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Wyświetlanie 1-15 z 159
Tytuł:
Niejasności związane z Bernarda Bolzana 'definicją' zbioru nieskończonego
The ambiguities associated with Bernard Bolzano's 'definition' of the infinite set
Autorzy:
Dadaczyński, Jerzy
Powiązania:
https://bibliotekanauki.pl/articles/690712.pdf
Data publikacji:
2009
Wydawca:
Copernicus Center Press
Tematy:
Bernard Bolzano
definition of infinite set
paradoxes of infinite set
Opis:
The aim of the paper is to remove the ambiguities contained in the 20th Section Bernard Bolzano's 'Paradoxien des Unendlichen'. Conclusion is that Bolzano originally wanted only to present in the 20th Section one of the (many) paradoxes of infinite sets: an infinite set may be equivalent with its subset. The proof in the 20th Section applies only to this property. Later added Bolzano to the text of the 20th Section a generalizing remark. Only this remark suggests that Bolzano anticipated the reflexive (Dedekindian) definition of the infinity set.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2009, 44; 100-115
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dualities for linear control differential systems with infinite matrices
Autorzy:
Mozyrska, D.
Bartosiewicz, Z.
Powiązania:
https://bibliotekanauki.pl/articles/970007.pdf
Data publikacji:
2006
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
infinite linear differential system
row-finite infinite matrix
approximate controllability
observability
Opis:
Infinite-dimensional linear dynamic systems described by infinite matrices are studied. Approximate controllability for systems with lower-diagonal matrices is investigated, whereas observability is studied for systems with row-finite and upper-diagonal matrices. Different necessary or sufficient conditions of approximate controllability and observability of such systems are given. They are used to show dualities between these properties. The theorems on dualities extend the results known for finite-dimensional systems.
Źródło:
Control and Cybernetics; 2006, 35, 4; 887-904
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The lq-controller synthesis problem for infinite-dimensional systems in factor form
Autorzy:
Grabowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/254801.pdf
Data publikacji:
2013
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
control of infinite-dimensional systems
semigroups
infinite-time lq-control problem
Opis:
The general lq-problem with infinite time horizon for well-posed infinite-dimensional systems has been investigated by George Weiss and Martin Weiss and by Olof Staffans with a complement by Kalle Mikkola and Olof Staffans. Our aim in this paper is to present a solution of a general lq-optimal controller synthesis problem for infinite-dimensional systems in factor form. The systems in factor form are an alternative to additive models, used in the theory of well-posed systems, which rely on leading the analysis exclusively within the basic state space. As a result of applying the simplified analysis in terms of the factor systems and an another derivation technique, we obtain an equivalent, however, astonishingly not the same formulae expressing the optimal controller in the time-domain and the method of spectral factorization. The results are illustrated by two examples of the construction of both the optimal control and optimal controller for some standard lq-problems met in literature: a control problem for a class of boundary controlled hyperbolic equations initiated by Chapelon and Xu, to which we give full solution and an example of the synthesis of the optimal control/controller for the standard lq-problem with infinite-time horizon met in the problem of improving a river water quality by artificial aeration, proposed by Zołopa and the author.
Źródło:
Opuscula Mathematica; 2013, 33, 1; 29-79
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Countable partitions of the sets of points and lines
Autorzy:
Schmerl, James
Powiązania:
https://bibliotekanauki.pl/articles/1205246.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
infinite partitions
Euclidean space
Opis:
The following theorem is proved, answering a question raised by Davies in 1963. If $L_0 ∪ L_1 ∪ L_2 ∪...$ is a partition of the set of lines of $ℝ^n$, then there is a partition $ℝ^n = S_0 ∪ S_1 ∪ S_2 ∪...$ such that $|ℓ ∩ S_i| ≤ 2$ whenever $ℓ ∈ L_i$. There are generalizations to some other, higher-dimensional subspaces, improving recent results of Erdős, Jackson & Mauldin.
