Klimek, Maciej
Overview
Works:  16 works in 50 publications in 2 languages and 639 library holdings 

Roles:  Author, Translator, Thesis advisor 
Publication Timeline
.
Most widely held works by
Maciej Klimek
Discovering curves and surfaces with Maple by
Grażyna Klimek(
Book
)
16 editions published in 1997 in English and held by 358 WorldCat member libraries worldwide
Disk contains all Maple code segments presented in book for use in Maple V (Release 3 or 4) for Microsoft Windows (3.xx or 95); complete contents of disk appear in file README. TXT on disk
16 editions published in 1997 in English and held by 358 WorldCat member libraries worldwide
Disk contains all Maple code segments presented in book for use in Maple V (Release 3 or 4) for Microsoft Windows (3.xx or 95); complete contents of disk appear in file README. TXT on disk
Pluripotential theory by
Maciej Klimek(
Book
)
12 editions published between 1991 and 2011 in English and Undetermined and held by 224 WorldCat member libraries worldwide
12 editions published between 1991 and 2011 in English and Undetermined and held by 224 WorldCat member libraries worldwide
Introduction to complex analytic geometry by
Stanisław Łojasiewicz(
Book
)
5 editions published in 1991 in English and Italian and held by 40 WorldCat member libraries worldwide
The subject of this book is analytic geometry, understood as the geometry of analytic sets (or, more generally, analytic spaces), i.e. sets described locally by systems of analytic equations. Though many of the results presented are relatively modern, they are already part of the classical toolkit of workers in analytic and algebraic geometry and in analysis, for example: the theorems of Chevalley on constructible sets, of RemmertStein on removable singularities, of AndreottiStoll on the fibres of a finite mapping, and of AndreottiSalmon on factoriality of the Grassmannian. The chapter on the relationship between analytic and algebraic geometry is particularly illuminating. This book should be regarded as an introduction. Its aim is to familiarize the reader with a basic range of problems, using means as elementary as possible. At the same time, the author's intention is to give the reader accesss to complete proofs without the need to rely on socalled 'wellknown' facts. All the necessary properties and theorems have been gathered in the first chapters  either with proofs or with references to standard and elementary textbooks
5 editions published in 1991 in English and Italian and held by 40 WorldCat member libraries worldwide
The subject of this book is analytic geometry, understood as the geometry of analytic sets (or, more generally, analytic spaces), i.e. sets described locally by systems of analytic equations. Though many of the results presented are relatively modern, they are already part of the classical toolkit of workers in analytic and algebraic geometry and in analysis, for example: the theorems of Chevalley on constructible sets, of RemmertStein on removable singularities, of AndreottiStoll on the fibres of a finite mapping, and of AndreottiSalmon on factoriality of the Grassmannian. The chapter on the relationship between analytic and algebraic geometry is particularly illuminating. This book should be regarded as an introduction. Its aim is to familiarize the reader with a basic range of problems, using means as elementary as possible. At the same time, the author's intention is to give the reader accesss to complete proofs without the need to rely on socalled 'wellknown' facts. All the necessary properties and theorems have been gathered in the first chapters  either with proofs or with references to standard and elementary textbooks
Iteration of analytic multifunctions by
Maciej Klimek(
Book
)
3 editions published in 1998 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1998 in English and held by 3 WorldCat member libraries worldwide
Modeling discrete time stochastic processes with block frames by
Maciej Klimek(
Book
)
2 editions published in 2011 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 2011 in English and held by 2 WorldCat member libraries worldwide
Metrics associated with extremal plurisubharmonic functions by
Maciej Klimek(
Book
)
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1994 in English and held by 2 WorldCat member libraries worldwide
Degenerate nonstationary flows and finite block frames by
Maciej Klimek(
Book
)
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
Mathematical visualization by
Maciej Klimek(
Book
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
Probabilistic approximation of partly filledin composite Julia sets by
Azza Alghamdi(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Approximation of pluricomplex Green functions A probabilistic approach by
Azza Alghamdi(
)
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
