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    Wyświetlanie 1-11 z 11
    Tytuł:
    On a property of weak resolvents and its application to a spectral problem
    Autorzy:
    Uetake, Yoichi
    Powiązania:
    https://bibliotekanauki.pl/articles/1294816.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    weak resolvent
    cyclic vector
    spectral radius
    Hardy class
    operator model theory
    scattering theory
    control theory
    Opis:
    We show that the poles of a resolvent coincide with the poles of its weak resolvent up to their orders, for operators on Hilbert space which have some cyclic properties. Using this, we show that a theorem similar to the Mlak theorem holds under milder conditions, if a given operator and its adjoint have cyclic vectors.
    Źródło:
    Annales Polonici Mathematici; 1997, 66, 1; 263-268
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Approximation of eigenvalues for a class of differential problems on an infinite interval
    Autorzy:
    Regińska, Teresa
    Powiązania:
    https://bibliotekanauki.pl/articles/748517.pdf
    Data publikacji:
    1978
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Spectral theory, Sturm-Liouville, and scattering theory
    eigenfunctions, eigenvalues, and expansions
    Eigenvalue problems
    Teoria spektralna, funkcje własne, wartości własne
    Opis:
    The author investigates the problem (1) Lu=λu, u(0)=0, u∈L2(0,∞), where L=d2/dt2+a(t)d/dt+b(t) and domL={u∈L2(0,∞):du/dt absolutely continuous, d2u/dt2∈L2(0,∞), u(0)=0}. She proves that under certain conditions it is possible to approximate the spectrum of (1) by means of the spectrum of a suitable problem of the form −u′′+c(t)u=λu, u(0)=0, u′(n)=α(n)u(n).
    The author investigates the problem (1) Lu=λu, u(0)=0, u∈L2(0,∞), where L=d2/dt2+a(t)d/dt+b(t) and domL={u∈L2(0,∞):du/dt absolutely continuous, d2u/dt2∈L2(0,∞), u(0)=0}. She proves that under certain conditions it is possible to approximate the spectrum of (1) by means of the spectrum of a suitable problem of the form −u′′+c(t)u=λu, u(0)=0, u′(n)=α(n)u(n).The review of the paper is available at MR0518666.
    Źródło:
    Mathematica Applicanda; 1978, 6, 13
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A first-order spectral phase transition in a class of periodically modulated Hermitian Jacobi matrices
    Autorzy:
    Pchelintseva, I.
    Powiązania:
    https://bibliotekanauki.pl/articles/255740.pdf
    Data publikacji:
    2008
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Jacobi matrices
    spectral phase transition
    absolutely continuous spectrum
    pure point spectrum
    discrete spectrum
    subordinacy theory
    asymptotics of generalized eigenvectors
    Opis:
    We consider self-adjoint unbounded Jacobi matrices with diagonal q(n) = b(n)n and off-diagonal entries λ(n) = n, where b(n) is a 2-periodical sequence of real numbers. The parameter space is decomposed into several separate regions, where the spectrum of the operator is either purely absolutely continuous or discrete. We study the situation where the spectral phase transition occurs, namely the case of b(1)b(2) = 4. The main motive of the paper is the investigation of asymptotics of generalized eigenvectors of the Jacobi matrix. The pure point part of the spectrum is analyzed in detail.
    Źródło:
    Opuscula Mathematica; 2008, 28, 2; 137-150
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Clustering based on eigenvectors of the adjacency matrix
    Autorzy:
    Lucińska, M.
    Wierzchoń, S. T.
