Temat: operator equation - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Well-Posed Linear Systems - a Survey With Emphasis on Conservative Systems
Autorzy:: Weiss, G.
Staffans, O. J.
Tucsnak, M.
Powiązania:: https://bibliotekanauki.pl/articles/908320.pdf
Data publikacji:: 2001
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: system liniowy
układ zachowawczy
równanie różniczkowe
well-posed linear systems
regular linear system
operator semigroup
consevative system
scattering theory
time-flow-inversion
differential equations in Hilbert space
beam equation
Opis:: We survey the literature on well-posed linear systems, which has been an area of rapid development in recent years. We examine the particular subclass of conservative systems and its connections to scattering theory. We study some transformations of well-posed systems, namely duality and time-flow inversion, and their effect on the transfer function and the generating operators. We describe a simple way to generate conservative systems via a second-order differential equation in a Hilbert space. We give results about the stability, controllability and observability of such conservative systems and illustrate these with a system modeling a controlled beam.
Źródło:: International Journal of Applied Mathematics and Computer Science; 2001, 11, 1; 7-33
1641-876X
2083-8492
Pojawia się w:: International Journal of Applied Mathematics and Computer Science
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener
Autorzy:: Azocar, A.
Guerrero, J. A.
Matkowski, J.
Merentes, N.
Powiązania:: https://bibliotekanauki.pl/articles/255944.pdf
Data publikacji:: 2010
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: phi-variation in the sense of Wiener
set-valued functions
left and right regularizations
uniformly continuous composition (Nemytskii) operator
Jensen equation
Opis:: We show that the one-sided regularizations of the generator of any uniformly continuous and convex compact valued composition operator, acting in the spaces of functions of bounded variation in the sense of Wiener, is an affine function.
Źródło:: Opuscula Mathematica; 2010, 30, 1; 53-60
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Uniformly continuous composition operators in the space of functions of two variables of bounded $\varphi$-variation in the sense of Wiener
Autorzy:: Guerrero, J. A.
Matkowski, J.
Merentes, N.
Powiązania:: https://bibliotekanauki.pl/articles/745206.pdf
Data publikacji:: 2010
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: $\vaprhi$-variation in the Wiener sense
composition operator
uniformly continuous operator
left-left regularization
Jensen equation
Opis:: Assume that the generator of a Nemytskii composition operator is a function of three variables: the first two real and third in a closed convex subset of a normed space, with values in a real Banach space. We prove that if this operator maps a certain subset of the Banach space of functions of two real variables of bounded Wiener $\varphi$-variation into another Banach space of a similar type, and is uniformly continuous, then the one-sided regularizations of the generator are affine in the third variable.
Źródło:: Commentationes Mathematicae; 2010, 50, 1
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Uniformly continuous composition operators in the space of bounded Φ-variation functions in the Schramm sense
Autorzy:: Ereu, T.
Merentes, N.
Sanchez, J. L.
Wróbel, M.
Powiązania:: https://bibliotekanauki.pl/articles/255979.pdf
Data publikacji:: 2012
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Phi-variation in the sense of Schramm
uniformly continuous operator
regularization
composition operator
Jensen equation
locally defined operators
Opis:: We prove that any uniformly continuous Nemytskii composition operator in the space of functions of bounded generalized Φ-variation in the Schramm sense is affine. A composition operator is locally defined. We show that every locally defined operator mapping the space of continuous functions of bounded (in the sense of Jordan) variation into the space of continous monotonic functions is constant.
Źródło:: Opuscula Mathematica; 2012, 32, 2; 239-247
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Uniformly bounded set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener
Autorzy:: Guerrero, J. A.
Matkowski, J.
Merentes, N.
Wróbel, M.
Powiązania:: https://bibliotekanauki.pl/articles/122662.pdf
Data publikacji:: 2015
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: ø-variation in the sense of Wiener
set-valued functions
left and right regularizations
uniformly bounded operator
composition Nemytskij operator
Jensen equation
Opis:: We show that the one-sided regularizations of the generator of any uniformly bounded set-valued Nemytskij composition operator mapping the space of bounded variation functions in the sense of Wiener into the space of bounded variation functions with closed bounded convex values (in the sense of Wiener) are affine functions.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 4; 41-51
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: Unified summation equations and their applications in tribology wear process
Autorzy:: Wierzcholski, K.
Powiązania:: https://bibliotekanauki.pl/articles/200950.pdf
Data publikacji:: 2013
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: unified operator of summation
summation equation
micro-bearing wear
Opis:: This paper presents some applications of summation equations with regard to the calculation prognosis of micro-bearing wear parameters. Summation equations are presented in a new form of difference and recurrence equations where the unknown micro-bearing wear function occurs as the argument of the reciprocal unified operator of summation (UOS). In this paper the properties of the UOS and reciprocal UOS as well as the unitary translation operator (UTO) are defined and applied to a micro-bearing wear determination. The approach of both dual and interaction between summation and recurrence equations and micro-bearing wear determination, makes this paper unique.
Źródło:: Bulletin of the Polish Academy of Sciences. Technical Sciences; 2013, 61, 2; 405-417
0239-7528
Pojawia się w:: Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: The reactance wave diffraction problem by a strip in a scale of Bessel potential spaces
Autorzy:: Castro, L. P.
Natroshvili, D.
Powiązania:: https://bibliotekanauki.pl/articles/255627.pdf
Data publikacji:: 2006
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Helmholtz equation
boundary-transmission problem
wave diffraction
convolution type operator
Wiener-Hopf operator
Fredholm property
factorization
Opis:: We consider a boundary-transmission problem for the Helmholtz equation, in a Bessel potential space setting, which arises within the context of wave diffraction theory. The boundary under consideration consists of a strip, and certain reactance conditions are assumed on it. Operator theoretical methods are used to deal with the problem and, as a consequence, several convolution type operators are constructed and associated to the problem. At the end, the well-posedness of the problem is shown for a range of regularity orders of the Bessel potential spaces, and for a set of possible reactance numbers (dependent on the wave number).
Źródło:: Opuscula Mathematica; 2006, 26, 2; 289-303
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: The practical stability of the discrete, fractional order, state space model of the heat transfer process
Autorzy:: Oprzędkiewicz, K.
Gawin, E.
Powiązania:: https://bibliotekanauki.pl/articles/230065.pdf
Data publikacji:: 2018
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: discrete non-integer order system
heat transfer
diffusion equation
Grünvald-Letnikov operator
practical stability
Opis:: In the paper the practical stability problem for the discrete, non-integer order model of one dimmensional heat transfer process is discussed. The conditions associating the practical stability to sample time and maximal size of finite-dimensional approximation of heat transfer model are proposed. These conditions are formulated with the use of spectrum decoposition property and practical stability conditions for scalar, positive, fractional order systems. Results are illustrated by a numerical example.
Źródło:: Archives of Control Sciences; 2018, 28, 3; 463-482
1230-2384
Pojawia się w:: Archives of Control Sciences
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: The positivity of the fractional order model of a two-dimensional temperature field
Autorzy:: Oprzędkiewicz, Krzysztof
Powiązania:: https://bibliotekanauki.pl/articles/27311454.pdf
Data publikacji:: 2023
Wydawca:: Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:: heat transfer equation
fractional order state equation
Caputo operator
positivity
thermal camera
non-integer order systems
równanie wymiany ciepła
równanie stanu rzędu ułamkowego
operator Caputo
kamera termowizyjna
systemy niecałkowitego rzędu
dodatniość
Opis:: The paper presents analysis of the positivity for a two-dimensional temperature field. The process under consideration is described by the linear, infinite-dimensional, noninteger order state equation. It is derived from a two-dimensional parabolic equation with homogenous Neumann boundary conditions along all borders and homogenous initial condition. The form of control and observation operators is determined by the construction of a real system. The internal and external positivity of the model are associated to the localization of heater and measurement. It has been proven that the internal positivity of the considered system can be achieved by the proper selection of attachment of a heater and place of a measurement as well as the dimension of the finite-dimensional approximation of the considered model. Conditions of the internal positivity associated with construction of real experimental system are proposed. The postivity is analysed separately for control and output of the system. This allows one to analyse the positivity of thermal systems without explicit control. Theoretical considerations are numerically verified with the use of experimental data. The proposed results can be applied i.e. to point suitable places for measuring of a temperature using a thermal imaging camera.
Źródło:: Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 4; art. no. e145675
0239-7528
Pojawia się w:: Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: The Generalized Saddle-Node Bifurcation of Degenerate Solution
Autorzy:: Liu, Ping
Wang, Yu-Wen
Powiązania:: https://bibliotekanauki.pl/articles/746396.pdf
Data publikacji:: 2005
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: Operator equation
bifurcation
generalized inverse of operator
Opis:: In this paper we discuss the bifurcation problem for the abstract operator equation of the form $F (u, \lambda) = \theta$ with a parameter $\lambda$, where $F\colon X \times R \to Y$ is a $C^1$ mapping, $X, Y$ are Banach spaces. By the bounded linear generalized inverse $A^+$ of $A = F_u (u_0 , \lambda_0 )$, an abstract bifurcation theorem for the case $\operatorname{dim}N (F_u (u_0 , \lambda_0 )) \geq \operatorname{codim} R(F_u (u_0 , \lambda_0 )) = 1$ has been obtained.
Źródło:: Commentationes Mathematicae; 2005, 45, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 11.

