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    Wyświetlanie 1-15 z 15
    Tytuł:
    Sensitivity and dynamic phase response to thermal radiation of a polarization-maintaining fiber
    Autorzy:
    Kyselak, M.
    Dvorak, F.
    Maschke, J.
    Vlcek, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/173541.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
    Tematy:
    fiber sensor
    polarization-maintaining fiber
    PMF
    optical fiber
    birefringence
    temperature field disturbance
    approximation equations
    approximation parameters
    Opis:
    This paper deals with the phase shift development between two polarization modes in birefringent fiber, caused by body heat transfer of different temperatures. The aim is to analyze sensitivity and dynamic behaviors, which are significant when optical fiber is used as a sensor of temperature field disturbance. The analysis is based on the values measured during thermal exposure of a section of type PANDA birefringent optical fiber to heat emitted by an exposure body of chosen temperature, placed at a defined distance. The effect of heat transfer through conduction and convection is suppressed by shielding with plastic wraps. The analyzed results, the Stokes parameters and subsequent phase shift, are measured by the polarimeter. The paper follows up on previously published measurement results.
    Źródło:
    Optica Applicata; 2018, 48, 2; 249-261
    0078-5466
    1899-7015
    Pojawia się w:
    Optica Applicata
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solution of the Fredholm integral equation of the second kind using spline functions
    Autorzy:
    Jabłoński, Zdzisław
    Powiązania:
    https://bibliotekanauki.pl/articles/748607.pdf
    Data publikacji:
    1982
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Theoretical approximation of solutions,Fredholm integral equations,Integral equations
    Opis:
    .
    The author presents a polynomial spline function method for solution of the linear Fredholm integral equation f(s)+K1f(s)=φ(s), where K1f(s)=∫CK(s,t)f(t)dt, τ∈[0,2π], and C is a Jordan curve. The method is as follows: The approximate equation for the function fδ(s) is (1) fδ+K1δfδ=φ, where K1δ=K1Tδ, and (2) Tδf(t)=∑n−1i=0f(ti)Wi4(t)Ni1(t). Here Wi4(t) is a spline function, i.e., a 3rd degree polynomial, and Ni1(t)=1 for t∈[ti,ti+1) and Ni1(t)=0 for t∉[ti,ti+1). The substitution of (2) into (1) leads to the equation fδ(s)+∑n−1i=0fδ(ti)K1ei4(s)=φ(s), where ei4(t)=Wi4(t)Ni1(t), i=0,⋯,n−1. The coefficients satisfy the equations fδ(tl)+∑i=0n−1fδ(ti)K1ei4(tl)=φ(tl),l=0,⋯,n−1. The author gives an estimate for ∥fδ−f∥C, and ends the article with an example.
    Źródło:
    Mathematica Applicanda; 1982, 10, 19
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the asymptotics of the difference equation with a proportional delay
    Autorzy:
    Kundrat, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/255684.pdf
    Data publikacji:
    2006
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    asymptotics of difference equations
    approximation methods for dynamical systems
    Opis:
    This paper deals with asymptotic properties of a vector difference equation with delayed argument Δxk = Axk +Bx(λk], 0 < λ < 1, k = 0,1,2,..., where A, B are constant matrices and the term [λk] is the integer part of λk. Our aim is to emphasize some resemblances between the asymptotic behaviour of this delay difference equation and its continuous counterpart.
    Źródło:
    Opuscula Mathematica; 2006, 26, 3; 499-506
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the numerical approximation of first-order Hamilton-Jacobi equations
    Autorzy:
    Abgrall, R.
    Perrier, V.
