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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:
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:
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:
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
Tytuł:
Infinite Elementary Divisor Structure-Preserving Transformations for Polynomial Matrices
Autorzy:
Karampetakis, N. P.
Vologiannidis, S.
Powiązania:
https://bibliotekanauki.pl/articles/908103.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
equivalence
transformation
infinite elementary divisors
autoregressive representations
Opis:
The main purpose of this work is to propose new notions of equivalence between polynomial matrices that preserve both the finite and infinite elementary divisor structures. The approach we use is twofold: (a) the 'homogeneous polynomial matrix approach', where in place of the polynomial matrices we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order to preserve their elementary divisor structure, and (b) the `polynomial matrix approach', where some conditions between the 1-D polynomial matrices and their transforming matrices are proposed.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 4; 493-503
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On some limit distributions for geometric random sums
Autorzy:
Malinowski, Marek
Powiązania:
https://bibliotekanauki.pl/articles/729662.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
random sum
infinite divisibility
semistability
geometric infinite divisibility
geometric stability
geometric semistability
characteristic function
limit distribution
Lévy process
Opis:
We define and give the various characterizations of a new subclass of geometrically infinitely divisible random variables. This subclass, called geometrically semistable, is given as the set of all these random variables which are the limits in distribution of geometric, weighted and shifted random sums. Introduced class is the extension of, considered until now, classes of geometrically stable [5] and geometrically strictly semistable random variables [10]. All the results can be straightforward transfered to the case of random vectors in $ℝ^d$.
Źródło:
Discussiones Mathematicae Probability and Statistics; 2008, 28, 2; 247-266
1509-9423
Pojawia się w:
Discussiones Mathematicae Probability and Statistics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On infinite partitions of lines and space
Autorzy:
Erdös, Paul
Jackson, Steve
Mauldin, R.
Powiązania:
https://bibliotekanauki.pl/articles/1205459.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
transfinite recursion
Martin's Axiom
forcing
geometry
infinite partitions
Opis:
Given a partition P:L → ω of the lines in $ℝ^n$, n ≥ 2, into countably many pieces, we ask if it is possible to find a partition of the points, $Q:ℝ^n → ω$, so that each line meets at most m points of its color. Assuming Martin's Axiom, we show this is the case for m ≥ 3. We reduce the problem for m = 2 to a purely finitary geometry problem. Although we have established a very similar, but somewhat simpler, version of the geometry conjecture, we leave the general problem open. We consider also various generalizations of these results, including to higher dimension spaces and planes.
Źródło:
Fundamenta Mathematicae; 1997, 152, 1; 75-95
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the existence of (k,l)-kernels in infinite digraphs: A survey
Autorzy:
Galeana-Sánchez, H.
Hernández-Cruz, C.
Powiązania:
https://bibliotekanauki.pl/articles/30148241.pdf
Data publikacji:
2014-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
kernel
k-kernel
infinite digraph
(k, l)-kernel
Opis:
Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent (if u, v ∈ N, u 6= v, then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l) set of vertices. A k-kernel is a (k, k −1)-kernel. This work is a survey of results proving sufficient conditions for the existence of (k, l)-kernels in infinite digraphs. Despite all the previous work in this direction was done for (2, 1)-kernels, we present many original results concerning (k, l)-kernels for distinct values of k and l. The original results are sufficient conditions for the existence of (k, l)- kernels in diverse families of infinite digraphs. Among the families that we study are: transitive digraphs, quasi-transitive digraphs, right/left pretransitive digraphs, cyclically k-partite digraphs, κ-strong digraphs, k-transitive digraphs, k-quasi-transitive digraphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 3; 431-466
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Turnpike properties of approximate solutions of autonomous variational problems
Autorzy:
Zaslavski, A. J.
Powiązania:
https://bibliotekanauki.pl/articles/969609.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
good function
infinite horizon problem
integrand
turnpike property
Opis:
In this work we study the structure of approximate solutions of autonomous variational problems with vector-valued functions. We are interested in turnpike properties of these solutions, which are independent of the length of the interval, for all sufficiently large intervals. We show that the turnpike properties are stable under small perturbations of integrands.
Źródło:
Control and Cybernetics; 2008, 37, 2; 491-512
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A non-singular description of parametrical resonance
Autorzy:
Romanów, F.
Hańćkowiak, J.