Tytuł:: Sur la méthode de l’intégrale particulière et sur ses conséquences pour l’équation de Riccati et pour les équations différentielles linéaires et homogènes d’ordre supérieur
Autorzy:: Kapcia, Andrzej
Powiązania:: https://bibliotekanauki.pl/articles/744820.pdf
Data publikacji:: 2007
Wydawca:: Polskie Towarzystwo Matematyczne
Tematy:: differential equation
linear
homogenous
order
particular solution
superclass
subclass
inverse operator
linearly independent
effective integrability
general solution
Opis:: This paper presents the method of particular solution for solving the Riccati equation and linear homogenous equations of second and third order, as well as its certain application to linear homogenous equations of n-th order. The conditions of effective integrability for equations (0.1) and (0.2) are expressed in symbolic (operator) form and also for equation (0.3) in fully expanded form. There have been proved three theorems which state the following: for any subclass of differential equations of the form (0.1), (0.2), (0.3), if there are known, respectively: a particular solution $y_0$, a particular solution u 0 , two linearly independent particular solutions $u_1 , u_2$, then it is possible to construct superclasses of differential equations of the given class, using classes cited in [6, 7, 8, 9]. Moreover, one may obtain their effectively integrable generalizations. Numerous examples provided illustrate the above results. The article presents also a practical way of applying the method of particular solution to linear equations of n-th order. This method enables us to integrate more general equations than those described in [4, 5, 14] of the form (0.1), (0.2), (0.3), (0.4) for which the particular solutions are cited therein.
Źródło:: Commentationes Mathematicae; 2007, 47, 2
0373-8299
Pojawia się w:: Commentationes Mathematicae
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 12.