Źródło:
Fundamenta Mathematicae; 1999, 160, 2; 183-196
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Geometrically strictly semistable laws as the limit laws
Autorzy:
Malinowski, Marek
Powiązania:
https://bibliotekanauki.pl/articles/729998.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
infinite divisibility
geometric infinite divisibility
geometric semistability
random sums
limit laws
characteristic function
Opis:
A random variable X is geometrically infinitely divisible iff for every p ∈ (0,1) there exists random variable $X_p$ such that $X\stackrel{d}{=} ∑_{k=1}^{T(p)}X_{p,k}$, where $X_{p,k}$'s are i.i.d. copies of $X_p$, and random variable T(p) independent of ${X_{p,1},X_{p,2},...}$ has geometric distribution with the parameter p. In the paper we give some new characterization of geometrically infinitely divisible distribution. The main results concern geometrically strictly semistable distributions which form a subset of geometrically infinitely divisible distributions. We show that they are limit laws for random and deterministic sums of independent random variables.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2007, 27, 1-2; 79-97
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sur l’invariance de la dimension infinie forte par t-équivalence
Autorzy:
Cauty, Robert
Powiązania:
https://bibliotekanauki.pl/articles/1205255.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
function space
strongly infinite-dimensional
Opis:
Let X and Y be metric compacta such that there exists a continuous open surjection from $C_p(Y)$ onto $C_p(X)$. We prove that if there exists an integer k such that $X^k$ is strongly infinite-dimensional, then there exists an integer p such that $Y^p$ is strongly infinite-dimensional.
Źródło:
Fundamenta Mathematicae; 1999, 160, 1; 95-100
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On weakly infinite-dimensional subspuees
Autorzy:
Borst, P.
Powiązania:
https://bibliotekanauki.pl/articles/1215030.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
weakly infinite-dimensional
transfinite dimension
Opis:
We will construct weakly infinite-dimensional (in the sense of Y. Smirnov) spaces X and Y such that Y contains X topologically and $dim Y = ω_0$ and $dim X = ω_0 + 1$. Consequently, the subspace theorem does not hold for the transfinite dimension dim for weakly infinite-dimensional spaces.
Źródło:
Fundamenta Mathematicae; 1991-1992, 140, 3; 225-235
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The LQ/KYP problem for infinite-dimensional systems
Autorzy:
Grabowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/255449.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
control of infinite-dimensional systems
semigroups
infinite-time LQ-control problem
Lur’e feedback systems
Opis:
Our aim is to present a solution to a general linear-quadratic (LQ) problem as well as to a Kalman-Yacubovich-Popov (KYP) problem for infinite-dimensional systems with bounded operators. The results are then applied, via the reciprocal system approach, to the question of solvability of some Lur'e resolving equations arising in the stability theory of infinite-dimensional systems in factor form with unbounded control and observation operators. To be more precise the Lur’e resolving equations determine a Lyapunov functional candidate for some closed-loop feedback systems on the base of some properties of an uncontrolled (open-loop) system. Our results are illustrated in details by an example of a temperature of a rod stabilization automatic control system.
Źródło:
Opuscula Mathematica; 2017, 37, 1; 21-64
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Small-gain theorem for a class of abstract parabolic systems
Autorzy:
Grabowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/255288.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
control of infinite-dimensional systems semigroups
infinite-time LQ-control problem
Lur'e feedback systems
Opis:
We consider a class of abstract control system of parabolic type with observation which the state, input and output spaces are Hilbert spaces. The state space operator is assumed to generate a linear exponentially stable analytic semigroup. An observation and control action are allowed to be described by unbounded operators. It is assumed that the observation operator is admissible but the control operator may be not. Such a system is controlled in a feedback loop by a controller with static characteristic being a globally Lipschitz map from the space of outputs into the space of controls. Our main interest is to obtain a perturbation theorem of the small-gain-type which guarantees that null equilibrium of the closed-loop system will be globally asymptotically stable in Lyapunov's sense.
Źródło:
Opuscula Mathematica; 2018, 38, 5; 651-680
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global convergence of successive approximations of the Darboux problem for partial functional differential equations with infinite delay
Autorzy:
Człapiński, T.
Powiązania:
https://bibliotekanauki.pl/articles/255121.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
successive approximations
Darboux problem
infinite delay
Opis:
We consider the Darboux problem for the hyperbolic partial functional differential equation with infinite delay. We deal with generalized (in the "almost everywhere" sense) solutions of this problem. We prove a theorem on the global convergence of successive approximations to a unique solution of the Darboux problem.
