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    Wyświetlanie 1-46 z 46
    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
    Artykuł
    Tytuł:
    On the construction of two-sided approximations to positive solutions of some elliptic problem
    Autorzy:
    Kolosova, S.
    Lukhanin, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/411231.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Oddział w Lublinie PAN
    Tematy:
    two-sided approximations
    operator equation
    positive solution
    concave operator
    conical interval
    Green's functions
    Green's quasifunction
    Opis:
    In this paper we have investigated the existence, uniqueness and possibility of constructing of two-sided approximations to the positive solution of a heat conduction problem with two sources. The investigation is based on methods in operator equations theory in half-ordered spaces. In this case we have considered a nonlinear operator equation that corresponds to the initial boundary value problem in a cone of non-negative continous functions. The properties of the corresponding operator define conditions which provide the existence and uniqueness of the solution. The conditions link the parameters of the problem implicitly meaning that they don’t provide the range of allowed values but need to be verified for each specific parameters value set separately. During the investigation we have provided the scheme of a two-sided iteration process which must satisfy the conditions in order to converge to the positive solution from both sides. The computational experiment have been conducted in two domains – unit disk and unit half disk. We have applied both two-sided approximations method and Green’s quasifunction method for the problem solving. The obtained results are presented as a surface and level lines plots and also as a table. The results in corresponding domains obtained by different methods have been compared with each other.
    Źródło:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes; 2016, 5, 4; 11-19
    2084-5715
    Pojawia się w:
    ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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:
    Inexact Newton’s method for generalized operator equations in Banach spaces
    Autorzy:
    Singh, V. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/122957.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    nonlinear operator equation
    Fréchet derivative
    Newton’s method
    inexact
    Newton method
    pochodna Frécheta
    metoda Newtona
    niedokładna metoda Newtona
    Opis:
    In the present paper, we introduce a new inexact Newton-like algorithm for solving the generalized operator equations containing non differentiable operators in Banach space setting and discuss its semilocal convergence analysis under the weak Lipschitz condition with larger convergence domain and tighter error bounds. The main result of this paper is the significant improvement over the Newton’s method as well as the inexact Newton method.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 4; 85-97
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hammerstein equations with an integral over a noncompact domain
    Autorzy:
    Stańczy, Robert
    Powiązania:
    https://bibliotekanauki.pl/articles/1294375.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Hammerstein operator
    Wiener-Hopf equation
    Opis:
    The existence of solutions of Hammerstein equations in the space of bounded and continuous functions is proved. It is obtained by the Schauder fixed point theorem using a compactness theorem. The result is applied to Wiener-Hopf equations and to ODE's.
    Źródło:
    Annales Polonici Mathematici; 1998, 69, 1; 49-60
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Non integer order, state space model of heat transfer process using Atangana-Baleanu operator
    Autorzy:
    Oprzędkiewicz, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/202078.pdf
    Data publikacji:
    2020
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    non integer order systems
    heat transfer equation
    infinite dimensional systems
    fractional order state equation
    Riesz operator
    Caputo operator
    Atangana-Baleanu operator
    Opis:
    In the paper a new, state space, non integer order model of an one-dimensional heat transfer process is proposed. The model uses a new operator with Mittag-Leffler kernel, proposed by Atangana and Beleanu. The non integer order spatial derivative is expressed by Riesz operator. Analytical formula of the step response is given, the convergence of the model is discussed too. Theoretical results are verified by experiments.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 1; 43-50
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Cone solutions of multi-order fractional difference systems
    Autorzy:
    Girejko, E.
    Mozyrska, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/206510.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    fractional difference operator
    fractional difference equation
    cone solutions
    Opis:
    The fractional difference system of equations with different fractional orders is considered. We obtain the existence and uniqueness results for the initial value problem. Cone solutions are presented. An example is given to illustrate the results.