    Powiązania:
    https://bibliotekanauki.pl/articles/929712.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    równanie Hamiltona-Jacobiego
    aproksymacja
    zagadnienie Cauchy'ego-Dirichleta
    siatka trójkątna
    approximation of Hamilton-Jacobi equations
    viscous solution
    Cauchy-Dirichlet problem
    triangular mesh
    Opis:
    Some methods for the numerical approximation of time-dependent and steady first-order Hamilton-Jacobi equations are reviewed. Most of the discussion focuses on conformal triangular-type meshes, but we show how to extend this to the most general meshes. We review some first-order monotone schemes and also high-order ones specially dedicated to steady problems.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 403-412
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Overview of adaptive and low-rank approximation algorithms for modeling influence of electromagnetic waves generated by cellphone antenna on human head
    Autorzy:
    Głut, Barbara
    Paszyński, Maciej
    Powiązania:
    https://bibliotekanauki.pl/articles/2097964.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    mesh generation
    mesh adaptation
    Pennes bioheat equations
    time-harmonic Maxwell equations
    sparse factorization
    low rank approximation
    Opis:
    This paper presents an overview of formulations and algorithms that are dedicated to modeling the influence of electromagnetic waves on the human head. We start from h adaptive approximation of a three-dimensional MRI scan of the human head. Next, we solve the time-harmonic Maxwell equations with a 1.8 GHz cellphone antenna. We compute the specific absorption rate used as the heat source for the Pennes bioheat equation modeling the heat generated by EM waves inside the head. We propose an adaptive algorithm mixed with time-stepping iterations where we simultaneously refine the computational mesh, solve the Maxwell and Pennes equations, and iterate the time steps. We employ the sparse Gaussian elimination algorithm with the low-rank compres-sion of the off-diagonal matrix blocks for the factorization of the matrices. We conclude with the statement that 15 minutes of talking with a 1.8 GHz antenna with one watt of power results in increased brain tissue temperatures (up to 38.4◦C).
    Źródło:
    Computer Science; 2021, 22 (4); 433--461
    1508-2806
    2300-7036
    Pojawia się w:
    Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The Lipschitz Picard successive step method in hydrodynamic lubrication problem
    Autorzy:
    Wierzcholski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/247949.pdf
    Data publikacji:
    2012
    Wydawca:
    Instytut Techniczny Wojsk Lotniczych
    Tematy:
    Unified Pickard method
    approximation of solutions
    system of partial differential equations
    Opis:
    The paper shows the successive steps of approximation of Picard unification for the solution of the non-isothermal fluid flow in thin layer including inertia forces and apparent viscosities described by the non-linear dependences. In this paper is presented a unified semi analytical method of solution of the asymmetrical, laminar, steady and unsteady, non-Newtonian lubrication problem flow between two non-rotational in general, convex, differentiable and movable surfaces when the time t depended gap between mentioned surfaces has quite an arbitrary geometry. The presented considerations relate not only to the rotational cooperating surfaces but also to the arbitrary non-rotational surfaces in general. The parallel and longitudinal intersections of mentioned surfaces are curvilinear and non-monotone in general. We consider the non-Newtonian lubricant for non-linear constitutive equations taking into account Reiner Rivlin power law relationship as well Rivlin-Ericksen formula for viscoelastic fluids. The non-Newtonian properties create non-linear dependencies between strain and stress. Moreover, the dynamic viscosity or apparent dynamic viscosity of numerous lubricant liquids with various additions often decreases along with shear rate increasing during motion. Dynamic viscosity of lubricant fluids inside very thin micro and nano boundary layers depends on Young’s modulus of the cell of surface body being in contact with the fluid.
    Źródło:
    Journal of KONES; 2012, 19, 1; 483-490
    1231-4005
    2354-0133
    Pojawia się w:
    Journal of KONES
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Singular integration in boundary element method for Helmholtz equation formulated in frequency domain
    Całki osobliwe w metodzie elementów brzegowych dla równania Helmholtza sformułowanego w przestrzeni częstotliwości
    Autorzy:
    Rymarczyk, Tomasz
    Sikora, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/2070239.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Lubelska. Wydawnictwo Politechniki Lubelskiej
    Tematy:
    partial differential equations
    numerical analysis
    function approximation
    integral equations
    równania różniczkowe cząstkowe
    analiza numeryczna
    aproksymacja funkcji
    równania całkowe
    Opis:
    Two ways of approximation of the BEM kernel singularity are presented in this paper. Based on these approximations extensive error analysis was carried on. As a criterion the preciseness and simplicity of approximation were selected. Simplicity because such approach would be applied for the tomography problems, so time of execution plays particularly significant role. One of the approximations which could be applied for the wide range of the arguments of the kernel were selected.
    Dwie metody aproksymacji osobliwości funkcji Greena zaproponowano w tej pracy. Bazując na tych aproksymacjach dokonano wnikliwej analizy błędów. Jako kryterium wybrano dokładność i prostotę zaproponowanych aproksymacji. Prostotę dlatego, że takie podejście będzie proponowane w zagadnieniach tomograficznych. Tak więc czas odgrywa zasadniczą rolę. Wybrano aproksymację, która może być stosowana dla szerokiego zakresu argumentów.
