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    Wyświetlanie 1-24 z 24
    Tytuł:
    Stability of the Popoviviu type functional equations on groups
    Autorzy:
    Chudziak, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255750.pdf
    Data publikacji:
    2011
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    stability
    Popoviciu equation
    quadratic equation
    additive function
    Opis:
    We consider the stability problem for a class of functional equations related to the Popoviciu equation.
    Źródło:
    Opuscula Mathematica; 2011, 31, 3; 317-325
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A mesh algorithm for principal quadratic forms
    Autorzy:
    Polak, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/106252.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    mesh algorithm
    quadratic form
    quadratic diophantine equation
    Opis:
    In 1970 a negative solution to the tenth Hilbert problem, concerning the determination of integral solutions of diophantine equations, was published by Y. W. Matiyasevich. Despite this result, we can present algorithms to compute integral solutions (roots) to a wide class of quadratic diophantine equations of the form q(x) = d, where q : Z is a homogeneous quadratic form. We will focus on the roots of one (i.e., d = 1) of quadratic unit forms (q11 = ... = qnn = 1). In particular, we will describe the set of roots Rq of positive definite quadratic forms and the set of roots of quadratic forms that are principal. The algorithms and results presented here are successfully used in the representation theory of finite groups and algebras. If q is principal (q is positive semi-definite and Ker q={v ∈ Zn; q(v) = 0}= Z · h) then |Rq| = ∞. For a given unit quadratic form q (or its bigraph), which is positive semi-definite or is principal, we present an algorithm which aligns roots Rq in a Φ-mesh. If q is principal (|Rq| is less than ∞), then our algorithm produces consecutive roots in Rq from finite subset of Rq, determined in an initial step of the algorithm.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica; 2011, 11, 1; 23-31
    1732-1360
    2083-3628
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska. Sectio AI, Informatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Anisotropic charged stars with quadratic equation state
    Autorzy:
    Malaver, Manuel
    Powiązania:
    https://bibliotekanauki.pl/articles/1178297.pdf
    Data publikacji:
    2017
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Anisotropic charged matter distribution; compact stellar objects; energy density; quadratic equation of state
    Opis:
    In this paper, we present a new model of static spherically symmetric relativistic compact stellar objects with anisotropic charged matter distribution and quadratic equation of state together with a prescribed form for the gravitational potential Z used by Bhar and Murad (2016). A graphical analysis of the physical properties indicate indicates that the new model well behaved and not admit singularities in the matter and the charge density.
    Źródło:
    World Scientific News; 2017, 86, 3; 333-344
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Quadratic integral equations in reflexive Banach space
    Autorzy:
    Salem, Hussein
    Powiązania:
    https://bibliotekanauki.pl/articles/729287.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Pettis integral
    fractional calculus
    fixed point theorem
    quadratic integral equation
    Opis:
    This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 1; 61-69
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Classes of relativistic stars with quadratic equation of state
    Autorzy:
    Malaver, Manuel
    Powiązania:
    https://bibliotekanauki.pl/articles/1194131.pdf
    Data publikacji:
    2016
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Charge anisotropic matter distribution
    Charge density
    Field equations
    Gravitational potential
    Radial pressure
    quadratic equation of state
    Opis:
    In this paper, we found new exact solutions to the Einstein-Maxwell system of equations with charged anisotropic matter distribution considering quadratic equation of state. We specify the gravitational potential Z(x) that depends of a adjustable parameter n and that allow integrate analytical the field equations in order to calculate the energy density, the radial pressure, the anisotropy, charge density and the mass function for different values of n. The obtained solutions can be written in terms of elementary and polynomial functions.
    Źródło:
    World Scientific News; 2016, 57; 58-68
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the equation of the \(\rho\)-orthogonal additivity
    Autorzy:
    Alsina, Claudi
    Sikorska, Justyna
    Santos Tomás, Maria
    Powiązania:
    https://bibliotekanauki.pl/articles/745300.pdf
    Data publikacji:
    2007
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Cauchy functional equation
    quadratic functional equation
    orthogonally additive function
    orthogonally quadratic function
    Birkhoff orthogonality
    smooth spaces
    Opis:
    We solve a conditional functional equation of the form \[ x \perp^{\rho} y\Rightarrow f (x + y) = f (x) + f (y), \] where \(f\) is a mapping from a real normed linear space \((X, \| · \|)\) with \(\text{dim} X \geq 2\) into an abelian group \((G, +)\) and \(\perp^\rho\) is a given orthogonality relation associated to the norm.
