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    Wyświetlanie 1-3 z 3
    Tytuł:
    On weak solutions of functional-differential abstract nonlocal Cauchy problems
    Autorzy:
    Byszewski, Ludwik
    Powiązania:
    https://bibliotekanauki.pl/articles/1310788.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    abstract Cauchy problems
    functional-differential equation
    nonlocal conditions
    weak solutions
    existence
    uniqueness
    asympto tic stability
    m-accretive operators
    Banach contraction theorem
    Opis:
    The existence, uniqueness and asymptotic stability of weak solutions of functional-differential abstract nonlocal Cauchy problems in a Banach space are studied. Methods of m-accretive operators and the Banach contraction theorem are applied.
    Źródło:
    Annales Polonici Mathematici; 1996-1997, 65, 2; 163-170
    0066-2216
    Pojawia się w:
    Annales Polonici Mathematici
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On a vector-valued local ergodic theorem in $L_∞$
    Autorzy:
    Sato, Ryotaro
    Powiązania:
    https://bibliotekanauki.pl/articles/1217311.pdf
    Data publikacji:
    1999
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    vector-valued local ergodic theorem
    reflexive Banach space
    d-dimensional semigroup of linear contractions
    contraction majorant
    Opis:
    Let $T = {T(u): u ∈ ℝ_d^{+}}$ be a strongly continuous d-dimensional semigroup of linear contractions on $L_1((Ω,Σ,μ);X)$, where (Ω,Σ,μ) is a σ-finite measure space and X is a reflexive Banach space. Since $L_1((Ω,Σ,μ);X)* = L_∞((Ω,Σ,μ);X*)$, the adjoint semigroup $T* = {T*(u): u ∈ ℝ_d^{+}}$ becomes a weak*-continuous semigroup of linear contractions acting on $L_∞((Ω,Σ,μ);X*)$. In this paper the local ergodic theorem is studied for the adjoint semigroup T*. Assuming that each T(u), $u ∈ ℝ_d^{+}$, has a contraction majorant P(u) defined on $L_1((Ω,Σ,μ);ℝ)$, that is, P(u) is a positive linear contraction on $L_1((Ω,Σ,μ);ℝ)$ such that $‖T(u)f(ω)‖ ≤ P(u)‖f(·)‖(ω)$ almost everywhere on Ω for every $⨍ ∈ L_1((Ω,Σ,μ);X)$, we prove that the local ergodic theorem holds for T*.
    Źródło:
    Studia Mathematica; 1999, 132, 3; 285-298
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Automatic simplification of the geometry of a cartographic line using contractive self-mapping – illustrated with an example of a polyline band
    Autorzy:
    Bac-Bronowicz, Joanna
    Banasik, Piotr
    Chrobak, Tadeusz
    Powiązania:
    https://bibliotekanauki.pl/articles/29433667.pdf
    Data publikacji:
    2023-12-07
    Wydawca:
    Oddział Kartograficzny Polskiego Towarzystwa Geograficznego
    Tematy:
    digital generalization
    contractive self-mapping
    Salichtchev’s minimum measures
    geometry of a polyline in the binary tree structure
    Lipschitz’s contraction triangle
    Banach theorem
    Opis:
    The present article is another attempt to adapt map geometry to automatic digital cartography. The paper presents a method of digital polyline generalisation that uses contractive self-mapping. It is a method of simplification, not just an algorithm for simplification. This method in its 1996 version obtained a patent entitled “Method of Eliminating Points in the Process of Numerical Cartographic Generalisation” – Patent Office of the Republic of Poland, No. 181014, 1996. The first results of research conducted using the presented method, with clearly defined data (without singular points of their geometry), were published in the works of the authors in 2021 and 2022. This article presents a transition from the DLM (Digital Landscape Model) to the DCM (Digital Cartographic Model). It demonstrates an algorithm with independent solutions for the band axis and both its edges. The presented example was performed for the so-called polyline band, which can represent real topographic linear objects such as rivers and boundaries of closed areas (buildings, lakes, etc.). An unambiguous representation of both edges of the band is its axis, represented in DLM, which can be simplified to any scale. A direct consequence of this simplification is the shape of the band representing the actual shape of both edges of the object that is classified in the database as a linear object in DCM. The article presents an example performed for the so-called polyline band, which represents real topographic linear objects (roads, rivers) and area boundaries. The proposed method fulfils the following conditions: the Lipschitz condition, the Cauchy condition, the Banach theorem, and the Salichtchev’s standard for object recognition on the map. The presented method is objective in contrast to the previously used approximate methods, such as generalisations that use graph theory and fractal geometry, line smoothing and simplification algorithms, statistical methods with classification of object attributes, artificial intelligence, etc. The presented method for changing the geometry of objects by any scale of the map is 100% automatic, repeatable, and objective; that is, it does not require a cartographer’s intervention.
    Źródło:
    Polish Cartographical Review; 2023, 55, 1; 73-86
    2450-6974
    Pojawia się w:
    Polish Cartographical Review
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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