    Źródło:
    Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska; 2021, 11, 4; 4--8
    2083-0157
    2391-6761
    Pojawia się w:
    Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dynamic programming approach to structural optimization problem - numerical algorithm
    Autorzy:
    Fulmański, P.
    Nowakowski, A.
    Pustelnik, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/255706.pdf
    Data publikacji:
    2014
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    elliptic equations
    optimal shape control
    structural optimization
    stationary Navier-Stokes equations
    dynamic programming
    sufficient optimality condition
    numerical approximation
    Opis:
    In this paper a new shape optimization algorithm is presented. As a model application we consider state problems related to fluid mechanics, namely the Navier-Stokes equations for viscous incompressible fluids. The general approach to the problem is described. Next, transformations to classical optimal control problems are presented. Then, the dynamic programming approach is used and sufficient conditions for the shape optimization problem are given. A new numerical method to find the approximate value function is developed.
    Źródło:
    Opuscula Mathematica; 2014, 34, 4; 699-724
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On optimal and quasi-optimal controls in coefficients for multi-dimensional thermistor problem with mixed Dirichlet-Neumann boundary conditions
    Autorzy:
    Kogut, Peter I.
    Powiązania:
    https://bibliotekanauki.pl/articles/970117.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    nonlinear elliptic equations
    control in coefficients
    p(x)-Laplacian
    approximation approach
    thermistor problem
    Opis:
    In this paper we deal with an optimal control problem in coefficients for the system of two coupled elliptic equations, also known as the thermistor problem, which provides a simultaneous description of the electric field u = u(x) and temperature θ(x). The coefficients of the operator div (B(x)∇θ(x)) are used as the controls in L∞(Ω). The optimal control problem is to minimize the discrepancy between a given distribution θd ∈ Lr(Ω) and the temperature of thermistor θ ∈ W1,γ 0 (Ω) by choosing an appropriate anisotropic heat conductivity matrix B. Basing on the perturbation theory of extremal problems and the concept of fictitious controls, we propose an “approximation approach” and discuss the existence of the so-called quasi-optimal and optimal solutions to the given problem.
    Źródło:
    Control and Cybernetics; 2019, 48, 1; 31-68
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Investigation of the Stability and Convergence of Difference Schemes for the Three-dimensional Equations of the Atmospheric Boundary Layer
    Autorzy:
    Temirbekov, A. N.
    Urmashev, B. A.
    Gromaszek, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/226826.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    atmospheric boundary layer equations
    difference scheme
    approximation error
    stability
    convergence algorithms
    numerical solution
    Opis:
    In this article we construct a finite-difference scheme for the three-dimensional equations of the atmospheric boundary layer. The solvability of the mathematical model is proved and quality properties of the solutions are studied. A priori estimates are derived for the solution of the differential equations. The mathematical questions of the difference schemes for the equations of the atmospheric boundary layer are studied. Nonlinear terms are approximated such that the integral term of the identity vanishes when it is scalar multiplied. This property of the difference scheme is formulated as a lemma. Main a priori estimates for the solution of the difference problem are derived. Approximation properties are investigated and the theorem of convergence of the difference solution to the solution of the differential problem is proved.
    Źródło:
    International Journal of Electronics and Telecommunications; 2018, 64, 3; 391-396
    2300-1933
    Pojawia się w:
    International Journal of Electronics and Telecommunications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Error estimates for the finite-element approximation of an elliptic control problem with pointwise state and control constraints
    Autorzy:
    Meyer, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/971011.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równanie eliptyczne
    aproksymacja numeryczna
    linear quadratic optimal control problems
    elliptic equations
    state constraints
    numerical approximation
    Opis:
    We consider a linear-quadratic elliptic optimal control problem with pointwise state constraints. The problem is fully discretized using linear ansatz functions for state and control. Based on a Slater-type argument, we investigate the approximation behavior for mesh size tending to zero. The obtained convergence order for the L²-error of the control and for H 1-error of the state is 1 - ε in the two-dimensional case and 1/2 - ε in three dimensions, provided that the domain satisfies certain regularity assumptions. In a second step, a state-constrained problem with additional control constraints is considered. Here, the control is discretized by constant ansatz functions. It is shown that the convergence theory can be adapted to this case yielding the same order of convergence. The theoretical findings are confirmed by numerical examples.