Powiązania:
https://bibliotekanauki.pl/articles/279246.pdf
Data publikacji:
2000
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
stability
infinite chain of equations
truncation
Gibbs phenomenon
Opis:
Employing the Mathieu equations we present a method for construction of Ince-Strutt diagrams, in which no cut-off of the infinite chain of equations for Fourier coefficients is necessary.
Niesingularny opis rezonansu parametrycznego. Na przykładzie równania Mathieu przedstawiamy niesingularną metodę konstrukcji diagramów Incea-Strutta, które obrazują na płaszczyźnie F parametrów równania obszary stabilności i niestabilności. Niesingularność metody została osiągnięta dzięki nie obrywaniu nieskończonych łańcuchów równań dla współczynników Fouriera. Pozwala to na zachowanie pierwotnego charakteru rozważanych równań (zagadnienie początkowe). Przedstawione rozważania sugerują poszerzenie oszarów niestabilności.
Źródło:
Journal of Theoretical and Applied Mechanics; 2000, 38, 4; 879-892
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The order of normalform hypersubstitutions of type (2)
Autorzy:
Denecke, Klaus
Mahdavi, Kazem
Powiązania:
https://bibliotekanauki.pl/articles/728816.pdf
Data publikacji:
2000
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypersubstitutions
terms
idempotent elements
elements of infinite order
Opis:
In [2] it was proved that all hypersubstitutions of type τ = (2) which are not idempotent and are different from the hypersubstitution whichmaps the binary operation symbol f to the binary term f(y,x) haveinfinite order. In this paper we consider the order of hypersubstitutionswithin given varieties of semigroups. For the theory of hypersubstitution see [3].
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 183-192
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Well-posedness and stability analysis of hybrid feedback systems using Shkalikovs theory
Autorzy:
Grabowski, P.
Powiązania:
https://bibliotekanauki.pl/articles/254925.pdf
Data publikacji:
2006
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite-dimensional control systems
semigroups
spectral methods
Riesz bases
Opis:
The modern method of analysis of the distributed parameter systems relies on the transformation of the dynamical model to an abstract differential equation on an appropriately chosen Banach or, if possible, Hilbert space. A linear dynamical model in the form of a first order abstract differential equation is considered to be well-posed if its right-hand side generates a strongly continuous semigroup. Similarly, a dynamical model in the form of a second order abstract differential equation is well-posed if its right-hand side generates a strongly continuous cosine family of operators. Unfortunately, the presence of a feedback leads to serious complications or even excludes a direct verification of assumptions of the Hille-Phillips-Yosida and/or the Sova-Fattorini Theorems. The class of operators which are similar to a normal discrete operator on a Hilbert space describes a wide variety of linear operators. In the papers [12, 13] two groups of similarity criteria for a given hybrid closed-loop system operator are given. The criteria of the first group are based on some perturbation results, and of the second, on the application of Shkalikov's theory of the Sturm-Liouville eigenproblems with a spectral parameter in the boundary conditions. In the present paper we continue those investigations showing certain advanced applications of the Shkalikov's theory. The results are illustrated by feedback control systems examples governed by wave and beam equations with increasing degree of complexity of the boundary conditions.
Źródło:
Opuscula Mathematica; 2006, 26, 1; 45-97
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Different Models of Chemotherapy Taking Into Account Drug Resistance Stemming from Gene Amplification
Autorzy:
Śmieja, J.
Świerniak, A.
Powiązania:
https://bibliotekanauki.pl/articles/908161.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
medycyna
automatyka
biomedical modelling
infinite dimensional systems
multivariable control
Opis:
This paper presents an analysis of some class of bilinear systems that can be applied to biomedical modelling. It combines models that have been studied separately so far, taking into account both the phenomenon of gene amplification and multidrug chemotherapy in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix whose form allows decomposing the model into two interacting subsystems. While the first one, of a finite dimension, can have any form, the other is infinite dimensional and tridiagonal. A methodology of the analysis of such models, based on system decomposition, is presented. An optimal control problem is defined in the l1 space. In order to derive necessary conditions for optimal control, the model description is transformed into an integro-differential form. Finally, biomedical implications of the obtained results are discussed.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 3; 297-305
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Strong maximum principles for infinite systems of parabolic differential-functional inequalities with initial constant estimates
Autorzy:
Brandys, Jolanta
Powiązania:
https://bibliotekanauki.pl/articles/745310.pdf
Data publikacji:
2007
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
infinite systems
parabolic differential-functional inequalities
strong maximum principle
Opis:
The purpose of this paper is to present strong maximum principles for infinite systems of parabolic differential-functional inequalities with initial inequalities in relatively arbitrary \((n+1)\)-dimensional time-space sets more general than the cylindrical domain.