    Źródło:
    Control and Cybernetics; 2013, 42, 2; 419-429
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    Tytuł:
    Markov operators: applications to diffusion processes and population dynamics
    Autorzy:
    Rudnicki, Ryszard
    Powiązania:
    https://bibliotekanauki.pl/articles/1208219.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Markov operator
    asymptotic stability
    diffusion process
    partial differential equation
    Opis:
    This note contains a survey of recent results concerning asymptotic properties of Markov operators and semigroups. Some biological and physical applications are given.
    Źródło:
    Applicationes Mathematicae; 2000, 27, 1; 67-79
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On Lipschitzian operators of substitution generated by set-valued functions
    Autorzy:
    Ludew, J. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/255565.pdf
    Data publikacji:
    2007
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Nemytskii operator
    Holder functions
    set-valued functions
    Jensen equation
    Opis:
    We consider the Nemytskii operator, i.e., the operator of substitution, defined by (Nφ)(x) := G(x,φ(x)), where G is a given multifunction. It is shown that if N maps a Hölder space Hα into Hβ and N fulfils the Lipschitz condition then G(x,y) = A(x,y) + B(x), where A(x,·) is linear and A(·,y), B ∈ Hβ. Moreover, some conditions are given under which the Nemytskii operator generated by (1) maps Hα into Hβ and is Lipschitzian.
    Źródło:
    Opuscula Mathematica; 2007, 27, 1; 13-24
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and uniqueness theorem for a hammerstein nonlinear integral equation
    Autorzy:
    Khachatryan, A. Kh.
    Khachatryan, Kh. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/255762.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    iteration
    Wiener-Hopf operator
    pointwise convergence
    Hammerstein type
    equation
    Opis:
    The existence of a solution, as well as some properties of the obtained solution for a Hammerstein type nonlinear integral equation have been investigated. For a certain class of functions the uniqueness theorem has also been proved.
    Źródło:
    Opuscula Mathematica; 2011, 31, 3; 393-398
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On some properties of the superposition operator on topological manifolds
    Autorzy:
    Dronka, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/255905.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    superposition operator
    continuous function
    topological manifold
    Hammerstein integral equation
    Opis:
    In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation is obtained.
    Źródło:
    Opuscula Mathematica; 2010, 30, 1; 69-77
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    Tytuł:
    On some application of biorthogonal spline systems to integral equations
    Autorzy:
    Wronicz, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/255125.pdf
    Data publikacji:
    2005
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    operator associated with step functions
    B-splines
    integral equation
    approximation
    Opis:
    We consider an operator PN : LP(I) -> Sn(deltaN), such that PN f = f for f mem Sn(deltaN), where Sn(deltaN) is the space of splines of degree n with repect to a given partition deltaN of the interval I. This operator is defined by means of a system of step functions biorthogonal to B-splines. Then we use this operator to approximation to the solution of the Fredholm integral equation of the second kind. Convergence rates for the aproximation of the solution of this equation are given.
    Źródło:
    Opuscula Mathematica; 2005, 25, 1; 149-160
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the nonoscillatory behavior of solutions of three classes of fractional difference equations
    Autorzy:
    Grace, Said Rezk
    Alzabut, Jehad
    Punitha, Sakthivel
    Muthulakshmi, Velu
    Adiguzel, Hakan
    Powiązania:
    https://bibliotekanauki.pl/articles/255333.pdf
    Data publikacji:
    2020
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Caputo difference operator
    nonoscillation criteria
    fractional difference equation mathematical inequalities
    Opis:
    In this paper, we study the nonoscillatory behavior of three classes of fractional difference equations. The investigations are presented in three different folds. Unlike most existing nonoscillation results which have been established by employing Riccati transfor mation technique, we employ herein an easily verifiable approach based on the fractional Taylor’s difference formula, some features of discrete fractional calculus and mathematical inequalities. The theoretical findings are demonstrated by examples. We end the paper by a concluding remark.