Źródło:
Opuscula Mathematica; 2014, 34, 2; 327-338
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cycle Double Covers of Infinite Planar Graphs
Autorzy:
Javaheri, Mohammad
Powiązania:
https://bibliotekanauki.pl/articles/31340892.pdf
Data publikacji:
2016-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cycle double cover
infinite planar graph
Opis:
In this paper, we study the existence of cycle double covers for infinite planar graphs. We show that every infinite locally finite bridgeless k-indivisible graph with a 2-basis admits a cycle double cover.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 523-544
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Reminiscenze leopardiane nell’ opera di Maria Konopnicka
Reminiscences of Leopardi in Maria Konopnicka’s Oeuvre
Reminiscencje Leopardiańskie W Dziełach Marii Konopnickiej
Autorzy:
Trzeciak, Małgorzata Ewa
Powiązania:
https://bibliotekanauki.pl/articles/2076640.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
poetry
infinite
Italy
reception
Leopardi
Konopnicka
Opis:
Drawing upon studies on the reception of Leopardi’s poetry in Poland, this essay investigates the influence of Leopardi’s works on Maria Konopnicka’s oeuvre as it argues that the influence was key to a certain change of poetic imagery in her works. Through an analysis of poems and other writings by Konopnicka, the article throws a new light on the reception of Leopardi’s poetry in Poland. This subject has so far been rather neglected by critics.
Źródło:
Kwartalnik Neofilologiczny; 2016, 2; 234-243
0023-5911
Pojawia się w:
Kwartalnik Neofilologiczny
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On infinite composition of affine mappings
Autorzy:
Máté, László
Powiązania:
https://bibliotekanauki.pl/articles/1205281.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
affine mapping
subshift
infinite tree
joint contraction
Opis:

 Let ${F_i = 1,...,N}$ be affine mappings of $ℝ^n$. It is well known that if
there exists j ≤ 1 such that for every $σ_1,...,σ _j ∈ {1,..., N}$ the composition
(1) $F_{σ1}∘...∘ F_{σ_j}$
is a contraction, then for any infinite sequence $σ_1, σ_2, ... ∈ {1,..., N}$ and any $z ∈ ℝ^n$, the sequence
(2)$F_{σ1}∘...∘ F_{σ_n}(z)$
is convergent and the limit is independent of z. We prove the following converse result: If
(2) is convergent for any $z ∈ ℝ^n$ and any $σ = {σ_1, σ_2,...}$ belonging to some subshift Σ
of N symbols (and the limit is independent of z), then there exists j ≥ 1 such that for every
$σ = {σ_1, σ_2,...} ∈ Σ$ the composition (1) is a contraction. This result can be considered
as a generalization of the main theorem of Daubechies and Lagarias [1], p. 239. The proof
involves some easy but non-trivial combinatorial considerations. The most important tool
is a weighted version of the König Lemma for infinite trees in graph theory
Źródło:
Fundamenta Mathematicae; 1999, 159, 1; 85-90
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Convergence of approximate solutions of variational problems
Autorzy:
Zaslavski, A. J.
Powiązania:
https://bibliotekanauki.pl/articles/970738.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
good function
infinite horizon
integrand
turnpike property
Opis:
We study the structure of approximate solutions of autonomous variational problems on large finite intervals. In our previous research, which was summarized in Zaslavski (2006b), we showed that approximate solutions are determined mainly by the integrand, and are essentially independent of the choice of time interval and data, except in regions close to the endpoints of the time interval. In the present paper we establish convergence of approximate solutions in regions close to the endpoints of the time intervals.
Źródło:
Control and Cybernetics; 2009, 38, 4B; 1607-1629
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The use of complexity hierarchies in descriptive set theory and automata theory
Autorzy:
Andretta, A.
Camerlo, R.
Powiązania:
https://bibliotekanauki.pl/articles/1964199.pdf
Data publikacji:
2005
Wydawca:
Politechnika Gdańska
Tematy:
hierarchies
infinite games
Borel reducibility
automata theory
Opis:
The concept of a reduction between subsets of a given space is described, giving rise to various complexity hierarchies, studied both in descriptive set theory and in automata theory. We discuss in particular the Wadge and Lipschitz hierarchies for subsets of the Baire and Cantor spaces and the hierarchy of Borel reducibility for finitary relations on standard Borel spaces. The notions of Wadge and Lipschitz reductions are related to corresponding perfect information games.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2005, 9, 3; 337-356
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 159

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