    Źródło:
    Commentationes Mathematicae; 2007, 47, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solvability of functional quadratic integral equations with perturbation
    Autorzy:
    Metwali, M. A. M.
    Powiązania:
    https://bibliotekanauki.pl/articles/254702.pdf
    Data publikacji:
    2013
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    quadratic integral equation
    measure of noncompactness
    Krasnoselskii fixed point theorem
    superposition operators
    Opis:
    We study the existence of solutions of the functional quadratic integral equation with a perturbation term in the space of Lebesgue integrable functions on an unbounded interval by using the Krasnoselskii fixed point theory and the measure of weak noncompactness.
    Źródło:
    Opuscula Mathematica; 2013, 33, 4; 725-739
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Existence of solutions of some quadratic integral equations
    Autorzy:
    Anichini, G.
    Conti, G.
    Powiązania:
    https://bibliotekanauki.pl/articles/255299.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    fixed-point property
    measure of noncompactness
    compact mappings
    acyclic valued
    quadratic integral equation
    Opis:
    In this paper we study the existence of continuous solutions of quadratic integral equations. The theory of quadratic integral equations has many useful applications in mathematical physics, economics, biology, as well as in describing real world problems. The main tool used in our investigations is a fixed point result for the multivalued solution's map with acyclic values.
    Źródło:
    Opuscula Mathematica; 2008, 28, 4; 433-440
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Nonincreasing solutions for quadratic integral equations of Convolution type
    Autorzy:
    El-Sayed, W. G.
    Abd El-Mowla, A. A. H.
    Powiązania:
    https://bibliotekanauki.pl/articles/357742.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    quadratic integral equation
    measure of noncompactness
    fixed-point theorem
    monotonic solutions
    równanie całkowe
    miara braku zgodności
    twierdzenie o punkcie stałym
    rozwiązania monotoniczne
    Opis:
    We study a nonlinear quadratic integral equation of Convolution type in the Banach space of real functions defined and continuous on a bounded and closed interval. By using a suitable measure of noncompactness, we show that the integral equation has monotonic solutions.
    Źródło:
    Journal of Mathematics and Applications; 2019, 42; 95-107
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the Existence of Continuous Positive Monotonic Solutions of a Self-Reference Quadratic Integral Equation
    Autorzy:
    EL-Sayed, Ahmed M.A.
    Ebead, Hanaa R.
    Powiązania:
    https://bibliotekanauki.pl/articles/1818643.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
    Tematy:
    self-reference
    quadratic integral equation
    existence of solutions
    uniqueness of solution
    continuous dependence
    Schauder fixed point theorem
    równanie całkowe
    rozwiązania
    zależność ciągła
    punkt stały Schaudera
    Opis:
    In this work we study the existence of positive monotonic solutions of a self-reference quadratic integral equation in the class of continuous real valued functions. The continuous dependence of the uniquesolution will be proved. Some examples will be given.
    Źródło:
    Journal of Mathematics and Applications; 2020, 43; 67--80
    1733-6775
    2300-9926
    Pojawia się w:
    Journal of Mathematics and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Diophantine equations and class number of imaginary quadratic fields
    Autorzy:
    Cao, Zhenfu
    Dong, Xiaolei
    Powiązania:
    https://bibliotekanauki.pl/articles/728808.pdf
    Data publikacji:
    2000
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    Diophantine equation
    imaginary quadratic field
    class number
    cryptographic problem
    Opis:
    Let A, D, K, k ∈ ℕ with D square free and 2 ∤ k,B = 1,2 or 4 and $μ_{i} ∈ {-1,1}(i = 1,2)$, and let $h(-2^{1-e}D)(e = 0 or 1)$ denote the class number of the imaginary quadratic field $ℚ(√(-2^{1-e}D))$. In this paper, we give the all-positive integer solutions of the Diophantine equation Ax² + μ₁B = K((Ay² + μ₂B)/K)ⁿ, 2 ∤ n, n > 1 and we prove that if D > 1, then $h(-2^{1-e}D) ≡ 0 (mod n)$, where D, and n satisfy $kⁿ - 2^{e+1} = Dx²$, x ∈ ℕ, 2 ∤ n, n > 1. The results are valuable for the realization of quadratic field cryptosystem.
