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    Wyświetlanie 1-28 z 28
    Tytuł:
    Extensions of dissipative operators with closable imaginary part
    Autorzy:
    Fischbacher, Christoph
    Powiązania:
    https://bibliotekanauki.pl/articles/2051880.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    extension theory
    dissipative operators
    ordinary differential operators
    Opis:
    Given a dissipative operator A on a complex Hilbert space H such that the quadratic form $f \mapsto Im\langle f,Af\rangle$ is closable, we give a necessary and sufficient condition for an extension of A to still be dissipative. As applications, we describe all maximally accretive extensions of strictly positive symmetric operators and all maximally dissipative extensions of a highly singular first-order operator on the interval.
    Źródło:
    Opuscula Mathematica; 2021, 41, 3; 381-393
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Finegrained 3D differential operators hint at the inevitability of their dual reciprocal portrayals
    Autorzy:
    Czajko, Jakub
    Powiązania:
    https://bibliotekanauki.pl/articles/1065412.pdf
    Data publikacji:
    2019
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Finegrained differential operators
    paired dual reciprocal spaces
    Opis:
    Extending differential operators during transition from 3D operations to prospective 4D operations imply the need to expand their 4D range far beyond the usual set-theoretical universe from which subsets of the domain are composed. The prospective infrastructural expansion related to the attempted extending of operations virtually requires an extra dual reciprocal space and thus implies presence of a certain multispatial structure of both the mathematical- and the corresponding to it physical reality. At this point the implication is only operational for it is deduced from the attempted extension of operational domain/scope of geometric differential operator, which, in turn, demands an expansion of their range. The necessary presence of an extra space is not being postulated but emerges from comparative evaluations of differential operators. The operational necessity of presence of paired dual reciprocal spaces or quasispatial structures also generalizes contravariance for multispatiality.
    Źródło:
    World Scientific News; 2019, 132; 98-120
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The form of the n-th iteration of the operator q=fd/dx
    Autorzy:
    Szymkat, Maciej
    Powiązania:
    https://bibliotekanauki.pl/articles/747433.pdf
    Data publikacji:
    1983
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Combinatorial identities, bijective combinatorics
    Partitions
    Ordinary differential operators
    Opis:
    Artykuł nie zawiera streszczenia
    Motivated by applications in linear dynamical systems, the author studies q^n(f), where q is the operator f●(d/dx) and qn is its n-th iteration. q^n(f) is a polynomial F(f(0),f(1),...,f(n)) in the derivatives f(0)=f,...,f(n) of f with integer coefficients. Special attention is paid to determining the coefficients of F. The author presents algorithms for computing the coefficients and also shows that the sum of all coefficients of F equals n!. The paper ends with some remarks on the number of coefficients of F, which is related to the number-theoretic unrestricted partition function.
    Źródło:
    Mathematica Applicanda; 1983, 11, 22
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Generalized analytic functions of Bogdan Ziemian
    Autorzy:
    Łysik, Grzegorz
    Powiązania:
    https://bibliotekanauki.pl/articles/1207960.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Mellin transformation
    Laplace distributions
    special functions
    singular differential operators
    Opis:
    Definitions, properties, examples and applications of generalized analytic functions introduced by B. Ziemian are presented.
    Źródło:
    Annales Polonici Mathematici; 2000, 74, 1; 35-41
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Simple eigenvectors of unbounded operators of the type "normal plus compact"
    Autorzy:
    Gil, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255388.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Hilbert space
    linear operators
    eigenvectors
    approximation
    integro-differential operators
    Schatten-von Neumann operators
    Opis:
    The paper deals with operators of the form A = S + B, where B is a compact operator in a Hilbert space H and S is an unbounded normal one in H, having a compact resolvent. We consider approximations of the eigenvectors of A, corresponding to simple eigenvalues by the eigenvectors of the operators An = S + Bn (n = 1, 2,...), where Bn is an n-dimensional operator. In addition, we obtain the error estimate of the approximation.