Źródło:
Commentationes Mathematicae; 2007, 47, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Constant 2-Labellings And An Application To (R, A, B)-Covering Codes
Autorzy:
Gravier, Sylvain
Vandomme, Èlise
Powiązania:
https://bibliotekanauki.pl/articles/31341603.pdf
Data publikacji:
2017-11-27
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
covering codes
weighted codes
infinite grid
vertex-weighted graphs
Opis:
We introduce the concept of constant 2-labelling of a vertex-weighted graph and show how it can be used to obtain perfect weighted coverings. Roughly speaking, a constant 2-labelling of a vertex-weighted graph is a black and white colouring of its vertex set which preserves the sum of the weights of black vertices under some automorphisms. We study constant 2-labellings on four types of vertex-weighted cycles. Our results on cycles allow us to determine (r, a, b)-codes in $ \mathbb{Z}^2 $ whenever |a − b| > 4, r ≥ 2 and we give the precise values of a and b. This is a refinement of Axenovich’s theorem proved in 2003.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 4; 891-918
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second order evolution differential functional equations with infinite delay
Autorzy:
Człapiński, Tomasz
Karpowicz, Adrian
Powiązania:
https://bibliotekanauki.pl/articles/962858.pdf
Data publikacji:
2018
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Measure of noncompactness
second order evolution equation
infinite delay
Opis:
We consider a second order semilinear functional evolution equation with infinite delay in a Banach space. We prove the existence of mild solutions for this equation using the measure of noncompactness technique and the Schauder fixed point theorem.
Źródło:
Commentationes Mathematicae; 2018, 58, 1-2; 93-104
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the convergence of certain integrals
Autorzy:
Hachani, Mohamed Amine
Powiązania:
https://bibliotekanauki.pl/articles/1395940.pdf
Data publikacji:
2019
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Entire functions
Hadamard’s three-circles theorem
infinite integrals
Opis:
Let \(M(r) := \max_{|z|=r} |f(z)|\), where \(f(z)\) is an entire function. Also let \(\alpha> 0\) and \(\beta>1\). We discuss the behavior of the integrand \(M(r)e^{-\alpha(log r)^\beta}\) as \(r \to \infty\) if \(\int_1^\infty M(r)e^{-\alpha(log r)^\beta}dr\) is convergent.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2019, 73, 1
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence results for Kirchhoff type systems with singular nonlinearity
Autorzy:
Firouzjai, A.
Afrouzi, G. A.
Talebi, S.
Powiązania:
https://bibliotekanauki.pl/articles/254877.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
sub-supersolution
infinite semipositone systems
singular weights
Kirchhoff-type
Opis:
Using the method of sub-super solutions, we study the existence of positive solutions for a class of singular nonlinear semipositone systems involving nonlocal operator.
Źródło:
Opuscula Mathematica; 2018, 38, 2; 187-199
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Extensão e infinito em Hilbert: pela filosofia da matemática
Autorzy:
Borges de Meneses, Ramiro Délio
Czarnecki, Paweł
Powiązania:
https://bibliotekanauki.pl/articles/2130398.pdf
Data publikacji:
2019
Wydawca:
Instytut Studiów Międzynarodowych i Edukacji Humanum
Tematy:
Continuity
Infinite
Hilbert
Cantor
Masthematical Analysis
and logical foundations
Opis:
According to Hilbert the infinite and extension are a regular idea, and a very important role in mat- hematics plays, because there are new possibilities according to logic foundations and philosophical implications to the infinite languages, from mathematic to philosophy by the Hilbert’s formalism.