    Źródło:
    Discussiones Mathematicae - General Algebra and Applications; 2000, 20, 2; 199-206
    1509-9415
    Pojawia się w:
    Discussiones Mathematicae - General Algebra and Applications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A direct approach to linear-quadratic stochastic control
    Autorzy:
    Duncan, T. E.
    Pasik-Duncan, B.
    Powiązania:
    https://bibliotekanauki.pl/articles/255863.pdf
    Data publikacji:
    2017
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    linear-quadratic Gaussian control
    Riccati equation for optimization
    stochastic control
    Opis:
    A direct approach is used to solve some linear-quadratic stochastic control problems for Brownian motion and other noise processes. This direct method does not require solving Hamilton-Jacobi-Bellman partial differential equations or backward stochastic differential equations with a stochastic maximum principle or the use of a dynamic programming principle. The appropriate Riccati equation is obtained as part of the optimization problem. The noise processes can be fairly general including the family of fractional Brownian motions.
    Źródło:
    Opuscula Mathematica; 2017, 37, 6; 821-827
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical error bound of optimal control for homogeneous linear systems
    Autorzy:
    Daraghmeh, Adnan
    Qatanani, Naji
    Powiązania:
    https://bibliotekanauki.pl/articles/229410.pdf
    Data publikacji:
    2019
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    time-invariant systems
    quadratic cost function
    linear quadratic regulator
    algebraic Riccati equation
    Hamiltonian function
    L2 norm
    Opis:
    In this article we focus on the balanced truncation linear quadratic regulator (LQR) with constrained states and inputs. For closed-loop, we want to use the LQR to find an optimal control that minimizes the objective function which called "the quadratic cost function” with respect to the constraints on the states and the control input. In order to do that we have used formal asymptotes for the Pontryagin maximum principle (PMP) and we introduce an approach using the so called The Hamiltonian Function and the underlying algebraic Riccati equation. The theoretical results are validated numerically to show that the model order reduction based on open-loop balancing can also give good closed-loop performance.
    Źródło:
    Archives of Control Sciences; 2019, 29, 2; 323-337
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Intersect a quartic to extract its roots
    Autorzy:
    Kulkarni, Raghavendra G.
    Powiązania:
    https://bibliotekanauki.pl/articles/744628.pdf
    Data publikacji:
    2017-12-01
    Wydawca:
    Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
    Tematy:
    Intersection of curves
    quartic polynomial
    quadratic polynomial
    roots
    resolvent cubic equation
    Opis:
    In this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the curve of a quadratic polynomial (which has two unknown coefficients) at its root point; so the root satisfies both the quartic and the quadratic equations. Elimination of the root term from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression in one unknown, which leads to determination of the two unknowns and subsequently the roots of quartic polynomial.
    Źródło:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2017, 16
    2300-133X
    Pojawia się w:
    Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Jacobi type conditions for singular extremals
    Autorzy:
    Dmitruk, A. V.
    Powiązania:
    https://bibliotekanauki.pl/articles/969606.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    singular extremal
    Goh transformation
    Legendre quadratic form
    Euler-Jacobi equation
    conjugate point
    Opis:
    We consider the class of optimal control problems linear in the control, and study a singular extremal. If the Lagrange multipliers are unique, the quadratic order optimality conditions have the form of sign definiteness of a quadratic functional (the second variation of Lagrange function) with totally zero Legendre coefficient. Using the Goh transformation, we convert it to a functional possibly satisfying the strengthened Legendre condition, involving also an additional parameter, and by applying the Hestenes approach, determine its sign definiteness in terms of the conjugate point, i.e. give Jacobi type conditions.
    Źródło:
    Control and Cybernetics; 2008, 37, 2; 285-306
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On properties of minimizers of a control problem with time-distributed functional related to parabolic equations
    Autorzy:
    Astashova, I. V.
    Filinovskiy, A. V.
    Powiązania:
    https://bibliotekanauki.pl/articles/255539.pdf
    Data publikacji:
    2019
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    parabolic equation
    extremal problem
    quadratic cost functional
    minimizer
    exact controllability
    dense controllability
    Opis:
    We consider a control problem given by a mathematical model of the temperature control in industrial hothouses. The model is based on one-dimensional parabolic equations with variable coefficients. The optimal control is defined as a minimizer of a quadratic cost functional. We describe qualitative properties of this minimizer, study the structure of the set of accessible temperature functions, and prove the dense controllability for some set of control functions.