    Źródło:
    Opuscula Mathematica; 2015, 35, 2; 161-169
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Degenerate evolution problems and Beta-type operators
    Autorzy:
    Attalienti, Antonio
    Campiti, Michele
    Powiązania:
    https://bibliotekanauki.pl/articles/1206074.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    approximation process
    $C_0$-semigroups of contractions
    Beta-type operators
    differential operators
    Opis:
    The present paper is concerned with the study of the differential operator Au(x):=α(x)u''(x)+β(x)u'(x) in the space C([0,1)] and of its adjoint Bv(x):=((αv)'(x)-β(x)v(x))' in the space $L^1(0,1)$, where α(x):=x(1-x)/2 (0≤x≤1). A careful analysis of their main properties is carried out in view of some generation results available in [6, 12, 20] and [25]. In addition, we introduce and study two different kinds of Beta-type operators as a generalization of similar operators defined in [18]. Among the corresponding approximation results, we show how they can be used in order to represent explicitly the solutions of the Cauchy problems associated with the operators A and Ã, where à is equal to B up to a suitable bounded additive perturbation.
    Źródło:
    Studia Mathematica; 2000, 140, 2; 117-139
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hyponormal differential operators with discrete spectrum
    Autorzy:
    Ismailov, Z. I.
    Unluyol, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/255909.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    hyponormal operators
    differential operators
    minimal and maximal operators
    extension of operators
    compact operators
    eigenvalues
    asymptotes of eigenvalues
    Opis:
    In this work, we first describe all the maximal hyponormal extensions of a minimal operator generated by a linear differential-operator expression of the first-order in the Hilbert space of vector-functions in a finite interval. Next, we investigate the discreteness of the spectrum and the asymptotical behavior of the modules of the eigenvalues for these maximal hyponormal extensions.
    Źródło:
    Opuscula Mathematica; 2010, 30, 1; 79-94
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Functorial Approach to the Behaviour of Multidimensional Control Systems
    Autorzy:
    Pommaret, J. F.
    Quadrat, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/908250.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    automatyka
    robotyka
    multidimensional systems
    weak primeness
    controllability
    algebraic analysis
    torsion and extension functors
    rings of differential operators
    Opis:
    We show how to use the extension and torsion functors in order to compute the torsion submodule of a differential module associated with a multidimensional control system. In particular, we show that the concept of the weak primeness of matrices corresponds to the torsion-freeness of a certain module.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2003, 13, 1; 7-13
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Towards a Non-conformable Fractional Calculus of n-Variables
    Autorzy:
    Martínez, Francisco
    Nápoles, Juan E. Valdés
    Powiązania:
    https://bibliotekanauki.pl/articles/1818655.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    function of several variables
    fractional partial differential operators
    funkcje wielu zmiennych
    operatory różniczkowe
    operatory cząsteczkowe
    operatory ułamkowe
    Opis:
    In this paper we present an extension of the non-conformable local fractional derivative, to the case of functions of severalvariables. Results analogous to those known from the classic multivariatecalculus are presented. To show the strength of this approach, we show anextension of the Second Lyapunov Method to the non-conformable localfractional case.
    Źródło:
    Journal of Mathematics and Applications; 2020, 43; 87--98
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximation by Durrmeyer-type operators
    Autorzy:
    Gupta, Vijay
    Srivastava, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/1311057.pdf
    Data publikacji:
    1996
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    modulus of smoothness
    global direct theorem
    differential and integral operators
    Opis:
    We define a new kind of Durrmeyer-type summation-integral operators and study a global direct theorem for these operators in terms of the Ditzian-Totik modulus of smoothness.
    Źródło:
    Annales Polonici Mathematici; 1996, 64, 2; 153-159
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On an approximation theorem of Wong-Zakai type for the Lasota operator
    Autorzy:
    Dawidowicz, Antoni L.
    Twardowska, Krystyna
    Powiązania:
    https://bibliotekanauki.pl/articles/748336.pdf
    Data publikacji:
    2007
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Stochastic integral equations, Stochastic ordinary differential equations, Random operators and equations
    Opis:
    W pracy pokazano, że stochastyczne równanie ewolucyjne z operatorem Lasoty jako infinitezymalnym generatorem silnie ciągłej półgrupy odwzorowań i z operatorem Hammersteina występującym przy zaburzeniu będącym procesem Wienera, spełnia twierdzenie aproksymacyjne typu Wonga–Zakai. Idea wprowadzenia operatora Lasoty związana jest z matematycznym modelem powstawania i różnicowania się komórek.
    The authors show that the stochastic evolution equation with Lasota infinitesimal generator satisfies the Wong-Zakai type approximation theorem.