Źródło:
Humanum. Międzynarodowe Studia Społeczno-Humanistyczne; 2019, 2 (33); 19-30
1898-8431
Pojawia się w:
Humanum. Międzynarodowe Studia Społeczno-Humanistyczne
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Arithmetically maximal independent sets in infinite graphs
Autorzy:
Bylka, Stanisław
Powiązania:
https://bibliotekanauki.pl/articles/744334.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
infinite graph
independent set
arithmetical maximal set
line graph
Opis:
Families of all sets of independent vertices in graphs are investigated. The problem how to characterize those infinite graphs which have arithmetically maximal independent sets is posed. A positive answer is given to the following classes of infinite graphs: bipartite graphs, line graphs and graphs having locally infinite clique-cover of vertices. Some counter examples are presented.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 167-182
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
O infinito segundo Hilbert: da análise matemática à filosofia
Autorzy:
Borges de Meneses, Ramiro Délio
Powiązania:
https://bibliotekanauki.pl/articles/2134346.pdf
Data publikacji:
2014
Wydawca:
Instytut Studiów Międzynarodowych i Edukacji Humanum
Tematy:
continuity
infinite
Hilbert
Cantor
mathematical analysis
and logical foundations
Opis:
According to Hilbert the infinite is a regular idea, and a very important role in mathematics plays, because there are new possibilities according to logic foundations and philosophical implications to the infinite languages, from mathematic to philosophy by the Hilbert’s formalism.
Źródło:
Humanum. Międzynarodowe Studia Społeczno-Humanistyczne; 2014, 1(12); 5-18
1898-8431
Pojawia się w:
Humanum. Międzynarodowe Studia Społeczno-Humanistyczne
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Giuseppe Veronesego konstruktywizm arytmetyczny a poznawalność nieskończoności. Studium wybranych wątków filozofii matematyki we wprowadzeniu do Grundzüge der Geometrie von mehreren Dimensionen
Giuseppe Veronese’s Arithmetical Constructivism and the Cognizability of Infinity: A Study of Selected Aspects of the Philosophy of Mathematics in the Introduction to Grundzüge der Geometrie von mehreren Dimensionen
Autorzy:
Dadaczyński, Jerzy
Powiązania:
https://bibliotekanauki.pl/articles/38429160.pdf
Data publikacji:
2022
Wydawca:
Uniwersytet Warszawski. Wydział Filozofii
Tematy:
Giuseppe Veronese
constructivism
natural numbers
infinity
infinite sequences
cognizability
Opis:
In the first part of the article, Giuseppe Veronese’s concept of arithmetical constructivism is reconstructed from his dispersed remarks. It is pointed out that although for Veronese time is a necessary condition for the construction of natural numbers by an individual subject and the subject cognizes time in an a priori way, it is not a (proto-)intuition of the subject. This is a fundamental difference between the concept proposed by Veronese and the constructivism of Kant and Brouwer. Veronese’s justification of the subject’s ability to cognize infinity, represented in his text by infinite sequences, is analyzed in the second part of the paper. The only condition for the cognition of the infinite sequence is to have a rule according to which its successive terms “follow one another.” The price of the ability to cognize the infinitive “whole” (sequence) may be the uncognizability of certain “parts” (terms of sequence). Infinite sequences, cognizable according to Veronese, are allowed as objects of mathematical research, although they do not meet the condition of constructability.
Źródło:
Filozofia Nauki; 2022, 30, 3; 33-50
1230-6894
2657-5868
Pojawia się w:
Filozofia Nauki
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The linear programming approach to deterministic optimal control problems
Autorzy:
Hernández-Hernández, Daniel
Hernández-Lerma, Onésimo
Taksar, Michael
Powiązania:
https://bibliotekanauki.pl/articles/1339290.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
linear programming (in infinite-dimensional spaces)
duality theory
optimal control
Opis:
Given a deterministic optimal control problem (OCP) with value function, say $J^*$, we introduce a linear program $(P)$ and its dual $(P^*)$ whose values satisfy $\sup(P^*) \leq\inf(P)\leq J^*(t,x)$. Then we give conditions under which (i) there is no duality gap
Źródło:
Applicationes Mathematicae; 1996-1997, 24, 1; 17-33
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution of Fredholm integrodifferential equation for an infinite elastic plate
Autorzy:
El-Bary, Alaa
Powiązania:
https://bibliotekanauki.pl/articles/729513.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
integrodifferential equation
Cauchy method
complex variable
infinite plate
curvilinear hole
Opis:
Many authors discussed the problem of an elastic infinite plate with a curvilinear hole, some of them considered this problem in z-plane and the others in the s-plane. They obtained an exact expression for Goursat's functions for the first and second fundamental problem. In this paper, we use the Cauchy integral method to obtain a solution to the first and second fundamental problem by using a new transformation. Some applications are investigated and also some special cases are discussed.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2004, 24, 1; 5-11
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adaptive compensators for pertrubed positive real infinite-dimensional systems
Autorzy:
Curtain, R. F.
