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    Wyświetlanie 1-7 z 7
    Tytuł:
    On operators of transition in Krein spaces
    Autorzy:
    Grod, A.
    Kuzhel, S.
    Sudilovskaya, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/255652.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Krein spaces
    indefinite metrics
    operator of transition
    operator Riccati equation
    Opis:
    The paper is devoted to investigation of operators of transition and the corresponding decompositions of Krein spaces. The obtained results are applied to the study of relationship between solutions of operator Riccati equations and properties of the associated operator matrix L. In this way, we complete the known result (see Theorem 5.2 in the paper of S. Albeverio, A. Motovilov, A. Skhalikov, Integral Equ. Oper. Theory 64 (2004), 455-486) and show the equivalence between the existence of a strong solution K (//K// < 1) of the Riccati equation and similarity of the J-self-adjoint operator L to a self-adjoint one.
    Źródło:
    Opuscula Mathematica; 2011, 31, 1; 49-59
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A direct approach to linear-quadratic stochastic control
    Autorzy:
    Duncan, T. E.
    Pasik-Duncan, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/255863.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    linear-quadratic Gaussian control
    Riccati equation for optimization
    stochastic control
    Opis:
    A direct approach is used to solve some linear-quadratic stochastic control problems for Brownian motion and other noise processes. This direct method does not require solving Hamilton-Jacobi-Bellman partial differential equations or backward stochastic differential equations with a stochastic maximum principle or the use of a dynamic programming principle. The appropriate Riccati equation is obtained as part of the optimization problem. The noise processes can be fairly general including the family of fractional Brownian motions.
    Źródło:
    Opuscula Mathematica; 2017, 37, 6; 821-827
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonoscillation of damped linear differential equations with a proportional derivative controller and its application to Whittaker-Hill-type and Mathieu-type equations
    Autorzy:
    Ishibashi, Kazuki
    Powiązania:
    https://bibliotekanauki.pl/articles/29519191.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nonoscillation
    proportional derivative controller
    Riccati technique
    Mathieu equation
    Whittaker-Hill equation
    Opis:
    The proportional derivative (PD) controller of a differential operator is commonly referred to as the conformable derivative. In this paper, we derive a nonoscillation theorem for damped linear differential equations with a differential operator using the conformable derivative of control theory. The proof of the nonoscillation theorem utilizes the Riccati inequality corresponding to the equation considered. The provided nonoscillation theorem gives the nonoscillatory condition for a damped Euler-type differential equation with a PD controller. Moreover, the nonoscillation of the equation with a PD controller that can generalize Whittaker-Hill-type equations is also considered in this paper. The Whittaker-Hill-type equation considered in this study also includes the Mathieu-type equation. As a subtopic of this work, we consider the nonoscillation of Mathieu-type equations with a PD controller while making full use of numerical simulations.
    Źródło:
    Opuscula Mathematica; 2023, 43, 1; 67-79
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences
    Autorzy:
    Schmeidel, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/255806.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    linear
    nonlinear
    difference equations
    third order
    oscillatory solution
    quasidifferences
    Riccati technique
    Opis:
    In this paper, third order difference equations are considered. We study the nonlinear third order difference equation with quasidifferences. Using Riccati transformation techniques, we establish some sufficient conditions for each solution of this equation to be either oscillatory or converging to zero. The result is illustrated with examples.
    Źródło:
    Opuscula Mathematica; 2006, 26, 2; 361-369
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A remark on the linearization technique in half-linear oscillation theory
    Autorzy:
    Dosly, O.
    Powiązania:
    https://bibliotekanauki.pl/articles/255798.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    half-linear oscillation theory
    oscillation and nonoscillation criteria
    Riccati technique
    perturbation principle
    Opis:
    We show that oscillatory properties of the half-linear second order differential equation (r(t)Φ(x'))' + c(t)Φ(x) = 0, Φ(x) = |x|p-2x, p > 1, can be investigated via oscillatory properties of a certain associated second order linear differential equation. In contrast to paper [6], we do not need to distinguish between the cases p ≥ 2 and p ∈ (1, 2]. Our results also improve the oscillation and nonoscillation criteria given in [4].
    Źródło:
    Opuscula Mathematica; 2006, 26, 2; 305-315
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On one oscillatory criterion for the second order linear ordinary differential equations
    Autorzy:
    Grigorian, G. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/255069.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Riccati equation
    normal and extremal solutions
    integral and interval oscillatory criteria
    generalized Hill's equation
    Opis:
    The Riccati equation method is used to establish an oscillatory criterion for second order linear ordinary differential equations. An oscillatory condition is obtained for the generalized Hill's equation. By means of examples the obtained result is compared with some known oscillatory criteria.
    Źródło:
    Opuscula Mathematica; 2016, 36, 5; 589-601
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On oscillatory behaviour of third-order half-linear dynamic equations on time scales
    Autorzy:
    Grace, Said R.
    Chhatria, Gokula Nanda
    Powiązania:
    https://bibliotekanauki.pl/articles/29519180.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    oscillation
    asymptotic behaviour
    dynamic equation
    time scales
    dynamic equations on time scales
    comparison method
    Riccati technique
    Opis:
    In this work, we study the oscillation and asymptotic behaviour of third-order nonlinear dynamic equations on time scales. The findings are obtained using an integral criterion as well as a comparison theorem with the oscillatory properties of a first-order dynamic equation. As a consequence, we give conditions which guarantee that all solutions to the aforementioned problem are only oscillatory, different from any other result in the literature. We propose novel oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are associated with a numerical example. We point out that the results are new even for the case $ \mathbb{T} = \mathbb{R} $ or $ \mathbb{T} = \mathbb{Z} $.
    Źródło:
    Opuscula Mathematica; 2022, 42, 6; 849-865
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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