    Źródło:
    Mathematica Applicanda; 2007, 35, 49/08
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the existence of viable solutions for a class of second order differential inclusions
    Autorzy:
    Cernea, Aurelian
    Powiązania:
    https://bibliotekanauki.pl/articles/729526.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    viable solutions
    ϕ-monotone operators
    differential inclusions
    Opis:
    We prove the existence of viable solutions to the Cauchy problem x'' ∈ F(x,x'), x(0) = x₀, x'(0) = y₀, where F is a set-valued map defined on a locally compact set $M ⊂ R^{2n}$, contained in the Fréchet subdifferential of a ϕ-convex function of order two.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 1; 67-78
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    SPDEs with pseudodifferential generators: the existence of a density
    Autorzy:
    Tindel, Samy
    Powiązania:
    https://bibliotekanauki.pl/articles/1208166.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    pseudodifferential operators
    stochastic partial differential equations
    Malliavin's calculus
    Opis:
    We consider the equation du(t,x)=Lu(t,x)+b(u(t,x))dtdx+σ(u(t,x))dW(t,x) where t belongs to a real interval [0,T], x belongs to an open (not necessarily bounded) domain $\mathcal O$, and L is a pseudodifferential operator. We show that under sufficient smoothness and nondegeneracy conditions on L, the law of the solution u(t,x) at a fixed point $(t,x)\in [0,T] \times \mathcal O$ is absolutely continuous with respect to the Lebesgue measure.
    Źródło:
    Applicationes Mathematicae; 2000, 27, 3; 287-308
    1233-7234
    Pojawia się w:
    Applicationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The interaction of linear boundary value and nonlinear functional conditions
    Autorzy:
    Fečkan, Michal
    Powiązania:
    https://bibliotekanauki.pl/articles/1311814.pdf
    Data publikacji:
    1993
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    differential equations
    linear and nonlinear conditions
    Fredholm operators
    Opis:
    The existence of solutions is studied for certain nonlinear differential equations with both linear and nonlinear conditions
    Źródło:
    Annales Polonici Mathematici; 1993, 58, 3; 299-310
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Integral and fractional equations, positive solutions, and Schaefer’s fixed point theorem
    Autorzy:
    Becker, L. C.
    Burton, T. A.
    Purnaras, I. K.
    Powiązania:
    https://bibliotekanauki.pl/articles/255409.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fixed points
    fractional differential equations
    integral equations
    Riemann-Liouville operators
    Opis:
    This is the continuation of four earlier studies of a scalar fractional differential equation of Riemann-Liouville type [formula] in which we first invert it as a Volterra integral equation [formula] and then transform it into [formula] where R is completely monotone with [formula] and J is an arbitrary positive constant. Notice that when x is restricted to a bounded set, then by choosing J large enough, we can frequently change the sign of the integrand in going from (b) to (c). Moreover, the same kind of transformation will produce a similar effect in a wide variety of integral equations from applied mathematics. Because of that change in sign, we can obtain an a priori upper bound on solutions of (b) with a parameter λ ∈ (0, 1] and then obtain an a priori lower bound on solutions of (c). Using this property and Schaefer’s fixed point theorem, we obtain positive solutions of an array of fractional differential equations of both Caputo and Riemann-Liouville type as well as problems from turbulence, heat transfer, and equations of logistic growth. Very simple results establishing global existence and uniqueness of solutions are also obtained in the same way.
    Źródło:
    Opuscula Mathematica; 2016, 36, 4; 431-458
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces
    Autorzy:
    Gudovich, Anastasie
    Kamenski, Mikhail
    Nistri, Paolo
    Powiązania:
    https://bibliotekanauki.pl/articles/729318.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    singular perturbations
    differential inclusions
    analytic semigroups
    multivalued compact operators
    Lipschitz selections
    Opis:
    We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset $Z_L(ε)$ of the solution set of the singularly perturbed system. This subset is the set of the Hölder continuous solutions defined in [0,d], d > 0 with prescribed exponent and constant L. We show that $Z_L(ε)$ is uppersemicontinuous at ε = 0 in the C[0,d]×C[δ,d] topology for any δ ∈ (0,d].
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 2; 207-234
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    New perspectives of analog and digital simulations of fractional order systems
    Autorzy:
    Charef, A.
    Charef, M.
    Djouambi, A.
