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    Wyświetlanie 1-12 z 12
    Tytuł:
    On the Distribution of Quadratic Form of Sample Mean and Variance
    O rozkładzie formy kwadratowej średniej i wariancji z próby
    Autorzy:
    Wywiał, Janusz
    Kończak, Grzegorz
    Powiązania:
    https://bibliotekanauki.pl/articles/905703.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    quadratic form
    mean
    variance
    distribution
    Opis:
    The quadratic form of the sample mean and sample variance was considered. The sample is from normal distribution. The density function of the quadratic form has been derived. The quadratic form can be applied as the test statistic for the hypothesis on expected value and variance of normal distribution. The table with approximated critical values of the test statistic has been derived.
    Źródło:
    Acta Universitatis Lodziensis. Folia Oeconomica; 2006, 196
    0208-6018
    2353-7663
    Pojawia się w:
    Acta Universitatis Lodziensis. Folia Oeconomica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hermitian and quadratic forms over local classical crossed product orders
    Autorzy:
    Hatzaras, Y.
    Theohari-Apostolidi, Th.
    Powiązania:
    https://bibliotekanauki.pl/articles/965780.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    crossed-product order
    quadratic form
    Opis:
    Let R be a complete discrete valuation ring with quotient field K, L/K be a Galois extension with Galois group G and S be the integral closure of R in L. If a is a factor set of G with values in the group of units of S, then (L/K,a) (resp. Λ =(S/R,a)) denotes the crossed product K-algebra (resp. crossed product R -order in A). In this paper hermitian and quadratic forms on Λ -lattices are studied and the existence of at most two irreducible non-singular quadratic Λ -lattices is proved (Theorem 3.5). Further the orthogonal decomposition of an arbitrary non-singular quadratic Λ -lattice is given.
    Źródło:
    Colloquium Mathematicum; 2000, 83, 1; 43-53
    0010-1354
    Pojawia się w:
    Colloquium Mathematicum
    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:
    Structure fractals and para-quaternionic geometry
    Autorzy:
    Ławrynowicz, Julian
    Vaccaro, Massimo
    Powiązania:
    https://bibliotekanauki.pl/articles/747163.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Fractal
    quaternion
    para-quaternion
    Clifford structure
    para-quaternionic structure
    bilinear form
    quadratic form
    Opis:
    It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions \(p = 2, 4\) and \(8\), respectively, but the procedure fails for \(p = 16\) in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are \(n = 2^7\). Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of the flower type related to complex and Pauli structures and, in relation to the iteration process \(p \to p + 2 \to p + 4 \to ...\), they have constructed \(2^4\)-dimensional “bipetals” for \(p = 9\) and \(2^7\)-dimensional “bisepals” for \(p = 13\). The objects constructed appear to have an interesting property of periodicity related to the gradating function on the fractal diagonal interpreted as the “pistil” and a family of pairs of segments parallel to the diagonal and equidistant from it, interpreted as the “stamens”. The first named author, M. Nowak-Kepczyk, and S. Marchiafava (2006, 2009a, b) gave an effective, explicit determination of the periods and expressed them in terms of complex and quaternionic structures, thus showing the quaternionic background of that periodicity. In contrast to earlier results, the fractal bundle flower structure, in particular petals, sepals, pistils, and stamens are not introduced ab initio; they are quoted a posteriori, when they are fully motivated. Physical concepts of dual and conjugate objects as well as of antiparticles led us to extend the periodicity theorem to structure fractals in para-quaternionic formulation, applying some results in this direction by the second named author. The paper is concluded by outlining some applications.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2011, 65, 2
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – 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:
    Algorithms for integral solutions of a class of diophantine equations
    Autorzy:
    Polak, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/206419.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    integral quadratic form
    unit form
    diophantine equations
    roots
    Euler bilinear form
    Euclidean diagrams
    mesh quiver
    algorithm
    Maple
    Opis:
    In 1970 a negative solution to the tenth Hilbert problem, concerning the determination of integral solutions of diophantine equations, has been published by Y. W. Matiyasevich (see Matiyasevich, 1970). Despite this result, we can present algorithms to compute integral solutions (roots) for a wide class of quadratic diophantine equations of the form q(x) = d, where q : Zn → Z is a homogeneous quadratic form. We will focus on the roots of one (i.e., d = 1) of quadratic Euler forms of selected posets from Loupias list (see Loupias, 1975). In particular, we will describe the roots of positive definite quadratic forms and the roots of quadratic forms that are principal (see Simson, 2010a). The algorithms and results we present here are successfully used in the representation theory of finite groups and algebras.
    Źródło:
    Control and Cybernetics; 2011, 40, 2; 491-514
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Second order conditions in optimal control problems with mixed equality-type constraints on a variable time interval
    Autorzy:
    Osmolovskii, N. P.
    Powiązania:
    https://bibliotekanauki.pl/articles/970741.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    piecewise continuous control
    maximum principle
    second order necessary or sufficient conditions
    critical cone
    quadratic form
    Opis:
    This paper provides an analysis of second-order necessary or sufficient optimality conditions of Pontryagin or bounded strong minima, for optimal control problems of ordinary differential equations, considered on a nonfixed time interval, with constraints on initial-final time-state as well as mixed state-control constraints of equality type satisfying condition of linear independence of gradients w.r.t. control.