    Powiązania:
    https://bibliotekanauki.pl/articles/331178.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    spectral clustering
    adjacency matrix eigenvalues
    adjacency matrix eigenvectors
    graph perturbation theory
    eigengap heuristics
    klastrowanie widmowe
    macierz sąsiedztwa
    teoria grafów
    Opis:
    The paper presents a novel spectral algorithm EVSA (eigenvector structure analysis), which uses eigenvalues and eigenvectors of the adjacency matrix in order to discover clusters. Based on matrix perturbation theory and properties of graph spectra we show that the adjacency matrix can be more suitable for partitioning than other Laplacian matrices. The main problem concerning the use of the adjacency matrix is the selection of the appropriate eigenvectors. We thus propose an approach based on analysis of the adjacency matrix spectrum and eigenvector pairwise correlations. Formulated rules and heuristics allow choosing the right eigenvectors representing clusters, i.e., automatically establishing the number of groups. The algorithm requires only one parameter—the number of nearest neighbors. Unlike many other spectral methods, our solution does not need an additional clustering algorithm for final partitioning. We evaluate the proposed approach using real-world datasets of different sizes. Its performance is competitive to other both standard and new solutions, which require the number of clusters to be given as an input parameter.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2018, 28, 4; 771-786
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Asymptotic properties of semigroups of Markov operators
    Autorzy:
    Lasota, Andrezj
    Powiązania:
    https://bibliotekanauki.pl/articles/748533.pdf
    Data publikacji:
    2002
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Ergodic theorems, spectral theory, Markov operators
    Fractals
    Discrete-time Markov processes on general state spaces
    Opis:
    .
    The author provides an overview of some main ideas and methods developed in the study of asymptotic behavior of Markov operators, and the following three properties of a Markov operator P are considered: (1) Asymptotic stability, (2) Asymptotic periodicity, (3) Sweeping with respect to a family A0⊂A: lim∫APnfdm=0 for all AA0 and fD. Applications of these results appear in the study of locally expanding mappings (on intervals, on the real line and on manifolds), integral operators (especially of Volterra types), dynamical systems with stochastic perturbations, and evolution equations. In an excellent book by the author and M. C. Mackey [Chaos, fractals, and noise, Second edition, Springer, New York, 1994; MR1244104], these and many more related results are presented in much more detail. The last section of the present paper concerns Markov operators acting on finite Borel measures on a Polish metric space. The author shows how this result yields insight into attractors of iterated function systems: they appear to be supports of invariant measures of corresponding Markov operators. The paper is the Wacław Sierpiński Lecture for the year 2002.
    Źródło:
    Mathematica Applicanda; 2002, 30, 44/03
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Surgery of Graphs: M-Function and Spectral Gap
    Autorzy:
    Kurasov, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/1030010.pdf
    Data publikacji:
    2017-12
    Wydawca:
    Polska Akademia Nauk. Instytut Fizyki PAN
    Tematy:
    quantum graphs
    spectral theory
    Opis:
    We discuss behaviour of the spectral gap for quantum graphs when two metric graphs are glued together. It appears that precise answer to this question can be given using a natural generalisation of the Titchmarsh-Weyl M-functions.
    Źródło:
    Acta Physica Polonica A; 2017, 132, 6; 1666-1671
    0587-4246
    1898-794X
    Pojawia się w:
    Acta Physica Polonica A
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Spontaneous decay of level from spectral theory point of view
    Autorzy:
    Ianovich, Eduard
    Powiązania:
    https://bibliotekanauki.pl/articles/2048989.pdf
    Data publikacji:
    2021
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    spectral theory
    quantum field theory
    self-adjoint operators
    absolutely continuous spectrum
    spontaneous decay
    Opis:
    In quantum field theory it is believed that the spontaneous decay of excited atomic or molecular level is due to the interaction with continuum of field modes. Besides, the atom makes a transition from upper level to lower one so that the probability to find the atom in the excited state tends to zero. In this paper it will be shown that the mathematical model in single-photon approximation may predict another behavior of this probability generally. Namely, the probability to find the atom in the excited state may tend to a nonzero constant so that the atom is not in the pure state finally. This effect is due to that the spectrum of the complete Hamiltonian is not purely absolutely continuous and has a discrete level outside the continuous part. Namely, we state that in the corresponding invariant subspace, determining the time evolution, the spectrum of the complete Hamiltonian when the field is considered in three dimensions may be not purely absolutely continuous and may have an eigenvalue. The appearance of eigenvalue has a threshold character. If the field is considered in two dimensions the spectrum always has an eigenvalue and the decay is absent.
