Informacja

Drogi użytkowniku, aplikacja do prawidłowego działania wymaga obsługi JavaScript. Proszę włącz obsługę JavaScript w Twojej przeglądarce.

English (EN)·Polski (PL)·Yкраїнський (UK)
Przejdź do strony domowej biblioteki Centralna Biblioteka Wojskowa Link otwiera się w nowym oknie Logo biblioteki Prolib Integro - strona głównaCentralna Biblioteka Wojskowa

Wyszukujesz frazę "derivative" wg kryterium: Temat

  Lista filtrów
Wyrównaj
    Wyświetlanie 1-13 z 13
    Tytuł:
    Variable order 3D models of bone remodelling
    Autorzy:
    Valério, D.
    Neto, J.
    Vinga, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/202197.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    variable-order derivative
    bone remodelling
    cancer
    przebudowa kości
    rak
    Opis:
    This paper presents simulations of a three-dimensional model of the bone remodelling process. The model consists of a set of variable order partial differential equations, in which the varying order depends on the presence of tumour cells. The simulations are of a two-dimensional bone, to make visualisation simpler. They show that this model corresponds to the known evolution of bone remodelling, and is simpler than integer order models found in the literature.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 3; 501-508
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A subinterval-based method for circuits with fractional order elements
    Autorzy:
    Sowa, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/201236.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional derivative
    circuit equations
    numerical method
    polynomial interpolation
    subinterval
    Opis:
    The paper deals with the solution of problems that concern fractional time derivatives. Specifically the author’s interest lies in solving circuit problems with so called fractional capacitors and fractional inductors. A numerical method is proposed that involves polynomial interpolation and the division of the entire time interval (for which computations are performed) into subintervals. Analytical formulae are derived for the integro-differentiation according to the Caputo fractional derivative. The rules that concern the subinterval dynamics throughout the computation are also presented in the paper. For exemplary linear circuit problems (AC and transient) involving fractional order elements the solutions have been obtained. These solutions are compared with ones obtained by means of traditional methods.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 3; 449-454
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Mathematical modeling of traveling autosolitons in fractional-order activator-inhibitor systems
    Autorzy:
    Datsko, B.
    Gafiychuk, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/200733.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional derivative
    nonlinear dynamics
    instability
    autosoliton
    pochodna ułamkowa
    dynamika nieliniowa
    niestabilność
    Opis:
    In the article, basic properties of traveling spatially nonhomogeneous auto-wave solutions in nonlinear fractional-order reactiondiffusion systems are investigated. Such solutions, called autosolitons, arise in a stability region of the system and can coexist with the spatially homogeneous states. By a linear stability analysis and computer simulation, it is shown that the order of the fractional derivative can substantially change the properties of such auto-wave solutions and significantly enrich nonlinear system dynamics. The results of the linear stability analysis are confirmed by computer simulations of the generalized fractional van der Pol-FitzHugh-Nagumo model. A common picture of traveling auto-waves including series in time-fractional two-component activator-inhibitor systems is presented. The results obtained in the article for the distributed system have also been of interest for nonlinear dynamical systems described by fractional ordinary differential equations.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 411-418
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Stabilization of autonomous linear time invariant fractional order derivative switched systems with different derivative in subsystems
    Autorzy:
    Balochian, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/200478.pdf
    Data publikacji:
    2014
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    linear time invariant fractional order derivative
    switching systems
    linear matrix inequality
    LMI
    Opis:
    In this paper, the stabilization problem of a autonomous linear time invariant fractional order (LTI-FO) switched system with different derivative order in subsystems is outlined. First, necessary and sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems based on the convex analysis and linear matrix inequality (LMI) for two subsystems is presented and proved. Also, sufficient condition for stability of an LTI-FO switched system with different derivative order in subsystems for more than two subsystems is proved. Then a sliding sector is designed for each subsystem of the LTI-FO switched system. Finally, a switching control law is designed to switch the LTI-FO switched system among subsystems to ensure the decrease of the norm of the switched system. Simulation results are given to show the effectiveness of the proposed variable structure controller.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2014, 62, 3; 495-503
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The application of hypergeometric functions to computing fractional order derivatives of sinusoidal functions
    Autorzy:
    Włodarczyk, M.
    Zawadzki, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/201316.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional degree derivative
    hypergeometric function
    Lommel function
    pochodna ułamkowa
    funkcja hipergeometryczna
    funkcja Lommela
    Opis:
    In the paper, the analytical forms of fractional order derivatives of sinusoidal function according to definitions of Riemann - Liouville and Caputo are presented. To determine the analytical form of the integrals appearing in definitions of derivatives of fractional order the Lommel functions from hypergeometrical functions family were applied. With the use of properties of the derivatives of fractional order - differential-integral there were presented the conception of generalized element of a single equation, which depending on the value of the derivative order, can be inductor, resistor, capacitor, or a hypothetical element of a fractional order differential equation.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 1; 243-248
