. 14, p. 55-68Article in journal (Refereed)
  • 40.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Matsuura, Masaya
    Okabe, Yasunori
    On a method for detecting certain signs of stock market crashes by non-linear stationarity tests2002In: International Journal of Pure and Applied Mathematics, Vol. 3, no 4, p. 443-484Article in journal (Refereed)
  • 41.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Matsuura, Masaya
    Department of Mathematics, Ehime University, Matsuyama, Japan.
    Okabe, Yasunori
    Department of Mathematics, Meiji University, Kawasaki, Japan.
    Stochastic flows and finite block frames2008In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 342, no 2, p. 816-829Article in journal (Refereed)
    Abstract [en]

    With the aim of understanding the mathematical structure of the fluctuation–dissipation theorem in non-equilibrium statistical physics and then constructing a mathematical principle in the modeling problem for time series analysis, we have developed the theory of KM2O-Langevin equations for discrete time stochastic processes. In this paper, as a new method for model analysis in the theory of KM2O-Langevin equations, we show that block frames provide a natural mathematical language for dealing with minimum norm expansions of multi-dimensional stochastic processes which do not necessarily satisfy stationarity and non-degeneracy conditions.

  • 42.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Pitera, Marcin
    Jagiellonian University, Krakow, Poland.
    The least squares method for option pricing revisitedManuscript (preprint) (Other academic)
  • 43.
    Klimek, Maciej
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
    Strandell, G.
    Tysk, J.
    Testing weak stationarity of stock returns2001In: Theory of Stochastic Processes, ISSN 0321-3900, Vol. 7(23), no 1-2, p. 196-202Article in journal (Refereed)
1 - 43 of 43
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