    Źródło:
    Opuscula Mathematica; 2020, 40, 5; 549-568
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    Tytuł:
    Non integer order, state space model of heat transfer process using Caputo-Fabrizio operator
    Autorzy:
    Oprzędkiewicz, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/201464.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    non-integer order systems
    heat transfer equation
    infinite dimensional systems
    fractional order state equation
    Riesz operator
    Caputo operator
    Caputo-Fabrizio operator
    systemy niecałkowitego rzędu
    układ niecałkowitego rzędu
    twierdzenie Riesza
    pochodna Caputo
    Opis:
    The paper is intended to show a new state space, non integer order model of an one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space semigroup model. The fractional order derivative with respect to time is by a new operator proposed by Caputo and Fabrizio, the non integer order spatial derivative is expressed by Riesz operator. The Caputo-Fabrizio operator can be directly implementated using MATLAB, because it does not require us to apply any approximation. Analytical formulae of step response are given, the system decomposition was discussed also. Main results from the paper show that the use of Caputo Fabrizio operator allows us to obtain the simple in implementation and analysis model of the considered heat transfer process. The accuracy of the proposed model in the sense of a MSE cost function is satisfying.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 3; 249-255
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Hermite-type adaptive semi-Lagrangian scheme
    Autorzy:
    Mehrenberger, M.
    Violard, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/929682.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    metoda adaptacyjna
    równanie Vlasova
    symulacja numeryczna
    operator hermitowski
    adaptive method
    Vlasov equation
    numerical simulation
    Hermite operator
    Opis:
    We study a new Hermite-type interpolating operator arising in a semi-Lagrangian scheme for solving the Vlasov equation in the 2D phase space. Numerical results on uniform and adaptive grids are shown and compared with the biquadratic Lagrange interpolation introduced in (Campos Pinto and Mehrenberger, 2004) in the case of a rotating Gaussian.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 329-334
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    Tytuł:
    On a mixed-type integral equation and fractional-order functional differential equations
    Autorzy:
    El-Sayed, A. M. A.
    Sherif, Nagwa
    Ibrahim, I. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/745693.pdf
    Data publikacji:
    2005
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Nonlinear functional integral equation
    fractional calculus
    Volterra operator
    mixed type integral equation
    Schauder fixed point theorem
    Opis:
    In this paper we study the existence of solution of a nonlinear integral equation of (mixed type) Volterra-Fredholm type. As an application we prove the existence of solution of an initial value problem of fractional order in the space of Lebesgue integrable functions on the interval \([0, 1]\).
    Źródło:
    Commentationes Mathematicae; 2005, 45, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New aspects on the fractional Euler-Lagrange equation with non-singular kernels
    Autorzy:
    Rangaig, Norodin A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1839747.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional derivative operator
    non-singular kernel operator
    fractional action-like integral
    fractional Euler-Lagrange equation
    operator pochodnej ułamkowej
    równanie Eulera-Lagrange'a
    Opis:
    In this paper, we presented some notes in utilizing the fractional integral counterparts of the fractional derivatives with non-singular kernels on the action-like integral in Lagrangian mechanics. Considering a fractional integral, it may suggest that a dissipative term on the resulting fractional Euler-Lagrange equation can be obtained due to the imposed kernel. However, in the case of nonsingular kernel operators, different aspects of the fractional action-like integral were observed, and corresponding (fractionally-modified) Euler-Lagrange were derived, which imposes new insights on the dynamical system under the fractional regime.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 89-100
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    Tytuł:
    New aspects on the fractional Euler-Lagrange equation with non-singular kernels
    Autorzy:
    Rangaig, Norodin A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1839731.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional derivative operator
    non-singular kernel operator
    fractional action-like integral
    fractional Euler-Lagrange equation
    operator pochodnej ułamkowej
    równanie Eulera-Lagrange'a
