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    Wyświetlanie 1-12 z 12
    Tytuł:
    Landau-type theorem for variable Lebesgue spaces
    Autorzy:
    Maligranda, Lech
    Wnuk, Witold
    Powiązania:
    https://bibliotekanauki.pl/articles/746364.pdf
    Data publikacji:
    2015
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Köthe dual spaces, associate spaces, Nakano spaces, variable Lebesgue spaces
    Opis:
    We describe, using elementary methods, the K\"othe dual of variable Lebesgue spaces \(L^{p(\cdot)},\) called also Nakano spaces, independenly for \(p(\cdot) \in (1, \infty)\) and \(p(\cdot) \in (0, 1)\). The case when \(p(\cdot) \in [1, \infty]\) is also included.
    Źródło:
    Commentationes Mathematicae; 2015, 55, 2
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Spaces defined by the level function and their duals
    Autorzy:
    Sinnamon, Gord
    Powiązania:
    https://bibliotekanauki.pl/articles/1290183.pdf
    Data publikacji:
    1994
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    function spaces
    Hölder's inequality
    Hardy's inequality
    dual spaces
    Opis:
    The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of $L^p$. These domains are shown to be Banach spaces which, although closely tied to $L^p$ spaces, are not reflexive. A related construction is given which characterizes their dual spaces.
    Źródło:
    Studia Mathematica; 1994, 111, 1; 19-52
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some remarks on level functions and their applications
    Autorzy:
    Foralewski, Paweł
    Leśnik, Karol
    Maligranda, Lech
    Powiązania:
    https://bibliotekanauki.pl/articles/745238.pdf
    Data publikacji:
    2016
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    level functions, dual spaces, Orlicz−Lorentz spaces, Halperin spaces, Cesàro spaces
    Opis:
    A comparison of the level functions considered by Halperin and Sinnamon is discussed. Moreover, connections between Lorentz-type spaces, down spaces, Cesàro spaces, and Sawyer's duality formula are explained. Applying Sinnamon's ideas, we prove the duality theorem for Orlicz−Lorentz spaces which generalizes a recent result by Kamińska, Leśnik, and Raynaud (and Nakamura). Finally, some applications of the level functions to the geometry of Orlicz−Lorentz spaces are presented.
    Źródło:
    Commentationes Mathematicae; 2016, 56, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Finegrained 3D differential operators hint at the inevitability of their dual reciprocal portrayals
    Autorzy:
    Czajko, Jakub
    Powiązania:
    https://bibliotekanauki.pl/articles/1065412.pdf
    Data publikacji:
    2019
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Finegrained differential operators
    paired dual reciprocal spaces
    Opis:
    Extending differential operators during transition from 3D operations to prospective 4D operations imply the need to expand their 4D range far beyond the usual set-theoretical universe from which subsets of the domain are composed. The prospective infrastructural expansion related to the attempted extending of operations virtually requires an extra dual reciprocal space and thus implies presence of a certain multispatial structure of both the mathematical- and the corresponding to it physical reality. At this point the implication is only operational for it is deduced from the attempted extension of operational domain/scope of geometric differential operator, which, in turn, demands an expansion of their range. The necessary presence of an extra space is not being postulated but emerges from comparative evaluations of differential operators. The operational necessity of presence of paired dual reciprocal spaces or quasispatial structures also generalizes contravariance for multispatiality.
    Źródło:
    World Scientific News; 2019, 132; 98-120
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On locally Hilbert spaces
    Autorzy:
    Gheondea, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/952830.pdf
    Data publikacji:
    2016
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    locally Hilbert space
    inductive limit
    projective limit
    orthocomplemented subspaces
    linear functional
    dual spaces
    Opis:
    This is an investigation of some basic properties of strictly inductive limits of Hilbert spaces, called locally Hilbert spaces, with respect to their topological properties, the geometry of their subspaces, linear functionals and dual spaces.
