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    Wyświetlanie 1-7 z 7
    Tytuł:
    Knots in $S^2 x S^1$ derived from Sym(2, ℝ)
    Autorzy:
    Lee, Sang
    Lim, Yongdo
    Park, Chan-Young
    Powiązania:
    https://bibliotekanauki.pl/articles/1205027.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    geodesic
    symmetric matrix
    Shilov boundary
    2-periodic knot
    Opis:
    We realize closed geodesics on the real conformal compactification of the space V = Sym(2, ℝ) of all 2 × 2 real symmetric matrices as knots or 2-component links in $S^2 × S^1$ and show that these knots or links have certain types of symmetry of period 2.
    Źródło:
    Fundamenta Mathematicae; 2000, 164, 3; 241-252
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Asymptotic behaviour and approximation of eigenvalues for unbounded block Jacobi matrices
    Autorzy:
    Malejki, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/255505.pdf
    Data publikacji:
    2010
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    symmetric unbounded Jacobi matrix
    block Jacobi matrix
    tridiagonal matrix
    point spectrum
    eigenvalue
    asymptotics
    Opis:
    The research included in the paper concerns a class of symmetric block Jacobi matrices. The problem of the approximation of eigenvalues for a class of a self-adjoint unbounded operators is considered. We estimate the joint error of approximation for the eigenvalues, numbered from 1 to N, for a Jacobi matrix J by the eigenvalues of the finite submatrix J(n) of order pn x pn, where N = max{k ∈ N : k ≤ rpn} and r ∈ (0, 1) is suitably chosen. We apply this result to obtain the asymptotics of the eigenvalues of J in the case p = 3.
    Źródło:
    Opuscula Mathematica; 2010, 30, 3; 311-330
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Realizacje dodatnie stabilne liniowych układów ciągłych niecałkowitego rzędu z macierzą systemową symetryczną Metzlera
    Positive stable realization problem for linear continuous-time fractional-order systems with symmetric system Metzler matrix
    Autorzy:
    Kaczorek, T.
    Borawski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/154961.pdf
    Data publikacji:
    2014
    Wydawca:
    Stowarzyszenie Inżynierów i Techników Mechaników Polskich
    Tematy:
    liniowy układ ciągły niecałkowitego rzędu
    realizacja dodatnia stabilna
    macierz symetryczna
    macierz Metzlera
    linear continuous-time fractional-order system
    positive stable realization
    symmetric matrix
    Metzler matrix
    Opis:
    Podano warunki dodatniości i stabilności liniowych układów ciągłych niecałkowitego rzędu. Sformułowano problem realizacji dodatnich stabilnych liniowych układów ciągłych niecałkowitego rzędu z macierzą systemową symetryczną Metzlera. Zaproponowano metodę sprowadzania macierzy stanu w postaci kanonicznej Frobeniusa do postaci symetrycznej stabilnej Metzlera. Metodę zobrazowano przykładem numerycznym.
    A dynamical system is called a fractional-order system if its state equations are given by fractional-order derivative of the state vector. Using that theory, more precise mathematical models of systems can be obtained. A dynamical system is called positive if its all inputs, outputs, state variables and initial conditions are nonnegative. Variety of models having positive behavior can be found in engineering, biology, economics etc. Conditions for positivity and stability of linear continuous-time fractional-order systems are presented in the paper. A positive stable realization problem for linear continuous-time fractional-order systems with symmetric system Metzler matrix is formulated. The method for finding the realization is given. The problem is solved and conditions for the existence of the realization are established. The paper is organized as follows. In Section 2 the conditions for internal positivity and stability of linear continuous-time fractional-order systems are given. This section also contains the formulation of the positive stable realization problem for linear continuous-time fractional-order systems with symmetric system Metzler matrix. In Section 3 the procedure for computation of the realization is given. An example illustrating the method proposed is presented in Section 4. Section 5 contains the concluding remarks.
    Źródło:
    Pomiary Automatyka Kontrola; 2014, R. 60, nr 10, 10; 822-825
    0032-4140
    Pojawia się w:
    Pomiary Automatyka Kontrola
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A method for solving a system of linear equations with a symmetric indefinite coefficient matrix
    Autorzy:
    Czochralska, Izabela
    Powiązania:
    https://bibliotekanauki.pl/articles/748583.pdf
    Data publikacji:
    2006
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Gaussian elimination, triangular and triangular-diagonal factorization of a matrix, numerically stable diagonalization of a symmetric indefinite matrix.