This PhD thesis focuses on probabilistic methods of approximation of pluricomplex Green functions and is based on four papers. The thesis begins with a general introduction to the use of pluricomplex Green functions in multidimensional complex analysis and a review of their main properties. This is followed by short description of the main results obtained in the enclosed papers. In Paper I, we study properties of the metric space of pluriregular sets, that is zero sets of continuous pluricomplex Green functions. The best understood nontrivial examples of such sets are composite Julia sets, obtained by iteration of finite families of polynomial mappings in several complex variables. We prove that the socalled chaos game is applicable in the case of such sets. We also visualize some composite Julia sets using escape time functions and Monte Carlo simulation. In Paper II, we extend results in Paper I to the case of infinite compact families of proper polynomials mappings. With composition as the semigroup operation, we generate families of infinite iterated function systems with compact attractors. We show that such attractors can be approximated probabilistically in a manner of the classic chaos game. In Paper III, we study numerical approximation and visualisation of pluricomplex Green functions based on the MonteCarlo integration. Unlike alternative methods that rely on locating a sequence of carefully chosen finite sets of points satisfying some optimal conditions for approximation purposes, our approach is simpler and more direct by relying on generation of pseudorandom points. We examine numerically the errors of approximation for some simple geometric shapes for which the pluricomplex Green functions are known. If the pluricomplex Green functions are not known, the errors in Monte Carlo integration can be expressed with the aid of statistics in terms of confidence intervals. Finally, in Paper IV, we study how perturbations of an orthonomalization procedure influence the resulting approximate Bergman functions. To this end we consider the concept of near orthonormality of a finite set of vectors in an inner product space, understood as closeness of the Gram matrix of those vectors to the identity matrix. We provide estimates for the errors resulting from using nearly orthogonal bases instead of orthogonal ones. The motivation for this work comes from Paper III: when Gram matrices are calculated via Monte Carlo integration, the outcomes of standard orthogonalisation algorithms are nearly orthonormal bases
1 edition published in 2018 in English and held by 1 WorldCat member library worldwide
This PhD thesis focuses on probabilistic methods of approximation of pluricomplex Green functions and is based on four papers. The thesis begins with a general introduction to the use of pluricomplex Green functions in multidimensional complex analysis and a review of their main properties. This is followed by short description of the main results obtained in the enclosed papers. In Paper I, we study properties of the metric space of pluriregular sets, that is zero sets of continuous pluricomplex Green functions. The best understood nontrivial examples of such sets are composite Julia sets, obtained by iteration of finite families of polynomial mappings in several complex variables. We prove that the socalled chaos game is applicable in the case of such sets. We also visualize some composite Julia sets using escape time functions and Monte Carlo simulation. In Paper II, we extend results in Paper I to the case of infinite compact families of proper polynomials mappings. With composition as the semigroup operation, we generate families of infinite iterated function systems with compact attractors. We show that such attractors can be approximated probabilistically in a manner of the classic chaos game. In Paper III, we study numerical approximation and visualisation of pluricomplex Green functions based on the MonteCarlo integration. Unlike alternative methods that rely on locating a sequence of carefully chosen finite sets of points satisfying some optimal conditions for approximation purposes, our approach is simpler and more direct by relying on generation of pseudorandom points. We examine numerically the errors of approximation for some simple geometric shapes for which the pluricomplex Green functions are known. If the pluricomplex Green functions are not known, the errors in Monte Carlo integration can be expressed with the aid of statistics in terms of confidence intervals. Finally, in Paper IV, we study how perturbations of an orthonomalization procedure influence the resulting approximate Bergman functions. To this end we consider the concept of near orthonormality of a finite set of vectors in an inner product space, understood as closeness of the Gram matrix of those vectors to the identity matrix. We provide estimates for the errors resulting from using nearly orthogonal bases instead of orthogonal ones. The motivation for this work comes from Paper III: when Gram matrices are calculated via Monte Carlo integration, the outcomes of standard orthogonalisation algorithms are nearly orthonormal bases
Supremum norms for quadratic polynomials by
Richard M Aron(
Book
)
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
On pertubations of pluriregular sets generated by sequences of polynomial maps by
Maciej Klimek(
Book
)
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
Change of expected value under equivalent probability measures and use of surrogate assets by
Maciej Klimek(
Book
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
Strong analyticity of partly filledin composite Julia sets by
Maciej Klimek(
Book
)
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
1 edition published in 2004 in English and held by 1 WorldCat member library worldwide
Generalized iterated function systems, multifunctions and Cantor sets by
Maciej Klimek(
)
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
A nontrivial example of a trivial strongly analytic multifunction by
Maciej Klimek(
Book
)
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Klimek, Grażyna Author
 Łojasiewicz, Stanisław 19262002 Author
 Alghamdi, Azza Author
 Kosek, Marta
 Kosek, Marta
 Zdunik, Anna Opponent
 Aron, Richard M. Author
 Uppsala universitet Teknisknaturvetenskapliga vetenskapsområdet Publisher
 Nyström, Kaj 1969 Thesis advisor
 Uppsala universitet Matematiska institutionen Publisher
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