    Źródło:
    Opuscula Mathematica; 2016, 36, 6; 735-747
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Multiplicative inversions involving real zero and neverending ascending infinity in the multispatial framework of paired dual reciprocal spaces
    Autorzy:
    Czajko, Jakub
    Powiązania:
    https://bibliotekanauki.pl/articles/1031265.pdf
    Data publikacji:
    2021
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Multiplicative inversions
    dual reciprocal spaces
    multispatial algebraic structures
    Opis:
    Inverses of complex numbers and of analytic functions are composites of mixed type for they are multiplicative inverses (i.e. reciprocals) of the modulus/magnitude combined with additive reverses of the argument/angle. Hence, the mixed inverses in the complex domain ℂ are not really reciprocals and therefore their lack of truly multiplicative reciprocity was a contributing reason that spurred the – unnecessary though still ongoing – prohibition of division by zero which is the natural reciprocal of the neverending ascending real infinity. Truly reciprocal algebraic operations are presented (via multiplicative algebraic inversions) by few examples within the new multispatial framework in terms of their abstract algebraic representations subscripted by the native algebraic bases of the mutually paired dual reciprocal (even though algebraic) spaces in which the inversive operations are performed.
    Źródło:
    World Scientific News; 2021, 151; 1-15
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Unrestricted division by zero as multiplication by the – reciprocal to zero – infinity
    Autorzy:
    Czajko, Jakub
    Powiązania:
    https://bibliotekanauki.pl/articles/1030823.pdf
    Data publikacji:
    2020
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Division by zero
    multiplication by infinity
    paired dual reciprocal spaces
    Opis:
    It is demonstrated that quite unrestricted operation of conventional division by the real number zero can be implemented via multiplication by the – reciprocal to zero – ascending infinity in paired dual reciprocal spaces, provided that the “real” zero and the infinity are mutually reciprocal (i.e. multiplicatively inverse). Since the infinity is not an absolute concept independent of the particular circumstances in which it is being determined, the value of the setvalued infinity is not fixed but depends on an influence function that is usually applied for evaluation of integral kernels, the operations proposed here are always defined relative to a certain abstract influence function. The conceptual and operational validity of the proposed unrestricted division and multiplication by zero, is authenticated operationally by fairly simple example, using an evaluation of Frullani’s integral.
    Źródło:
    World Scientific News; 2020, 145; 180-197
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Fréchet spaces of continuous vector-valued functions: Complementability in dual Fréchet spaces and injectivity
    Autorzy:
    Domański, P.
    Drewnowski, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/1293180.pdf
    Data publikacji:
    1992
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    Fréchet spaces of (weakly, weak*) continuous vector-valued functions injective Fréchet spaces
    spaces complemented in dual Fréchet spaces
    complemented copies of $c_0$
    Josefson-Nissenzweig theorem
    Opis:
    Fréchet spaces of strongly, weakly and weak*-continuous Fréchet space valued functions are considered. Complete solutions are given to the problems of their injectivity or embeddability as complemented subspaces in dual Fréchet spaces.
    Źródło:
    Studia Mathematica; 1992, 102, 3; 257-267
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dual Reciprocal Scalar Potentials Paired via Differential Operators in Frenet Frames Make the Operators to Act Simultaneously in Each of Two Paired 3D Reciprocal Spaces
    Autorzy:
    Czajko, Jakub
    Powiązania:
    https://bibliotekanauki.pl/articles/1046557.pdf
    Data publikacji:
    2019
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    3D intraspatial and interspatial duality principles
    3D potentials in inertially moving trihedron
    Paired 3D dual reciprocal spaces
    scalar covariant differential operator SCovar
    Opis:
    Extending the operating domain of 3D geometric differential operator expands also the range of its operations onto paired 3D dual reciprocal spaces as well as the scope of their validity into paired 3D multispatial structures. Intraspatial duality principle for paired 3D dual reciprocal spaces is inferred from differential operations performed on the dual reciprocal 3D spaces. The new scalar differential operator SCovar as multiplicative inverse of the scalar gradient differential operator SGrad is proposed here to deliver scalar components of covariant differentials in order to accommodate both the operational and structural legitimacy of differential and integral operations performed in 3D dual reciprocal spaces. From preliminarily formulated abstract intraspatial duality principle a generalized interspatial duality principle is deduced and the connection of paired multispatial structures established. It is shown that the finegrained geometric differential operator GDiff acts simultaneously in each of the paired dual reciprocal spaces, which is its formerly unknown operational feature.