    Źródło:
    Control and Cybernetics; 2009, 38, 4B; 1535-1556
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    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:
    A second-order sufficient condition for a weak local minimum in an optimal control problem with an inequality control constraint
    Autorzy:
    Osmolovskii, Nikolai P.
    Powiązania:
    https://bibliotekanauki.pl/articles/2183496.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    critical cone
    quadratic form
    first order tangent
    second order tangent
    second order optimality conditions
    weak local minimum
    inequality control constraint
    Pontryagin’s maximum principle
    Opis:
    This paper is devoted to a sufficient second-order condition for a weak local minimum in a simple optimal control problem with one control constraint G(u) ≤ 0, given by a C2-function. A similar second-order condition was obtained earlier by the author for a strong minimum in a much more general problem. In the present paper, we would like to take a narrower perspective than before and thus provide shorter and simpler proofs. In addition, the paper uses the first and second order tangents to the set U, defined by the inequality G(u) ≤ 0. The main difficulty of the proof, clearly shown in the paper, refers to the set, where the gradient Hu of the Hamiltonian is small, but the condition of quadratic growth of the Hamiltonian is satisfied. The paper can be valuable for self-explanation and provides a basis for extensions.
    Źródło:
    Control and Cybernetics; 2022, 51, 2; 151--169
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Second-order sufficient conditions for an extremum in optimal control
    Autorzy:
    Osmolovskij, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/206727.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    ekstremala łamana
    forma kwadratowa
    minimum silne
    minimum słabe
    stożek krytyczny
    warunek dostatecznej optymalności
    zasada maksimum
    accessory problem
    broken extremal
    control discontinuities
    critical cone
    maximum principle
    quadratic form
    strong minimum
    suffcient optimality condition
    weak minimum
    Opis:
    Suffcient quadratic optimality conditions for a weak and a strong minimum are stated in an optimal control problem on a fixed time interval with mixed state-control constraints, under the assumption that the gradients of all active mixed constraints with respect to control are linearly independent. The conditions are stated for the cases of both continuous and discontinuous controls and guarantee in each case a lower bound of the cost function increase at t1e reference point. They are formulated in terms of an accessory problem with quadratic form, which must be positive-definite on the so-called critical cone. In the case of discontinuous control the quadratic form has some new terms related to the control discontinuity.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 803-831
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Testing of the Prediction Unbiasedness on the Basis of Janus Quotient
    O testowaniu nieobciążoności predykcji na podstawie współczynnika Janusowego
    Autorzy:
    Wywiał, Janusz
    Powiązania:
    https://bibliotekanauki.pl/articles/1808297.pdf
    Data publikacji:
    2009-06-30
    Wydawca:
    Główny Urząd Statystyczny
    Tematy:
    test statistic
    prediction error
    unbiasednees
    Janus quotient
    quadratic form of normally distributed vector
    approximation of distribution function
    residual variance
    prediction variance
    Test statystyczny
    błąd predykcji
    nieobciążoność
    współczynnik Janusowy
    forma
    kwadratowa wektora o rozkładzie normalnym
    aproksymacja funkcji dystrybuanty
    wariancja resztowa
    wariancja predykcji
    Opis:
    The problem of choosing the appropriate predictor is being considered. Generally, in this paper the analysis is focused on the problem of unbiasedness of the predictors. Several tests attempting to verify the unbiasedness of three predictors of the linear trend are proposed. They are based on some modifications of the well-known Janus quotient being a ratio of the variance of prediction errors and the residual variance. In general each of the considered test statistic can be represented as the ratio of two quadratic forms of normal vectors. These two quadratic forms can be dependent, so its distribution function has to be approximated. An example of testing hypothesis on unbiasedness is presented. The obtained results can be generalized in the case of prediction on the basis of regression models.
    W pracy jest rozważany problem wyboru odpowiedniego predykatora. Przyjęto, że postulowanym kryterium tego wyboru jest jego nieobciążoność. W pracy są proponowane testy na nieobciążoność predykcji trzech predyktorów trendu liniowego. Punktem wyjścia konstrukcji sprawdzianów testów jest znany współczynnik Janusowy używany do oceny dokładności ciągów wyznaczanych prognoz, który jest ilorazem wariancji predykcji ex-post i wariancji resztowej. Z formalnego punktu widzenia każdy z rozważanych sprawdzianów testów jest ilorazem dwóch form kwadratowych wektora zmiennych o rozkładzie normalnym. Te formy kwadratowe mogą być zależne. Dlatego w celu wyznaczenia rozkładu prawdopodobieństwa sprawdzianu testu jest adaptowana jedna ze znanych metod pozwalających na przybliżone wyliczanie wartości jego dystrybuanty. Rozważania zilustrowano przykładem. Otrzymane w pracy wyniki można uogólnić na przypadek predykcji na podstawie modelu regresji.
    Źródło:
    Przegląd Statystyczny; 2009, 56, 2; 42-51
    0033-2372
    Pojawia się w:
    Przegląd Statystyczny
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-12 z 12

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