    Źródło:
    Opuscula Mathematica; 2019, 39, 5; 595-609
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Local quadratic convergence of SQP for elliptic optimal control problems with mixed control-state constraints
    Autorzy:
    Griesse, R.
    Metla, N.
    Rosch, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/969868.pdf
    Data publikacji:
    2010
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    sequential quadratic programming
    mixed control-state constraints
    implicit function theorem
    generalized equation
    Opis:
    Semilinear elliptic optimal control problems with pointwise control and mixed control-state constraints are considered. Necessary and sufficient optimality conditions are given. The equivalence of the SQP method and Newton's method for a generalized equation is discussed. Local quadratic convergence of the SQP method is proved.
    Źródło:
    Control and Cybernetics; 2010, 39, 3; 717-738
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fixed terminal time fractional optimal control problem for discrete time singular system
    Autorzy:
    Chiranjeevi, Tirumalasetty
    Devarapalli, Ramesh
    Babu, Naladi Ram
    Vakkapatla, Kiran Babu
    Rao, R. Gowri Sankara
    Garcìa Màrquez, Fausto Pedro
    Powiązania:
    https://bibliotekanauki.pl/articles/2175112.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    fractional order differential equation
    discrete time singular system
    fractional derivative
    linear quadratic optimal control problem
    Opis:
    This paper presents the formulation and numerical simulation for linear quadratic optimal control problem (LQOCP) of free terminal state and fixed terminal time fractional order discrete time singular system (FODSS). System dynamics is expressed in terms of Riemann-Liouville fractional derivative (RLFD), and performance index (PI) in terms of state and costate. Because of its complexity, finding analytical and numerical solutions to singular system (SS) is difficult. As a result, we use coordinate transformation to convert FODSS to its corresponding fractional order discrete time nonsingular system (FODNSS). After that, we obtain the necessary conditions by employing a Hamiltonian approach. The relevant conditions are solved using the general solution approach. For the analysis of formulation and solution algorithm, a numerical example is illustrated. Results are obtained for various values. According to state of the art, this is the first time that a formulation and numerical simulation of free terminal state and fixed terminal time optimal control problem (OCP) of FODSS is presented.
    Źródło:
    Archives of Control Sciences; 2022, 32, 3; 489--506
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system
    Autorzy:
    Kumar E, V.
    Jerome, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/140600.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    algebraic Riccatti equation
    linear quadratic regulator
    magnetic levitation
    system
    weighting matrices
    command following
    cost function
    Opis:
    This paper presents an analytical approach for solving the weighting matrices selection problem of a linear quadratic regulator (LQR) for the trajectory tracking application of a magnetic levitation system. One of the challenging problems in the design of LQR for tracking applications is the choice of Q and R matrices. Conventionally, the weights of a LQR controller are chosen based on a trial and error approach to determine the optimum state feedback controller gains. However, it is often time consuming and tedious to tune the controller gains via a trial and error method. To address this problem, by utilizing the relation between the algebraic Riccati equation (ARE) and the Lagrangian optimization principle, an analytical methodology for selecting the elements of Q and R matrices has been formulated. The novelty of the methodology is the emphasis on the synthesis of time domain design specifications for the formulation of the cost function of LQR, which directly translates the system requirement into a cost function so that the optimal performance can be obtained via a systematic approach. The efficacy of the proposed methodology is tested on the benchmark Quanser magnetic levitation system and a detailed simulation and experimental results are presented. Experimental results prove that the proposed methodology not only provides a systematic way of selecting the weighting matrices but also significantly improves the tracking performance of the system.
    Źródło:
    Archives of Electrical Engineering; 2016, 65, 1; 151-168
    1427-4221
    2300-2506
    Pojawia się w:
    Archives of Electrical Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bound State Solutions of the Klein Gordon Equation with Woods-Saxon Plus Attractive Inversely Quadratic Potential Via Parametric Nikiforov-Uvarov Method
    Autorzy:
    Ita, B. I.
    Louis, H.
    Magu, T. O.
    Nzeata-Ibe, N. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1179619.pdf
    Data publikacji:
    2017
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Attractive inversely quadratic potential
    Bound state solutions
    Klein-gordon equation
    Nikiforov-Uvarov method
    Woods-saxon potential
    Opis:
    We study the bound state solutions of the Klein-Gordon equation with Woods-Saxon plus attractive inversely quadratic potential using the parametric Nikiforov-Uvarov Method. We obtained the bound state energy eigenvalues and the corresponding normalized eigen functions expressed in terms of hypergeometric functions. Two special cases of this potential are discussed.