    Źródło:
    World Scientific News; 2019, 137; 96-118
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Duality and some topological properties of vector-valued function spaces
    Autorzy:
    Feledziak, Krzysztof
    Powiązania:
    https://bibliotekanauki.pl/articles/746589.pdf
    Data publikacji:
    2008
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    vector-valued function spaces
    locally solid topologies
    KB-spaces
    Levy topologies
    Lebesgue topologies
    order dual
    order continuous dual
    perfectness
    Opis:
    Let \(E\) be an ideal of \(L^0\) over \(\sigma\)-finite measure space \((\Omega, \Sigma, \mu)\) and let \((X, \| \cdot \|_X)\) be a real Banach space. Let \(E(X)\) be a subspace of the space \(L^0(X)\) of \(\mu\)-equivalence classes of all strongly \(\Sigma\)-measurable functions \(f\colon \Omega \to X\) and consisting of all those \(f\in L^0(X)\), for which the scalar function \(\tilde{f} = \|f (\cdot)\|_X\) belongs to \(E\). Let \(E\) be equipped with a Hausdorff locally convex-solid topology \(\xi\) and let \(\xi\) stand for the topology on \(E(X)\) associated with \(\xi\). We examine the relationship between the properties of the space \((E(X), \xi)\) and the properties of both the spaces \((E, \xi)\) and \((X, \|· \|_X)\). In particular, it is proved that \(E(X)\) (embedded in a natural way) is an order closed ideal of its bidual iff \(E\) is an order closed ideal of its bidual and \(X\) is reflexive. As an application, we obtain that \(E(X)\) is perfect iff \(E\) is perfect and \(X\) is reflexive.
    Źródło:
    Commentationes Mathematicae; 2008, 48, 1
    0373-8299
    Pojawia się w:
    Commentationes Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Cyberparki jako hybrydowe przestrzenie uczenia się: rozważania na marginesie projektu COST
    Autorzy:
    Agnieszka, Kruszwicka,
    Michał, Klichowski,
    Powiązania:
    https://bibliotekanauki.pl/articles/892536.pdf
    Data publikacji:
    2019-04-29
    Wydawca:
    Uniwersytet Warszawski. Wydawnictwa Uniwersytetu Warszawskiego
    Tematy:
    public green spaces
    outdoor learning
    technology-enhanced learning
    dual-task costs
    smartphone
    Opis:
    CyberParks will be hybrid spaces of future cities. Learning in CyberParks will take the form of technology-enhanced outdoor learning and will become an important concept that can be used in practice in order to provide an answer to numerous problems of educational institutions, related to students’ lack of contact with nature and consolidation of their sedentary lifestyle. In this paper we discuss evidences from the CyberParks COST project and we present recommendations regarding the constructions of CyberParks. We point out, for example, that when designing CyberParks one has to think not only about the technological infrastructure, but also about making sitting spots for using learning technology. We also present the original project of such an object.
    Źródło:
    Kwartalnik Pedagogiczny; 2019, 64(1(251)); 71-83
    0023-5938
    Pojawia się w:
    Kwartalnik Pedagogiczny
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A functional S-dual in a strong shape category
    Autorzy:
    Bauer, Friedrich
    Powiązania:
    https://bibliotekanauki.pl/articles/1205409.pdf
    Data publikacji:
    1997
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    S-duality
    functional S-dual
    virtual spaces
    weak homotopy type
    compact-open strong shape
    Opis:
    In the S-category ${\got P}$ (with compact-open strong shape mappings, cf. §1, instead of continuous mappings, and arbitrary finite-dimensional separable metrizable spaces instead of finite polyhedra) there exists according to [1], [2] an S-duality. The S-dual $DX, X = (X,n) ∈ {\got P}$, turns out to be of the same weak homotopy type as an appropriately defined functional dual $\overline{(S^0)^X}$ (Corollary 4.9). Sometimes the functional object $\overline{X^Y}$ is of the same weak homotopy type as the "real" function space $X^Y$ (§5).
    Źródło:
    Fundamenta Mathematicae; 1997, 154, 3; 261-274
    0016-2736
    Pojawia się w:
    Fundamenta Mathematicae
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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