Demetriou, M. A.
Ito, K.
Powiązania:
https://bibliotekanauki.pl/articles/908105.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
automatyka
robotyka
infinite dimensional systems
positive real systems
adaptive controllers
Opis:
The aim of this investigation is to construct an adaptive observer and an adaptive compensator for a class of infinite-dimensional plants having a known exogenous input and a structured perturbation with an unknown constant parameter, such as the case of static output feedback with an unknown gain. The adaptive observer uses the nominal dynamics of the unperturbed plant and an adaptation law based on the Lyapunov redesign method. We obtain conditions on the system to ensure uniform boundedness of the estimator dynamics and the parameter estimates, and the convergence of the estimator error. For the case of a known periodic exogenous input we design an adaptive compensator which forces the system to converge to a unique periodic solution. We illustrate our approach with a delay example and a diffusion example for which we obtain convincing numerical results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 4; 441-452
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Transmission problems for the Helmholtz equation for a rectilinear-circular lune
Autorzy:
Denysenko, V.
Powiązania:
https://bibliotekanauki.pl/articles/255476.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Helmholtz equation
transmission problem
infinite system of linear algebraic equations
Opis:
The question related to the construction of the solution of plane transmission problem for the Helmholtz equation in a rectilinear-circular lune is considered. An approach is proposed based on the method of partial domains and the principle of reflection for the solutions of the Helmholtz equation through the segment.
Źródło:
Opuscula Mathematica; 2007, 27, 2; 197-203
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cantor on Infinitesimals. Historical and Modern Perspective
Autorzy:
Błaszczyk, Piotr
Fila, Marlena
Powiązania:
https://bibliotekanauki.pl/articles/750052.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:
infinitesimals
infinite numbers
real numbers
hyperreals
ordinal numbers
Conway numbers
Opis:
In his 1887's Mitteilungen zur Lehre von Transfiniten, Cantor seeks to prove inconsistency of infinitesimals. We provide a detailed analysis of his argument from both historical and mathematical perspective. We show that while his historical analysis are questionable, the mathematical part of the argument is false.
Źródło:
Bulletin of the Section of Logic; 2020, 49, 2
0138-0680
2449-836X
Pojawia się w:
Bulletin of the Section of Logic
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A comparative analysis of (s, Q) and (s, S) ordering policies in a queuing-inventory system with stock-dependent arrival and queue-dependent service process
Autorzy:
Sugapriya, Chandrasekaran
Nithya, Murugesan
Jeganathan, Kathirvel
Selvakumar, Subramanian
Harikrishnan, Thanushkodi
Powiązania:
https://bibliotekanauki.pl/articles/27315339.pdf
Data publikacji:
2023
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
stock-dependent arrival
queue-dependent service
infinite waiting hall
ordering principles
Opis:
This article deals with a Markovian queuing-inventory system (MQIS) under the stochastic modeling technique. The arrival stream of this system is dependent on the present stock level at an instant. Meanwhile, the system focuses on reducing the waiting time of a unit by assuming a queue-dependent service policy (QDSP). The system consists of an infinite waiting hall to receive an arriving unit. The MQIS assumes that no unit of arrival is allowed when the stock level of the system is empty. The discussion of this MQIS runs over the two types of ordering principles named 1) (s, Q) 2) (s, S). According to both ordering principles, the assumed arrival and service patterns have been considered separately and classified as Model-I (M-I) and Model-II (M-II) respectively. The steady state of the system for both M-I and M-II is analysed and resolved under the Neuts matrix-geometric technique. The system performance measures of the system are also computed. The expected cost function of both M-I and M-II are constructed as well. Further, the necessary numerical illustrations are provided and distinguished for M-I and M-II to explore the proposed model. This paper finds the optimum ordering policy to execute the stock-dependent arrival and queue-dependent service strategies.