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Heat conduction in a finite medium using the fractional single-phase-lag model
    Autorzy:
    Siedlecka, Urszula
    Powiązania:
    https://bibliotekanauki.pl/articles/200748.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    single-phase-lagging heat conduction
    Caputo derivative
    fractional heat conduction
    przewodzenie ciepła
    Pochodna Caputo
    Opis:
    In the paper, a solution of the time-fractional single-phase-lagging heat conduction problem in finite regions is presented. The heat conduction equation with the Caputo time-derivative is complemented by the Robin boundary conditions. The Laplace transform with respect to the time variable and an expansion in the eigenfunctions series with respect to the space variable was applied. A method for the numerical inversion of the Laplace transforms was used. Formulation and solution of the problem cover the heat conduction in a finite slab, hollow cylinder and hollow sphere. The effect of the fractional order of the Caputo derivative and the phase-lag parameter on the temperature distribution in a slab has been numerically investigated.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2019, 67, 2; 401-407
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An analytical solution to the problem of time-fractional heat conduction in a composite sphere
    Autorzy:
    Kukla, S.
    Siedlecka, U.
    Powiązania:
    https://bibliotekanauki.pl/articles/202020.pdf
    Data publikacji:
    2017
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    heat conduction
    multilayered sphere
    Caputo fractional derivative
    przewodzenie ciepła
    powłoka wielowarstwowa
    pochodna ułamkowego rzędu Caputo
    Opis:
    An analytical solution to the problem of time-fractional heat conduction in a sphere consisting of an inner solid sphere and concentric spherical layers is presented. In the heat conduction equation, the Caputo time-derivative of fractional order and the Robin boundary condition at the outer surface of the sphere are assumed. The spherical layers are characterized by different material properties and perfect thermal contact is assumed between the layers. The analytical solution to the problem of heat conduction in the sphere for time-dependent surrounding temperature and for time-space-dependent volumetric heat source is derived. Numerical examples are presented to show the effect of the harmonically varying intensity of the heat source and the harmonically varying surrounding temperature on the temperature in the sphere for different orders of the Caputo time-derivative.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 2; 179-186
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Eigenvalues assignment in descriptor linear systems by state and its derivative feedbacks
    Autorzy:
    Kaczorek, Tadeusz
    Powiązania:
    https://bibliotekanauki.pl/articles/27311425.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    eigenvalue assignment
    descriptor
    linear system
    state derivative
    feedback
    przypisanie wartości własnej
    deskryptor
    układ liniowy
    pochodna stanu
    informacja zwrotna
    Opis:
    The eigenvalues assignment problems for descriptor linear systems with state and its derivative feedbacks are considered herein. Necessary and sufficient conditions for the existence of solutions to the problems are established. The Euler and Tustin approximations of the continuous-time systems are analyzed. Procedures for computation of the feedbacks are given and illustrated by numerical examples.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 5; art. no. e145765
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Results on the controllability of Caputo’s fractional descriptor systems with constant delays
    Autorzy:
    Beata, Sikora
    Powiązania:
    https://bibliotekanauki.pl/articles/27311455.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Czasopisma i Monografie PAN
    Tematy:
    descriptor systems
    fractional-order systems
    Caputo derivative
    Drazin inverse
    controllability
    pochodna Caputo
    odwrotność Drazina
    sterowalność
    system deskryptorowy
    system ułamkowego rzędu
    Opis:
    The paper investigates the controllability of fractional descriptor linear systems with constant delays in control. The Caputo fractional derivative is considered. Using the Drazin inverse and the Laplace transform, a formula for solving of the matrix state equation is obtained. New criteria of relative controllability for Caputo’s fractional descriptor systems are formulated and proved. Both constrained and unconstrained controls are considered. To emphasize the importance of the theoretical studies, an application to electrical circuits is presented as a practical example.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 4; art. no. e146287
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Applying a fractional coil model for power system ferroresonance analysis
    Autorzy:
    Majka, Ł.
    Powiązania:
    https://bibliotekanauki.pl/articles/200329.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    ferroresonant circuit
    fractional derivative
    ferromagnetic core coil
    hysteresis
    modeling
    measurement verification
    nonlinear dynamics
    power system
    pochodna ułamkowa
    histereza
    modelowanie
    nieliniowa dynamika
    układ zasilania
    Opis:
    This paper addresses the problem of modeling the nonlinear coil used for ferroresonant circuit analysis. The effect of ferroresonance is described and a general modeling approach is presented. The hysteresis modeling problem is also shortly discussed, on the example of a ferromagnetic coil. A brief overview of available literature and contributors to this area are provided. A series RLC circuit supplied from an AC source is discussed. The application of the fractional derivative in the modeling of an iron core coil is presented and suggestions of model implementations are given. The computations performed are illustrated by means of waveform data obtained from computer simulations and compared with those obtained from measurements performed in a specially prepared laboratory setup.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 467-474
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The implicit numerical method for the one-dimensional anomalous subdiffusion equation with a nonlinear source term
