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    Wyświetlanie 1-4 z 4
    Tytuł:
    Generalized trend constants of Lipschitz mappings
    Autorzy:
    Szczepanik, Mariusz
    Powiązania:
    https://bibliotekanauki.pl/articles/747268.pdf
    Data publikacji:
    2018
    Wydawca:
    Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
    Tematy:
    Banach space
    Lipschitz mapping
    fixed point
    Opis:
    In 2015, Goebel and Bolibok defined the initial trend coefficient of a mapping and the class of initially nonexpansive mappings. They proved that the fixed point property for nonexpansive mappings implies the fixed point property for initially nonexpansive mappings. We generalize the above concepts and prove an analogous fixed point theorem. We also study the initial trend coefficient more deeply.
    Źródło:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2018, 72, 2
    0365-1029
    2083-7402
    Pojawia się w:
    Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the contingent of the graph of the sum of two mappings
    Autorzy:
    Turowska, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/122062.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
    Tematy:
    mappings
    graph
    Lipschitz mapping
    odwzorowania
    graf
    odwzorowanie Lipschitza
    Opis:
    It is shown that the graph of the sum of two Lipschitz mappings of the real line into a normed space of infinite dimension, whose graphs have tangents, need not have a tangent. Moreover, it turns out that the contingent of the graph of their linear combination may depend on the coefficients of that combination in quite "nonlinear" way.
    Źródło:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2013, 18; 55-66
    2450-9302
    Pojawia się w:
    Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Representations of hypersurfaces and minimal smoothness of the midsurface in the theory of shells
    Autorzy:
    Delfour, M. C.
    Powiązania:
    https://bibliotekanauki.pl/articles/970297.pdf
    Data publikacji:
    2008
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    thin shell
    asymptotic shell
    midsurface
    smoothness
    representation of a surface
    oriented distance function
    bi-Lipschitz mapping
    tubular neighborhood
    Opis:
    Many hypersurfaces ω in R^N can be viewed as a subset of the boundary Γ of an open subset Ω of R^N. In such cases, the gradient and Hessian matrix of the associated oriented distance function ba to the underlying set Ω completely describe the normal and the N fundamental forms of ω, and a fairly complete intrinsic theory of Sobolev spaces on C1'1-hypersurfaces is available in Delfour (2000). In the theory of thin shells, the asymptotic model only depends on the choice of the constitutive law, the midsurface, and the space of solutions that properly handles the loading applied to the shell and the boundary conditions. A central issue is the minimal smoothness of the midsurface to still make sense of asymptotic membrane shell and bending equations without ad hoc mechanical or mathematical assumptions. This is possible for a C1'1-midsurface with or without boundary and without local maps, local bases, and Christoffel symbols via the purely intrinsic methods developed by Delfour and Zolesio (1995a) in 1992. Anicic, LeDret and Raoult (2004) introduced in 2004 a family of surfaces ω that are the image of a connected bounded open Lipschitzian domain in R² by a bi-Lipschitzian mapping with the assumption that the normal field is globally Lipschizian. >From this, they construct a tubular neighborhood of thickness 2h around the surface and show that for sufficiently small h the associated tubular neighborhood mapping is bi-Lipschitzian. We prove that such surfaces are C1'1-surfaces with a bounded measurable second fundamental form. We show that the tubular neighborhood can be completely described by the algebraic distance function to ω and that it is generally not a Lipschitzian domain in R³ by providing the example of a plate around a flat surface ω verifying all their assumptions. Therefore, the G1-join of K-regular patches in the sense of Le Dret (2004) generates a new K-regular patch that is a C1'1-surface and the join is C1'1. Finally, we generalize everything to hypersurfaces generated by a bi-Lipschitzian mapping defined on a domain with facets (e.g. for sphere, torus). We also give conditions for the decomposition of a C1'1-hypersurface into C1'1-patches.
    Źródło:
    Control and Cybernetics; 2008, 37, 4; 879-911
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    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 1-4 z 4

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