Źródło:
Operations Research and Decisions; 2023, 33, 2; 121--153
2081-8858
2391-6060
Pojawia się w:
Operations Research and Decisions
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Study of the anti-plane problem of a Dugdale-Barenblatt crack in a welded strip using the integral equation method
Autorzy:
Chaouche, Amine Brick
Ferdjani, Hicheme
Tala-Ighil, Nacer
Powiązania:
https://bibliotekanauki.pl/articles/279531.pdf
Data publikacji:
2019
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
crack
Dugdale-Barenblatt model
weld joint
singular integral equation
infinite strip
Opis:
The elasto-static anti-plane problem of a Dugdale-Barenblatt crack in a welded infinite strip is formulated in terms of a singular integral equation (SIE). The weld joint is modeled as a tri-material structure: the weld metal (WM), the base metal (BM) and the heat-affected zone (HAZ). The HAZ is modeled with an exponentially variable shear modulus. The SIE is solved using Tchebychev polynomials. The influence of the elastic mismatching (the ratio between the shear modulus of WM and BM) and width of the HAZ on the fracture load and on the crack propagation is investigated.
Źródło:
Journal of Theoretical and Applied Mechanics; 2019, 57, 2; 475-487
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monotone iteration for infinite systems of parabolic equations
Autorzy:
Pudełko, A.
Powiązania:
https://bibliotekanauki.pl/articles/255193.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite systems
parabolic equations
Cauchy problem
monotone iteration method
differentail inequality
Opis:
In the paper the Cauchy problem for and infinite system of parabolic type equations is studied. The general operators of the parabolic type of second order with variable coefficients are considered and the system is weakly coupled. Among the obtained results there is a theorem on differential inequality as well as the existence and uniqueness theorem in the class of continuous-bounded functions obtained by monotone iterative method.
Źródło:
Opuscula Mathematica; 2005, 25, 2; 307-318
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Relationship Between the Infinite Eigenvalue Assignment for Singular Systems and the Solvability of Polynomial Matrix Equations
Autorzy:
Kaczorek, T.
Powiązania:
https://bibliotekanauki.pl/articles/908199.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
automatyka
robotyka
assignment
infinite eigenvalue
singular
polynomial matrix equation
system
reliationship
Opis:
Two related problems, namely the problem of the infinite eigenvalue assignment and that of the solvability of polynomial matrix equations are considered. Necessary and sufficient conditions for the existence of solutions to both the problems are established. The relationships between the problems are discussed and some applications from the field of the perfect observer design for singular linear systems are presented.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 2; 161-167
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A game-theoretic model of social adaptation in an infinite population
Autorzy:
Wieczorek, A.
Wiszniewska, A.
Powiązania:
https://bibliotekanauki.pl/articles/1338932.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
prey-predator game
social adaptation
equilibrated distribution
infinite population
iterative process
Opis:
The paper deals with the question of existence and properties of equilibrated distributions of individual characteristics in an infinite population. General game-theoretic methods are applied and special attention is focused on the case of fitness functions depending only on the distance of an individual characteristic from a reference point and from the mean characteristics. Iterative procedures leading to equilibrated distributions are also considered.
Źródło:
Applicationes Mathematicae; 1998-1999, 25, 4; 417-430
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A relaxation theorem for partially observed stochastic control on Hilbert space
Autorzy:
Ahmed, N.
Powiązania:
https://bibliotekanauki.pl/articles/729417.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
partially observed control
infinite dimensional Hilbert space
relaxed controls
Zakai equation
Opis:
In this paper, we present a result on relaxability of partially observed control problems for infinite dimensional stochastic systems in a Hilbert space. This is motivated by the fact that measure valued controls, also known as relaxed controls, are difficult to construct practically and so one must inquire if it is possible to approximate the solutions corresponding to measure valued controls by those corresponding to ordinary controls. Our main result is the relaxation theorem which states that the set of solutions corresponding to ordinary controls is weakly dense in the set of solutions corresponding to relaxed controls. This is presented in Theorem 5.3 after giving some existence results on optimal controls for the infinite dimensional Zakai equation used for its proof.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 295-314
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations
Autorzy:
Ahmed, N.