    Autorzy:
    Błasik, Marek
    Powiązania:
    https://bibliotekanauki.pl/articles/2086846.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional derivative
    fractional integral
    integro-differential equations
    numerical method
    finite difference method
    pochodna ułamkowa
    całkowanie ułamkowe
    równanie całkowo-różniczkowe
    metoda numeryczna
    metoda elementów skończonych
    Opis:
    In the paper, the numerical method of solving the one-dimensional subdiffusion equation with the source term is presented. In the approach used, the key role is played by transforming of the partial differential equation into an equivalent integro-differential equation. As a result of the discretization of the integro-differential equation obtained an implicit numerical scheme which is the generalized Crank-Nicolson method. The implicit numerical schemes based on the finite difference method, such as the Carnk-Nicolson method or the Laasonen method, as a rule are unconditionally stable, which is their undoubted advantage. The discretization of the integro-differential equation is performed in two stages. First, the left-sided Riemann-Liouville integrals are approximated in such a way that the integrands are linear functions between successive grid nodes with respect to the time variable. This allows us to find the discrete values of the integral kernel of the left-sided Riemann-Liouville integral and assign them to the appropriate nodes. In the second step, second order derivative with respect to the spatial variable is approximated by the difference quotient. The obtained numerical scheme is verified on three examples for which closed analytical solutions are known.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 6; e138240, 1--9
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Direct least squares and derivative-free optimisation techniques for determining mine-induced horizontal ground displacement
    Autorzy:
    Rusek, Janusz
    Tajduś, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/2090675.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    horizontal ground displacement
    mining
    direct least squares
    derivative-free optimisation
    genetic algorithms
    differential evolution
    particle swarm optimization
    przemieszczenie poziome gruntu
    górnictwo
    optymalizacja bez pochodnych
    optymalizacja roju cząstek
    algorytmy genetyczne
    ewolucja różnicowa
    bezpośrednie najmniejsze kwadraty
    Opis:
    The paper presents the results of analyses concerning a new approach to approximating trajectory of mining-induced horizontal displacements. Analyses aimed at finding the most effective method of fitting data to the trajectory of mining-induced horizontal displacements. Two variants were made. In the first, the direct least square fitting (DLSF) method was applied based on the minimization of the objective function defined in the form of an algebraic distance. In the second, the effectiveness of differential-free optimization methods (DFO) was verified. As part of this study, the following methods were tested: genetic algorithms (GA), differential evolution (DE) and particle swarm optimization (PSO). The data for the analysis were measurements of on the ground surface caused by the mining progressive work at face no. 698 of the German Prospel-Haniel mine. The results obtained were compared in terms of the fitting quality, the stability of the results and the time needed to carry out the calculations. Finally, it was found that the direct least square fitting (DLSF) approach is the most effective for the analyzed registration data base. In the authors’ opinion, this is dictated by the angular range in which the measurements within a given measuring point oscillated.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 1; e135840, 1--12
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Direct least squares and derivative-free optimisation techniques for determining mine-induced horizontal ground displacement
    Autorzy:
    Rusek, Janusz
    Tajduś, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/2173560.pdf
    Data publikacji:
    2021
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    horizontal ground displacement
    mining
    direct least squares
    derivative-free optimisation
    genetic algorithms
    differential evolution
    particle swarm optimization
    przemieszczenie poziome gruntu
    górnictwo
    optymalizacja bez pochodnych
    optymalizacja roju cząstek
    algorytmy genetyczne
    ewolucja różnicowa
    bezpośrednie najmniejsze kwadraty
    Opis:
    The paper presents the results of analyses concerning a new approach to approximating trajectory of mining-induced horizontal displacements. Analyses aimed at finding the most effective method of fitting data to the trajectory of mining-induced horizontal displacements. Two variants were made. In the first, the direct least square fitting (DLSF) method was applied based on the minimization of the objective function defined in the form of an algebraic distance. In the second, the effectiveness of differential-free optimization methods (DFO) was verified. As part of this study, the following methods were tested: genetic algorithms (GA), differential evolution (DE) and particle swarm optimization (PSO). The data for the analysis were measurements of on the ground surface caused by the mining progressive work at face no. 698 of the German Prospel-Haniel mine. The results obtained were compared in terms of the fitting quality, the stability of the results and the time needed to carry out the calculations. Finally, it was found that the direct least square fitting (DLSF) approach is the most effective for the analyzed registration data base. In the authors’ opinion, this is dictated by the angular range in which the measurements within a given measuring point oscillated.
    Źródło:
    Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 1; art. no. e135840
    0239-7528
    Pojawia się w:
    Bulletin of the Polish Academy of Sciences. Technical Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-13 z 13

      Ta witryna wykorzystuje pliki cookies do przechowywania informacji na Twoim komputerze. Pliki cookies stosujemy w celu świadczenia usług na najwyższym poziomie, w tym w sposób dostosowany do indywidualnych potrzeb. Korzystanie z witryny bez zmiany ustawień dotyczących cookies oznacza, że będą one zamieszczane w Twoim komputerze. W każdym momencie możesz dokonać zmiany ustawień dotyczących cookies