    Voda, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/229183.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    adjustable fractional operators
    Charef approximation
    fractional differential equation
    ractional integrator
    fractional systems
    Opis:
    In the recent decades, fractional order systems have been found to be useful in many areas of physics and engineering. Hence, their efficient and accurate analog and digital simulations and numerical calculations have become very important especially in the fields of fractional control, fractional signal processing and fractional system identification. In this article, new analog and digital simulations and numerical calculations perspectives of fractional systems are considered. The main feature of this work is the introduction of an adjustable fractional order structure of the fractional integrator to facilitate and improve the simulations of the fractional order systems as well as the numerical resolution of the linear fractional order differential equations. First, the basic ideas of the proposed adjustable fractional order structure of the fractional integrator are presented. Then, the analog and digital simulations techniques of the fractional order systems and the numerical resolution of the linear fractional order differential equation are exposed. Illustrative examples of each step of this work are presented to show the effectiveness and the efficiency of the proposed fractional order systems analog and digital simulations and implementations techniques
    Źródło:
    Archives of Control Sciences; 2017, 27, 1; 91-118
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence and controllability of fractional-order impulsive stochastic system with infinite delay
    Autorzy:
    Guendouzi, Toufik
    Powiązania:
    https://bibliotekanauki.pl/articles/729324.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    existence result
    approximate controllability
    fractional stochastic differential equations
    resolvent operators
    infinite delay
    Opis:
    This paper is concerned with the existence and approximate controllability for impulsive fractional-order stochastic infinite delay integro-differential equations in Hilbert space. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of impulsive fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the obtained theory.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 1; 65-87
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Une fonction β-lipschitzienne qui n'est pas une perturbation compacted'une fonction dissipative
    Autorzy:
    Uhl, Roland
    Powiązania:
    https://bibliotekanauki.pl/articles/1311540.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    ordinary differential equations in Banach spaces
    existence
    measures of noncompactness
    dissipative operators
    Opis:
    Résumé. On présente une fonction continue f: c₀ → c₀ qui satisfait à une condition lipschitzienne par rapport à la mesure de non-compacité de Hausdorff (ou Kuratowski), mais telle que f n'est pas la somme d'une fonction dissipative et d'une fonction compacte. Cet exemple attache de l'importance au théorème d'existence de Sabina Schmidt (1989) pour des équations différentielles dans les espaces de Banach.
    Źródło:
    Annales Polonici Mathematici; 1995, 61, 2; 189-193
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical approximations of difference functional equations and applications
    Autorzy:
    Kamont, Z.
    Powiązania:
    https://bibliotekanauki.pl/articles/255105.pdf
    Data publikacji:
    2005
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    functional differential equations
    stability and convergence
    interpolating operators
    nonlinear estimates of Perron type
    Opis:
    We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.
    Źródło:
    Opuscula Mathematica; 2005, 25, 1; 109-130
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonlocal impulsive problems for fractional differential equations with time-varying generating operators in Banach spaces
    Autorzy:
    Wang, J.
    Yang, Y.
    Wei, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/255546.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nonlocal conditions
    impulsive equations
    fractional differential equations
    time-varying generating operators
    PC-mild solution
    Opis:
    In this paper, we study the existence and uniqueness of the PC-mild solution for a class of impulsive fractional differential equations with time-varying generating operators and nonlocal conditions. By means of the generalized Ascoli-Arzela Theorem given by us and the fixed point theorem, some existence and uniqueness results are obtained. Finally, an example is given to illustrate the theory.
    Źródło:
    Opuscula Mathematica; 2010, 30, 3; 361-381
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multipoint normal differential operators of first order
    Autorzy:
    Ismailov, Z. I.
    Powiązania:
    https://bibliotekanauki.pl/articles/952785.pdf
    Data publikacji:
    2009
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    differential operator
    formally normal and normal operator
    multipoint minimal and maximal operators
    extension
    selfadjoint
    accretive and unitary operators
    class of compact operators
    spectrum of operators and its discreteness
    asymptotics of eigenvalues
    direct sum of spaces and operators
    Opis:
    In this paper we discuss all normal extensions of a minimal operator generated by a linear multipoint differential-operator expression of first order in the Hilbert space of vector-functions on the finite interval in terms of boundary and interior point values. Later on, we investigate the structure of the spectrum, its discreteness and the asymptotic behavior of the eigenvalues at infinity for these extensions.
    Źródło:
    Opuscula Mathematica; 2009, 29, 4; 399-414
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The study of Delsarte-Lions type binary transformations, their differential-geometric and operator structure with applications. Pt. 2
    Autorzy:
    Prykarpatsky, Y. A.