    Opis:
    The subject of this article is a numerically stable method for solving nonsingular Cramerian systems of linear equations, with a symmetric indefinite coefficient matrix. It consists in adapting the algorithm presented in [1] that can stably and effectively diagonalize any indefinite symmetric matrix. It is in fact some modification of the Gaussian symmetric elimination procedure.
    Źródło:
    Mathematica Applicanda; 2006, 34, 48/07
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    About a certain relation between two polynomials of the same degree
    Autorzy:
    Piwowarczyk, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/229447.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Czytelnia Czasopism PAN
    Tematy:
    roots of polynomials
    symmetric polynomials
    companion matrix
    eigenvalues
    transformations
    Opis:
    This article presents several different methods for solving the problem of how to find a certain relation defined in chapter 2. The first method deals with the identities known in the theory of symmetric polynomials as the elements of a certain vector space. The second method is designed around the matrix transformations between symmetric polynomials. The third method is designed around the property of a linear operator and its characteristic polynomial. The fourth method is designed in the area of complex numbers, and introduces the multiplication group of 'complex roots of one'. Significant improvement in the third and fourth method is made by introducing so called 'block method'. It facilitates all calculations by making them much shorter. The article ends with an example showing symmetry and regularity of all procedures. Finally, the article shows how to solve the problem for any degree n of the polynomial, and for any degree k. At the end of the paper solutions for n < 5 and k < 5 are tabulated.
    Źródło:
    Archives of Control Sciences; 2011, 21, 1; 85-103
    1230-2384
    Pojawia się w:
    Archives of Control Sciences
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Every reasonably sized matrix group is a subgroup of $S_∞$
    Autorzy:
    Kallman, Robert
    Powiązania:
    https://bibliotekanauki.pl/articles/1205071.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    infinite symmetric group
    matrix groups
    nonarchimedian absolute values
    field extensions
    topological groups
    Opis:
    Every reasonably sized matrix group has an injective homomorphism into the group $S_∞$ of all bijections of the natural numbers. However, not every reasonably sized simple group has an injective homomorphism into $S_∞$.
    Źródło:
    Fundamenta Mathematicae; 2000, 164, 1; 35-40
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Geometric properties of noncommutative symmetric spaces of measurable operators and unitary matrix ideals
    Autorzy:
    Czerwińska, Malgorzata M.
    Kaminska, Anna H.
    Powiązania:
    https://bibliotekanauki.pl/articles/746224.pdf
    Data publikacji:
    2017
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Symmetric spaces of measurable operators
    unitary matrix spaces
    rearrangement invariant spaces
    k-extreme points
    k-convexity
    complex extreme points
    complex convexity
    monotonicity
    (local) uniform (complex and real) convexity
    p-convexity
    Opis:
    This is a review article of geometric properties of noncommutative symmetric spaces of measurable operators \(E(\mathcal{M},\tau)\), where \(\mathcal{M}\) is a semifinite von Neumann algebra with a faithful, normal, semifinite trace \(\tau\), and \(E\) is a symmetric function space. If \(E\subset c_0\) is a symmetric sequence space then the analogous properties in the unitary matrix ideals \(C_E\) are also presented. In the preliminaries we provide basic definitions and concepts illustrated by some examples and occasional proofs. In particular we list and discuss the properties of general singular value function, submajorization in the sense of Hardy, Littlewood and Pólya, Köthe duality, the spaces \(L_p\left(\mathcal{M},\tau\right)\), \(1\leq p < \infty\), the identification of \(C_E\) and \(G(B(H), \operatorname{tr})\) for some symmetric function space \(G\), the commutative case when \(E\) is identified with \(E(\mathcal{N}, \tau)\) for \(\mathcal{N}\) isometric to \(L_\infty\) with the standard integral trace, trace preserving \(*\)-isomorphisms between \(E\) and a \(*\)-subalgebra of \(E\left(\mathcal{M},\tau\right)\), and a general method for removing the assumption of non-atomicity of \(\mathcal{M}\). The main results on geometric properties are given in separate sections. We present the results on (complex) extreme points, (complex) strict convexity, strong extreme points and midpoint local uniform convexity, \(k\)-extreme points and \(k\)-convexity, (complex or local) uniform convexity, smoothness and strong smoothness, (strongly) exposed points, (uniform) Kadec−Klee properties, Banach−Saks properties, Radon−Nikodym property and stability in the sense of Krivine−Maurey. We also state some open problems.
    Źródło:
    Commentationes Mathematicae; 2017, 57, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-7 z 7

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