    Opis:
    In this paper, we presented some notes in utilizing the fractional integral counterparts of the fractional derivatives with non-singular kernels on the action-like integral in Lagrangian mechanics. Considering a fractional integral, it may suggest that a dissipative term on the resulting fractional Euler-Lagrange equation can be obtained due to the imposed kernel. However, in the case of nonsingular kernel operators, different aspects of the fractional action-like integral were observed, and corresponding (fractionally-modified) Euler-Lagrange were derived, which imposes new insights on the dynamical system under the fractional regime.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 89-100
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    Tytuł:
    Application of Darboux transformation to multidimensinal inhomogeneous problems
    Autorzy:
    Kwiatkowski, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/1938593.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Gdańska
    Tematy:
    Darboux transform
    Green function
    interwine relation
    ladder operator
    inhomogeneous partial differential equation
    Opis:
    General properties of ladder operators applied to inhomogeneous problems are studied in the context of their usefulness for solving practical problems with stress put on the possibility of embedding the interwine relation onto a wider class of operators. From those general remarks an algorithm using the Darboux transform for construction of the Green function for linear partial differential equations is formed and a sample implementation thereof is shown along with some examples of solutions.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2016, 20, 2; 187-195
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Monotonic solutions for quadratic integral equations
    Autorzy:
    Cichoń, Mieczysław
    Metwali, Mohamed
    Powiązania:
    https://bibliotekanauki.pl/articles/729338.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    integral equation
    monotonic solution
    measure of noncompactness
    Darbo fixed point theorem
    superposition operator
    Opis:
    Using the Darbo fixed point theorem associated with the measure of noncompactness, we establish the existence of monotonic integrable solution on a half-line ℝ₊ for a nonlinear quadratic functional integral equation.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 2; 157-171
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    Tytuł:
    Backward stochastic variational inequalities driven by multidimensional fractional Brownian motion
    Autorzy:
    Borkowski, D.
    Jańczak-Borkowska, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/254731.pdf
    Data publikacji:
    2018
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    backward stochastic differential equation
    fractional Brownian motion
    backward stochastic variational inequalities
    subdifferential operator
    Opis:
    We study the existence and uniqueness of the backward stochastic variational inequalities driven by m-dimensional fractional Brownian motion with Hurst parameters Hk (k = 1,... m) greater than 1/2. The stochastic integral used throughout the paper is the divergence type integral.
    Źródło:
    Opuscula Mathematica; 2018, 38, 3; 307-326
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional discrete-continuous model of heat transfer process
    Autorzy:
    Oprzędkiewicz, Krzysztof
    Dziedzic, Klaudia
    Powiązania:
    https://bibliotekanauki.pl/articles/1409413.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    non integer order systems
    heat transfer equation
    finite difference
    Caputo operator
    positive systems
    Opis:
    The paper proposes a new, state space, finite dimensional, fractional order model of a heat transfer in one dimensional body. The time derivative is described by Caputo operator. The second order central difference describes the derivative along the length. The analytical formulae of the model responses are proved. The stability, convergence, and positivity of the model are also discussed. Theoretical results are verified by experiments.
    Źródło:
    Archives of Control Sciences; 2021, 31, 2; 287-306
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    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
    Artykuł
    Tytuł:
    Approximation of abstract linear integrodifferential equations
    Autorzy:
    Oka, Hirokazu
    Tanaka, Naoki
    Powiązania:
    https://bibliotekanauki.pl/articles/1206081.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    approximation of integrodifferential equation
    approximation of
    Banach space
    resolvent operator
    semigroup of class $(C_0)$
    Opis:
    This paper is devoted to the approximation of abstract linear integrodifferential equations by finite difference equations. The result obtained here is applied to the problem of convergence of the backward Euler type discrete scheme.