    Samoilenko, A. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255528.pdf
    Data publikacji:
    2007
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Delsarte transmutation operators
    generalized de Rham-Hodge differential complex
    Delsarte-Lions type transformations
    Gelfand-Levitan-Marchenko type integral equations
    multidimensional differential operator pencils
    Opis:
    The Gelfand-Levitan integral equations for Delsarte-Lions type transformations in multidimension are studied. The corresponding spectral and analytical properties of Delsarte-Lions transformed operators are analyzed by means of the differential-geometric and topological tools. An approach for constructing Delsarte-Lions type transmutation operators for multidimensional differential expressions is devised.
    Źródło:
    Opuscula Mathematica; 2007, 27, 1; 113-130
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Difference problems generated by infinite systems of nonlinear parabolic functional differential equations with the Robin conditions
    Autorzy:
    Czernous, W.
    Jaruszewska-Walczak, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/255694.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    nonlinear parabolic equations
    functional differential equations
    infinite systems
    Volterra type operators
    nonlinear estimates of Perron type
    truncation methods
    Opis:
    We consider the classical solutions of mixed problems for infinite, countable systems of parabolic functional differential equations. Difference methods of two types are constructed and convergence theorems are proved. In the first type, we approximate the exact solutions by solutions of infinite difference systems. Methods of second type are truncation of the infinite difference system, so that the resulting difference problem is finite and practically solvable. The proof of stability is based on a comparison technique with nonlinear estimates of the Perron type for the given functions. The comparison system is infinite. Parabolic problems with deviated variables and integro-differential problems can be obtained from the general model by specifying the given operators.
    Źródło:
    Opuscula Mathematica; 2014, 34, 2; 311-326
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    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:
    Wellposedness of optimal control problems for systems with unbounded controls and partially analytic generators
    Autorzy:
    Lasiecka, I.
    Powiązania:
    https://bibliotekanauki.pl/articles/206185.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równanie różniczkowe i algebraiczne Riccatiego
    differential and algebraic Riccati equations
    singular estimate
    structural acoustic interactions
    thermoelastic plates
    unbounded control operators
    Opis:
    Wellposedness of differential and algebraic Riccati equations for control systems with unbounded control operators is considered. It is shown that the full-classical Riccati theory is recovered for a class of dynamics, whose generators are partially analytic. Partial analyticity is quantitatively expressed by the validity of the so-called "singular estimates", which is imposed on the composition operator E[sup At]B (A is the generator, B is unbounded control operator. This class comprises the PDE coupled systems with hyperbolic and parabolic components. Two illustrative examples are given in the paper: boumdary/point control of thermal plates with hyperbolic character and point control of structural acoustic interactions. The latter are described by wave equation coupled at an interface to a plate equation.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 751-777
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On weak solutions of functional-differential abstract nonlocal Cauchy problems
    Autorzy:
    Byszewski, Ludwik
    Powiązania:
    https://bibliotekanauki.pl/articles/1310788.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    abstract Cauchy problems
    functional-differential equation
    nonlocal conditions
    weak solutions
    existence
    uniqueness
    asympto tic stability
    m-accretive operators
    Banach contraction theorem
    Opis:
    The existence, uniqueness and asymptotic stability of weak solutions of functional-differential abstract nonlocal Cauchy problems in a Banach space are studied. Methods of m-accretive operators and the Banach contraction theorem are applied.
    Źródło:
    Annales Polonici Mathematici; 1996-1997, 65, 2; 163-170
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Combined algorithm for finding conservation laws and implectic operators for the Boussinesq-Burgers nonlinear dynamical system and its finite dimensional reductions
    Autorzy:
    Kindybaliuk, A.
    Prytula, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/122896.pdf
    Data publikacji:
    2014
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    nonlinear dynamical system
    conservation laws
    implectic operators
    method of undetermined coefficients
    differential algebraic algorithm
    combined algorithm
    finite dimensional reduction
    Hamiltonian system
    exact solutions
    Boussinesq-Burgers equation
    nieliniowy układ dynamiczny
    prawa zachowania
    algebraiczny algorytm różniczkowy
    system Hamiltona
    rozwiązania dokładne
    równanie Boussinesqa-Burgersa
    Opis:
    In the article the combined algorithm for finding conservation laws and implectic operators has been proposed. Using the Novikov-Bogoyavlensky method the finite dimensional reductions have been found. The structure of invariant submanifolds has been examined. Having analyzed phase portraits of Hamiltonian systems, partial periodical solutions have been found.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 3; 85-99
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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