Tytuł:: Regularity of the multidimensional scaling functions: estimation of the $L^{p}$-Sobolev exponent
Autorzy:: Kotowicz, Jarosław
Powiązania:: https://bibliotekanauki.pl/articles/1338933.pdf
Data publikacji:: 1999
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: $L^p$-Sobolev exponent
transfer operator
refinement equation
scaling functions
spectral radius
Opis:: The relationship between the spectral properties of the transfer operator corresponding to a wavelet refinement equation and the $L^p$-Sobolev regularity of solution for the equation is established.
Źródło:: Applicationes Mathematicae; 1998-1999, 25, 4; 431-447
1233-7234
Pojawia się w:: Applicationes Mathematicae
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 13.

Tytuł:: Perturbation theory, M-essential Spectra of 2 x 2 operator matrices and application to transport operators
Autorzy:: Jeribi, Aref
Moalla, Nedra
Yengui, Sonia
Powiązania:: https://bibliotekanauki.pl/articles/2052375.pdf
Data publikacji:: 2021
Wydawca:: Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:: operator matrices
essential spectrum
Fredholm perturbation
transport equation
macierz operatora
widma
perturbacja Fredholma
równanie transportu
Opis:: In this article we give some results on perturbation theory of 2 x 2 block operator matrices on the product of Banach spaces. Furthermore, we investigate their M-essential spectra. Finally, we apply the obtained results to determine the M-essential spectra of two group transport operators with general boundary conditions in the Banach space $L_{p}([-a, a] \times [-1, 1]) \times L_{p}([-a, a] x [-1, 1]), p \geq 1 and a > 0$.
Źródło:: Journal of Mathematics and Applications; 2021, 44; 35-55
1733-6775
2300-9926
Pojawia się w:: Journal of Mathematics and Applications
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 14.

Tytuł:: Optimal control of nonlinear evolution equations
Autorzy:: Papageorgiou, Nikolaos
Yannakakis, Nikolaos
Powiązania:: https://bibliotekanauki.pl/articles/729352.pdf
Data publikacji:: 2001
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: evolution triple
compact embedding
monotone operator
pseudomonotone operator
L-generalized pseudomonotonicity
integration by parts
evolution inclusion
saddle point
necessary conditions
adjoint equation
distributed parameter systems
Opis:: In this paper, first we consider parametric control systems driven by nonlinear evolution equations defined on an evolution triple of spaces. The parametres are time-varying probability measures (Young measures) defined on a compact metric space. The appropriate optimization problem is a minimax control problem, in which the system analyst minimizes the maximum cost (risk). Under general hypotheses on the data we establish the existence of optimal controls.
Then we pass to nonparametric systems, which are governed by nonlinear evolution equations with nonmonotone operators. We prove two existence results for such evolution inclusions, which are of independent interest and extend significantly the results existing in the literature. Then we solve time-optimal and Meyer-type optimization problems. In Section 5, we derive necessary conditions for saddle point optimality in the minimax control problem. We conclude the paper with three examples of distributed parameter control systems.
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 1; 5-50
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 15.

Tytuł:: On the strong convergence to equilibrium of the Foiaş solutions of the transport equation
Autorzy:: Malczak, Jan
Powiązania:: https://bibliotekanauki.pl/articles/1312034.pdf
Data publikacji:: 1992
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: transport equation
Foiaş solution
Markov operator
asymptotic stability
Opis:: We define the Foiaş solutions of the transport equation and we prove that the strong asymptotic stability of the Foiaş solutions is equivalent to the asymptotic stability of the solutions of the transport equation in L¹.
Źródło:: Annales Polonici Mathematici; 1992, 57, 2; 193-203
0066-2216
Pojawia się w:: Annales Polonici Mathematici
Dostawca treści:: Biblioteka Nauki

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