    Źródło:
    World Scientific News; 2017, 74; 280-287
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Matrix Quadratic Equations, Column/row Reduced Factorizations and an Inertia Theorem for Matrix Polynomials
    Autorzy:
    Karelin, I.
    Lerer, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/908122.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    macierz
    równanie różniczkowe Riccatiego
    matrix quadratic equations
    Bezoutians
    inertia
    column (row) reduced polynomials
    factorization
    algebraic Riccati equation
    extremal solutions
    Opis:
    It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial G(lambda) (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of G(lambda). The proof of these results depends heavily on a new inertia theorem for matrix polynomials which is also one of the main results in this paper.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 6; 1285-1310
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Extension of the one-dimensional Stoney algorithm to a two-dimensional case
    Autorzy:
    Gniazdowski, Zenon
    Powiązania:
    https://bibliotekanauki.pl/articles/91318.pdf
    Data publikacji:
    2019
    Wydawca:
    Warszawska Wyższa Szkoła Informatyki
    Tematy:
    Stoney formula
    Stoney equation
    2D Stoney algorithm
    tensor of curvature
    stress in a thin film
    anisotropy
    quadric
    quadratic form
    Opis:
    This article presents the extension of the one-dimensional Stoney algorithm to a two-dimensional case. The proposed extension consists in modifying the method of curvature estimation. The surface profile of the wafer before deposition of the thin film and after its deposition was locally approximated by the quadric. From this quadric, a quadratic form and the first degree surface were separated. An eigenproblem was solved for the matrix of this quadratic form. From eigenvectors a new coordinate system was created in which a new formula of the quadric was found. In this new coordinate system, the two-dimensional problem of estimating thecurvaturetensorhasbeensolvedbysolvingtwoindependentone-dimensional problems of curvature estimation. Returning to the primary coordinate system, in this primary system, a solution to the two-dimensional problem was obtained. The article proposes five versions of the two-dimensional Stoney algorithm, with diverse complexity and accuracy. The recommendation for the version of the algorithm that could be practically used was also presented.
    Źródło:
    Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki; 2019, 13, 20; 41-66
    1896-396X
    2082-8349
    Pojawia się w:
    Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Network optimality conditions
    Autorzy:
    Osmolovskii, Nikolai P.
    Qian, Meizhi
    Sokołowski, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/31343935.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    network
    optimal control problem
    weak local minimum
    Pontryagin’s maximum principle
    critical cone
    quadratic form
    second order optimality conditions
    Riccati equation
    Opis:
    Optimality conditions for optimal control problems arising in network modeling are discussed. We confine ourselves to the steady state network models. Therefore, we consider only control systems described by ordinary differential equations. First, we derive optimality conditions for the nonlinear problem for a single beam. These conditions are formulated in terms of the local Pontryagin maximum principle and the matrix Riccati equation. Then, the optimality conditions for the control problem for networks posed on an arbitrary planar graph are discussed. This problem has a set of independent variables xi varying within their intervals [0, li], associated with the corresponding beams at network edges. The lengths li of intervals are not specified and must be determined. So, the optimization problem is non-standard, it is a combination of control and design of networks. However, using a linear change of the independent variables, it can be reduced to a standard one, and we show this. Two simple numerical examples for the single-beam problem are considered.
    Źródło:
    Control and Cybernetics; 2023, 52, 2; 129-180
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Analysis of the Lagrange-SQP-Newton method for the control of a phase field equation
    Autorzy:
    Heinkenschloss, M.
    Troeltzsch, F.
    Powiązania:
    https://bibliotekanauki.pl/articles/206519.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równania paraboliczne
    równania różniczkowe
    stabilność
    sterowanie optymalne
    control constraints
    Lagrange-SQP-Newton method
    optimal control
    phase field equation
    programming method
    sequential quadratic
    Opis:
    This paper investigates the local convergence of the Lagrange-SQP-Newton method applied to an optimal control problem governed by a phase field equation with distributed control. The phase field equation is a system of two semilinear parabolic differential equations. Stability analysis of optimization problems and regularity results for parabolic differential equations are used to proof convergence of the controls with respect to the L[sup 2](Q) norm and with respect to the L[sup infinity](Q) norm.
    Źródło:
    Control and Cybernetics; 1999, 28, 2; 177-211
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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