    Źródło:
    Control and Cybernetics; 2008, 37, 1; 51-83
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hamiltonian model of electromechanical actuator in natural reference frame.: Part I: Topology-based approximation algorithm
    Autorzy:
    Burlikowski, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/140394.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    równania Hamiltona
    simpleks
    kompleks symplicjalny
    aproksymacja symplicjalna
    transformacja afiniczna
    Hamiltonian equations
    simplex
    simplical complex
    simplical approximation
    affine transformation
    Opis:
    In the paper a novel mathematical model of electromechanical actuator is presented. It is based on application of Hamiltonian equations in the description of electromechanical energy conversion. It results in employment of flux linkages as state variables in the state space equations. For simplicity only a 3-phase wye connected stator winding without a neutral wire is considered in detail. The procedure can be generalised to any number of phases. Topology-based approach is used in the model implementation. Procedures for evaluation of all quantities (currents, energy/coenergy, electromagnetic torque) present in model equations are described. Eddy currents and hysteresis phenolmenon are neglected in formulation of the model to enable application of state-space description.
    Źródło:
    Archives of Electrical Engineering; 2011, 60, 3; 317-330
    1427-4221
    2300-2506
    Pojawia się w:
    Archives of Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Finite element error analysis for state-constrained optimal control of the Stokes equations
    Autorzy:
    Los Reyes, J. C. de
    Meyer, C.
    Vexler, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/969607.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równanie Stokesa
    aproksymacja numeryczna
    element skończony
    linear quadratic optimal control problems
    Stokes equations
    state constraints
    numerical approximation
    finite elements
    Opis:
    An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerned with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the L∞-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the L∞-finite-eleinent-error can be verified for different numerical settings. Finally the results of two numerical experiments are presented.
    Źródło:
    Control and Cybernetics; 2008, 37, 2; 251-284
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximate state-space and transfer function models for 2x2 linear hyperbolic systems with collocated boundary inputs
    Autorzy:
    Bartecki, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/330464.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    distributed parameter system
    hyperbolic equations
    approximation model
    state space
    transfer function
    układ o parametrach rozłożonych
    równanie hiperboliczne
    model aproksymacyjny
    przestrzeń stanu
    funkcja przesyłowa
    Opis:
    Two approximate representations are proposed for distributed parameter systems described by two linear hyperbolic PDEs with two time- and space-dependent state variables and two collocated boundary inputs. Using the method of lines with the backward difference scheme, the original PDEs are transformed into a set of ODEs and expressed in the form of a finite number of dynamical subsystems (sections). Each section of the approximation model is described by state-space equations with matrix-valued state, input and output operators, or, equivalently, by a rational transfer function matrix. The cascade interconnection of a number of sections results in the overall approximation model expressed in finite-dimensional state-space or rational transfer function domains, respectively. The discussion is illustrated with a practical example of a parallel-flow double-pipe heat exchanger. Its steady-state, frequency and impulse responses obtained from the original infinite-dimensional representation are compared with those resulting from its approximate models of different orders. The results show better approximation quality for the “crossover” input–output channels where the in-domain effects prevail as compared with the “straightforward” channels, where the time-delay phenomena are dominating.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2020, 30, 3; 475-491
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A review: differential transform method for semi-analytical solution of differential equations
    Autorzy:
    Rashidi, M. M.
    Rabiei, F.
    Naser Nia, S.
    Abbasbandy, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/265637.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    metoda transformacji różniczkowej
    równania różniczkowe
    metoda półanalityczna
    differential transform method
    differential transform - Pad'e approximation
    semi-analytical method
    differential equations
    fuzzy differential transformation method
    gS-differentiability
    Opis:
    In this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the convergence and accuracy of DTM approximations, are discussed. Then both techniques of DTM and DTM-Padé, which have been successfully applied to partial differential equations, as well as the application of these methods in fluid mechanic and heat transfer are presented. In addition, the extension of DTM for integral differential equations and the fuzzy differential transformation method (FDTM) for fuzzy problems are discussed.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2020, 25, 2; 122-129
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-15 z 15

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