    Źródło:
    Studia Mathematica; 2000, 140, 1; 1-14
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    Tytuł:
    Impulsive functional-differential equations of first order
    Autorzy:
    Skóra, Lidia
    Powiązania:
    https://bibliotekanauki.pl/articles/744828.pdf
    Data publikacji:
    2007
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    impulsive functional-differential equation
    Volltera operator
    upper and lower solutions
    monotone iterative technique
    global solutions
    Opis:
    In this paper we present some existence results for impulsive functional-differential equations of first order.
    Źródło:
    Commentationes Mathematicae; 2007, 47, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Critical cases in neutral functional differential equations, arising from hydraulic engineering
    Autorzy:
    Răsvan, Vladimir
    Powiązania:
    https://bibliotekanauki.pl/articles/2216162.pdf
    Data publikacji:
    2022
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    1D hyperbolic partial differential equations
    neutral functional differential equation
    difference operator
    critical case
    differential equations
    Opis:
    This paper starts from several applications described by initial/boundary value problems for 1D (time and one space variable) hyperbolic partial differential equations whose basic properties and stability of equilibria are studied throughout the same properties for certain associated neutral functional differential equations. It is a common fact that asymptotic stability for neutral functional differential equations is normally obtained under the assumption of asymptotic stability of the difference operator associated to the aforementioned neutral functional differential equations. However the physically meaningful applications presented in the paper have the associated difference operator(s) in critical cases (their stability is, generally speaking, non-asymptotic). Consequently the stability of the considered application models is either non-asymptotic or fragile (in a sense introduced in the paper). The models represent an overview gathered from various fields, processed here in order to emphasize the associated neutral functional differential equations which, consequently, are a challenge to the usual approaches. In the concluding part there are suggested possible ways to overcome these difficulties.
    Źródło:
    Opuscula Mathematica; 2022, 42, 4; 605-633
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    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
    Artykuł
    Tytuł:
    On Nonlinear Fractional Neutral Differential Equation with the ψ-Caputo Fractional Derivative
    Autorzy:
    Nabil, Tamer
    Powiązania:
    https://bibliotekanauki.pl/articles/1818657.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    Krasnoselskii's fixed point theory
    ψ − Caputo operator
    neutral differential equation
    ulam stability
    existence of solution
    teoria punktu stałego Krasnoselskiego
    operator Caputa
    równanie różniczkowe
    stabilność Ulama
    Opis:
    In this article, the solvability of fractional neutral differential equation involving ψ−Caputo fractional operator is considered usinga Krasnoselskii’s fixed point approach. Also, we establish the uniquenessof the solution under certain conditions. Ulam stabilities for the proposedproblem are discussed. Finally, examples are displayed to aid the applicability of the theory results.
    Źródło:
    Journal of Mathematics and Applications; 2020, 43; 99--112
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator
    Autorzy:
    Oprzędkiewicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/2173561.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order systems
    heat transfer equation
    fractional order state equation
    fractional order backward difference
    Grünwald-Letnikov operator
    practical stability
    systemy ułamkowego rzędu
    równanie wymiany ciepła
    równanie stanu rzędu ułamkowego
    różnica wsteczna rzędu ułamkowego
    operator Grünwalda-Letnikowa
    stabilność praktyczna
    Opis:
    In the paper a new, state space, fully discrete, fractional model of a heat transfer process in one dimensional body is addressed. The proposed model derives directly from fractional heat transfer equation. It employes the discrete Grünwald-Letnikov operator to express the fractional order differences along both coordinates: time and space. The practical stability and numerical complexity of the model are analysed. Theoretical results are verified using experimental data.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 1; art. no. e135843
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator
    Autorzy:
    Oprzędkiewicz, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/2090693.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order systems
    heat transfer equation
    fractional order state equation
    fractional order backward difference
    Grünwald-Letnikov operator
    practical stability
    systemy ułamkowego rzędu
    równanie wymiany ciepła
    równanie stanu rzędu ułamkowego
    różnica wsteczna rzędu ułamkowego
    operator Grünwalda-Letnikowa
    stabilność praktyczna
    Opis:
    In the paper a new, state space, fully discrete, fractional model of a heat transfer process in one dimensional body is addressed. The proposed model derives directly from fractional heat transfer equation. It employes the discrete Grünwald-Letnikov operator to express the fractional order differences along both coordinates: time and space. The practical stability and numerical complexity of the model are analysed. Theoretical results are verified using experimental data.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 1; e135843, 1--10
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Non integer order, discrete, state space model of heat transfer process using Grünwald-Letnikov operator
    Autorzy:
    Oprzędkiewicz, K.
