Numer czasopisma
Opuscula Mathematica
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ISSN: 1232-9274
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Data wydania
2008
Rocznik
Vol. 28
Numer
No. 4
Prawa dostępu
Dostęp: otwarty dostęp
Uwagi:
Prawa: CC BY 4.0 
Uznanie autorstwa 4.0 Międzynarodowe (CC BY 4.0)
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Opis
Rocznik czasopisma (rel.)
Rocznik czasopisma
Opuscula Mathematica
Vol. 28 (2008)
Artykuły numeru (rel.)
Artykuł
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Professor Andrzej Lasota - a biographical note
(2008) Myjak, Józef
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Andrzej Lasota's selected results
(2008) Myjak, Józef
In this article we recall Andrzej Lasota's selected results which either indicated new directions of research, or layed the foundations for new approaches, or solved interesting problems. The area of mathematical interests of Professor Andrzej Lasota was very large: ordinary differential equations, partial differential equations, dynamical systems, multifunctions, differential inclusions, functional differential equations, equations with retarded arguments, ergodic theory, invariant measures, chaos, stochastic differential equations, control theory, fixed point theory, theory of Markov operators, theory of fractals, theory of dimensions, biomathematics. In all these branches he obtained original and essential results.
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The work of professor Andrzej Lasota on asymptotic stability and recent progress
(2008) Bartoszek, Wojciech
The paper is devoted to Professor Andrzej Lasota's contribution to the ergodic theory of stochastic operators. We have selected some of his important papers and shown their influence on the evolution of this topic. We emphasize the role A. Lasota played in promoting abstract mathematical theories by showing their applications. The article is focused exclusively on ergodic properties of discrete stochastic semigroups {Pn : n ≥ 0}. Nevertheless, almost all of Lasota's results presented here have their one-parameter continuous semigroup analogs.
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Professor Andrzej Lasota's theories in engineering
(2008) Rusek, Piotr
Professor Lasota's achievements in the field of engineering are based on two principal aspects: profound theoretical backgrounds and perfect knowledge of phenomenological processes. That allowed him to solve many different problems of engineering.
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Existence of solutions of some quadratic integral equations
(2008) Anichini, Giuseppe; Conti, Giuseppe
In this paper we study the existence of continuous solutions of quadratic integral equations. The theory of quadratic integral equations has many useful applications in mathematical physics, economics, biology, as well as in describing real world problems. The main tool used in our investigations is a fixed point result for the multivalued solution's map with acyclic values.
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Asymptotic properties of solutions of some interative functional inequalities
(2008) Brydak, Dobiesław; Choczewski, Bogdan; Czerni, Marek
Continuous solutions of iterative linear inequalities of the first and second order are considered, belonging to a class FT of functions behaving at the origin as a prescribed function T.
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On periodic and stable solutions of the Lasota equation in different phase spaces
(2008) Dawidowicz, Antoni Leon; Poskrobko, Anna
We study properties of the Lasota partial differential equation in two different spaces: Vα (Hölder continuous functions) and Lp. The aim of this paper is to generalize the results of [1].
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Fractal sets satisfying the strong open set condition in complete metric spaces
(2008) Goodman, Gerald S.
Let K be a Hutchinson fractal in a complete metric space X, invariant under the action S of the union of a finite number of Lipschitz contractions. The Open Set Condition states that X has a non-empty subinvariant bounded open subset V, whose images under the maps are disjoint. It is said to be strong if V meets K. We show by a category argument that when [formula] and the restrictions of the contractions to V are open, the strong condition implies that [formula] termed the core of V, is non-empty. In this case, it is an invariant, proper, dense, subset of K, made up of points whose addresses are unique. Conversely, [formula] implies the SOSC, without any openness assumption.
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Dostęp ograniczony
Invariant measures whose supports possess the strong open set property
(2008) Goodman, Gerald S.
Let X be a complete metric space, and S the union of a finite number of strict contractions on it. If P is a probability distribution on the maps, and K is the fractal determined by S, there is a unique Borel probability measure µp on X which is invariant under the associated Markov operator, and its support is K. The Open Set Condition (OSC) requires that a non-empty, subinvariant, bounded open set [formula] exists whose images under the maps are disjoint, it is strong if [formula].In that case, the core of [formula] is non-empty and dense in K. Moreover, when X is separable, V has full µp-measure for every P. We show that the strong condition holds for V satisfying the OSC iff [formula], and we prove a zero-one law for it. We characterize the complement of V relative to K, and we establish that the values taken by invariant measures on cylinder sets defined by K, or by the closure of V, form multiplicative cascades.