Powiązania:
https://bibliotekanauki.pl/articles/729348.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
optimal control
stochastic systems
infinite dimension
HJB equation
stationary feedback control
Opis:
In this paper, we consider optimal feedback control for stochastc infinite dimensional systems. We present some new results on the solution of associated HJB equations in infinite dimensional Hilbert spaces. In the process, we have also developed some new mathematical tools involving distributions on Hilbert spaces which may have many other interesting applications in other fields. We conclude with an application to optimal stationary feedback control.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 1; 97-126
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Thermal stresses around two upper cracks placed symmetrically about a lower crack in an infinite orthotropic plane under uniform heat flux
Autorzy:
Itou, S
Powiązania:
https://bibliotekanauki.pl/articles/279201.pdf
Data publikacji:
2014
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
heat flux
three parallel cracks
stress intensity factor
infinite orthotropic plane
Opis:
Two upper collinear cracks are placed parallel to a lower crack in an infinite orthotropic plane under uniform heat flux perpendicular to the cracks. The surfaces of the cracks are assumed to be thermally insulated. The mixed boundary value conditions with respect to the temperature field and those with respect to the stress field are reduced to dual integral equations using the Fourier transform technique. In order to satisfy the boundary conditions outside the cracks, the differences in temperature and displacement at each crack surface are expanded in a series of functions that are zero outside the cracks. The unknown coefficients in each series are evaluated using the Schmidt method. The stress intensity factors are then calculated numerically for selected crack configurations.
Źródło:
Journal of Theoretical and Applied Mechanics; 2014, 52, 3; 617-628
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solutions of vibration problems for thin infinite plates subjected to harmonic loads
Autorzy:
Klanner, M.
Ellermann, K.
Powiązania:
https://bibliotekanauki.pl/articles/281616.pdf
Data publikacji:
2017
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
Kirchhoff plate theory
infinite plate
ring load
circular load
Hankel transform
Opis:
New closed form solutions for harmonic vibrations of infinite Kirchhoff plates subjected to a constant harmonic ring load, a constant harmonic circular load and an alternating harmonic circular load are derived. Two different approaches are used to define the closed form solutions. The first approach uses the integration of the harmonic point force and the addition theorem for Bessel functions, while the second approach applies the Hankel transform to solve the inhomogeneous partial differential equation of the Kirchhoff plate theory. The new closed form particular solutions can especially be used in Trefftz like methods and extend their field of application.
Źródło:
Journal of Theoretical and Applied Mechanics; 2017, 55, 3; 949-961
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Composite semi-infinite optimization
Autorzy:
Dentcheva, D.
Ruszczyński, A.
Powiązania:
https://bibliotekanauki.pl/articles/970266.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
semi-infinite optimization
nonsmooth optimization
composite optimization
stochastic programming
stochastic dominance
Opis:
We consider a semi-infinite optimization problem in Banach spaces, where both the objective functional and the constraint operator are compositions of convex nonsmooth mappings and differentiable mappings. We derive necessary optimality conditions for these problems. Finally, we apply these results to non-convex stochastic optimization problems with stochastic dominance constraints, generalizing earlier results.
Źródło:
Control and Cybernetics; 2007, 36, 3; 633-646
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Determination of the optode array representation using optical properties at systole and diastole
Autorzy:
Jumadi, N A
Beng, G K
Mohd-Ali, M. A.
Zahedi, E
Powiązania:
https://bibliotekanauki.pl/articles/173805.pdf
Data publikacji:
2013
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
optical simulation
optical properties
optode array
semi-infinite tissue layer
statistical
analysis
Opis:
The necessity to develop an optode array in order to probe the fetus oxygenation noninvasively regardless of the fetus position has been highlighted in previous literature. In this paper, a series of optical simulations are carried out to determine the best representation of optode array by using optical properties at systolic and diastolic states. The selection is based on the highest flux values accumulated at respective detectors. To accomplish the objective, a homogenous three-layer semi-infinite tissue model is implemented to represent the pregnant woman model. The geometry of the model as well as Monte Carlo simulation are carried out using commercial software, whereas the optical properties related to systolic and diastolic states are defined for all wavelengths. A statistical noise analysis is also introduced in order to find a sufficient number of rays to be launched into the optical tissue system.
Źródło:
Optica Applicata; 2013, 43, 4; 747-759
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Every reasonably sized matrix group is a subgroup of $S_∞$
Autorzy:
Kallman, Robert
Powiązania:
https://bibliotekanauki.pl/articles/1205071.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
infinite symmetric group
matrix groups
nonarchimedian absolute values
field extensions
topological groups
Opis:
Every reasonably sized matrix group has an injective homomorphism into the group $S_∞$ of all bijections of the natural numbers. However, not every reasonably sized simple group has an injective homomorphism into $S_∞$.
Źródło:
Fundamenta Mathematicae; 2000, 164, 1; 35-40
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
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