    Dziedzic, K.
    Więckowski, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/200257.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    non integer order systems
    heat transfer
    fractional order state equation
    fractional order backward difference
    Grünwald-Letnikov operator
    convergence
    Opis:
    The paper is intented to show a new, state space, discrete, non integer order model of a one-dimensional heat transfer process. The proposed model derives directly from time continuous, state space model and it uses the discrete Grünwald-Letnikov operator to express the fractional order difference with respect to time. Stability and spectrum decomposition for the proposed model are recalled, the accuracy and convergence are analyzed too. The convergence of the proposed model does not depend on parameters of heater and measuring sensors. The dimension of the model assuring stability and predefined rate of convergence and stability is estimated. Analytical results are confirmed by experiments.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 5; 905-914
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    General remarks on dynamic projection method
    Autorzy:
    Leble, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1938597.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Gdańska
    Tematy:
    partial differential equations
    dynamical system
    Cauchy problem
    diffusion equation
    projection operator
    idempotent operators
    eigen mode
    mode interaction
    boundary regime propagation
    Opis:
    A brief history and a mathematical description of the dynamic projection operators technique is presented. An example of the general Cauchy problem for evolution equations in 1+ 1 dimensions is studied in detail. A boundary regime propagation is formulated in terms of operators and illustrated by the simplest one-dimensional diffusion equation. The problem of temperature waves is discussed.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2016, 20, 2; 113-130
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
    Tytuł:
    A new algorithm for a CFE-approximated solution of a discrete-time noninteger-order state equation
    Autorzy:
    Oprzędkiewicz, K.
    Stanisławski, R.
    Gawin, E.
    Mitkowski, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/199796.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order calculus
    discrete-time noninteger-order state equation
    continuous fraction expansion
    Al-Alaoui operator
    równanie dyskretne
    aproksymacja Al-Alaoui
    CFE
    Opis:
    In the paper, a new method for solution of linear discrete-time fractional-order state equation is presented. The proposed method is simpler than other methods using directly discrete-time version of the Grünwald-Letnikov operator. The method is dedicated to use with any approximator to the operator expressed by a discrete transfer function, e.g. CFE-based Al-Alaoui approximation. A simulation example confirms the usefulness of the method.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 4; 429-437
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Group invariant solution of some time fractional evolution equations
    Autorzy:
    Mandal, H.
    Bira, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/122890.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional coupled Burger’s equation
    fractional DSSH equations
    Riemann Liouville’s fractional derivative
    Erdélyi-Kober operator
    symmetry analysis
    exact solution
    równania ewolucji
    ułamkowe równania różniczkowe
    ułamkowe równania DSSH
    pochodna ułamkowa Riemanna Liouville'a
    operator Erdélyi-Kober
    Opis:
    In this paper, we consider some classes of a system of nonlinear fractional differential equations (FDEs) arising in some important physical phenomena. Using symmetry group of transformations, the given systems of fractional partial differential equations (FPDEs) are reduced to systems of fractional ordinary differential equations (FODEs). Further, using the group invariant condition, we solve the reduced systems of FODEs and exact solutions of the given equations are constructed. Finally, the physical significance of the solutions are investigated graphically based on the exact solutions in order to highlight the importance of the study.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 4; 35-46
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    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
    Artykuł
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