    Źródło:
    Opuscula Mathematica; 2021, 41, 6; 849-859
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the central limit theorem for some birth and death processes
    Autorzy:
    Chojecki, Tymoteusz
    Powiązania:
    https://bibliotekanauki.pl/articles/747125.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Central limit theorem
    Markov chain
    Lamperti’s problem
    birth and death processes
    Kipnis-Varadhan theory
    spectral gap
    Opis:
    Suppose that \(\{Xn: n \geq 0\}\) is a stationary Markov chain and \(V\) is a certain function on a phase space of the chain, called an observable. We say that the observable satisfies the central limit theorem (CLT) if \(Y_n :=N^{-1/2}\sum_{n=0}^N V (X_n)\) converge in law to a normal random variable, as \(N \to+\infty\). For a stationary Markov chain with the \(L^2\) spectral gap the theorem holds for all \(V\) such that \(V (X_0)\) is centered and square integrable, see Gordin [7]. The purpose of this article is to characterize a family of observables \(V\) for which the CLT holds for a class of birth and death chains whose dynamics has no spectral gap, so that Gordin’s result cannot be used and the result follows from an application of Kipnis-Varadhan theory.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2011, 65, 1
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The approximate location of imperfection in a unit circle using the spectrum of Laplace operator as a research tool
    Widmo operatora Laplacea jako narzędzie do wykrywania przybliżonej lokalizacji uszkodzeń w kole jednostkowym
    Autorzy:
    Brzęk, M.
    Zagórowska, M.
    Mitkowski, W.
    Powiązania:
    https://bibliotekanauki.pl/articles/282126.pdf
    Data publikacji:
    2015
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Laplace operator
    location of imperfections
    spectrum analysis
    spectral theory
    eigenvalues
    operator Laplacea
    Opis:
    In the following article we will try to find the dependence between the location of imperfections in a closed domain and the spectrum of the Laplace operator for this region. In the theoretical part we will define the spectral problem which is solved by eigenvalues. These eigenvalues are dependent on location and size of the imperfection. However, we are interested in the inverse task which consists in localizing the imperfection of the domain on a basis of the spectrum of the operator.
    W artykule przeanalizowano zastosowanie widma operatora Laplace'a jako narzędzia do przybliżonej lokalizacji uszkodzeń w kole jednostkowym. W części teoretycznej zdefiniowano zagadnienie spektralne rozwiązywane za pomocą wartości własnych. Znalezione wartości zależą od położenia i rozmiaru uszkodzeń. W artykule został zdefiniowany problem odwrotny, który polega na znalezieniu miejsca uszkodzenia na podstawie znanego widma.
    Źródło:
    Automatyka / Automatics; 2015, 19, 1; 9-15
    1429-3447
    2353-0952
    Pojawia się w:
    Automatyka / Automatics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Inviscid instability of the hyperbolic-tangent velocity profile-spectral "tau" solution
    Autorzy:
    Bogusławski, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1955811.pdf
    Data publikacji:
    2001
    Wydawca:
    Politechnika Gdańska
    Tematy:
    parallel free shear layer
    free shear layer
    linear stability theory
    spectral approximation
    Tau method
    Q-R algorithm
    Opis:
    The paper presents a spectral solution of the Rayleigh equation for the case of parallel, free shear layer with the hyperbolic-tangent mean velocity profile. The expansion of the eigenfunction into the Chebyshev polynomial series allowed transformation of the differential eigenvalue problem into the general algebraic one. The standard algebraic eigenvalue problem was obtained by the use of Gary & Helgasson transformation. The results were compared with the shooting method. Although the calculations were carried out in order to validate the method, some additional study of the velocity ratio and momentum thickness influence on the temporal eigenmode growth rate was also performed.
    Źródło:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2001, 5, 2; 155-164
    1428-6394
    Pojawia się w:
    TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Convergence in the generalized sense relative to Banach algebras of operators and in LMC-algebras
    Autorzy:
    Barnes, Bruce A.
    Powiązania:
    https://bibliotekanauki.pl/articles/1289118.pdf
    Data publikacji:
    1995
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    convergence in the generalized sense
    spectral theory
    LMC-algebra
    Opis:
    The notion of convergence in the generalized sense of a sequence of closed operators is generalized to the situation where the closed operators involved are affiliated with a Banach algebra of operators. Also, the concept of convergence in the generalized sense is extended to the context of a LMC-algebra, where it applies to the spectral theory of the algebra.
    Źródło:
    Studia Mathematica; 1995, 115, 1; 87-103
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-11 z 11

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