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    Tytuł:
    Stability of Multi-Dimensional Discrete Systems With Varying Structure
    Autorzy:
    Dymkov, M.
    Gaishun, I.
    Powiązania:
    https://bibliotekanauki.pl/articles/908265.pdf
    Data publikacji:
    1999
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    układ wielowymiarowy
    złożenie krzywoliniowe
    stabilność
    multi-dimensional systems
    total solvability
    curvilinear composition
    stability
    Opis:
    A new class of multi-dimensional discrete systems with varying structureis introduced. The notions of total solvability, p_t-boundedness, p_t-stability and asymptotic stability are defined. For studying properties of the solutions for the considered systems a curvilinear composition of mappings along discrete curves is used. Total solvability conditions similar to the Frobenius ones are obtained. Sufficient conditions for p_t-stability and asymptotic stability based on the Lyapunov functional method are also established. A two-dimensional system of Volterra equations is presented as an example of equations with varying structure.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 1999, 9, 4; 789-799
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Does Science Progress Towards Ever Higher Solvability Through Feedbacks Between Insights and Routines?
    Autorzy:
    Marciszewski, Witold
    Powiązania:
    https://bibliotekanauki.pl/articles/561316.pdf
    Data publikacji:
    2018
    Wydawca:
    Polskie Towarzystwo Semiotyczne
    Tematy:
    Algorithm
    arithmetic
    axiom
    axiomatic formalized theory
    concept
    decidability
    feedback
    insight (intuition)
    mathematics
    mechanism
    mentalism
    oracle
    problem
    problem-solving
    progress
    routine procedure
    science
    solvability
    Opis:
    The affirmative answer to the title question is justified in two ways: logical and empirical. (1) The logical justification is due to Gödel’s discovery (1931) that in any axiomatic formalized theory, having at least the expressive power of PA (Peano Arithmetic), at any stage of development there must appear unsolvable problems. However, some of them become solvable in a further development of the theory in question, owing to subsequent investigations. These lead to new concepts, expressed with additional axioms or rules. Owing to the so-amplified axiomatic basis, new routine procedures like algorithms, can be reached. Those, in turn, help to gain new insights which lead to still more powerful axioms, and consequently again to ampler algorithmic resources. Thus scientific progress proceeds to an ever higher scope of solvability. (2) The existence of such feedback cycles – in a formal way rendered with Turing’s systems of logic based on ordinal (1939) – gets empirically supported by the history of mathematics and other exact sciences. An instructive instance of such a process is found in the history of the number zero. Without that insight due to some ancient Hindu mathematicians there could not arise such an axiomatic theory as PA. It defines the algorithms of arithmetical operations, which in turn help intuitions; those, in turn, give rise to algorithmic routines, not available in any of the previous phases of the process in question. While the logical substantiation of the point of this essay is a well-established result of logico-semantic inquiries, its empirical claim, based on historical evidences, remains open for discussion. Hence the author’s intention to address philosophers and historians of science, and to encourage their critical responses.
    Źródło:
    Studia Semiotyczne; 2018, 32, 2; 153-185
    0137-6608
    Pojawia się w:
    Studia Semiotyczne
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the solvability of Dirichlet problem for the weighted p-Laplacian
    Autorzy:
    Mielczarek, Dominik
    Rydlewski, Jerzy
    Szlachtowska, Ewa
    Powiązania:
    https://bibliotekanauki.pl/articles/729562.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
    Tematy:
    weighted p-Laplacian
    weak solutions
    solvability
    semi-inner product spaces
    Opis:
    In this paper we are concerned with the existence and uniqueness of the weak solution for the weighted p-Laplacian. The purpose of this paper is to discuss in some depth the problem of solvability of Dirichlet problem, therefore all proofs are contained in some detail. The main result of the work is the existence and uniqueness of the weak solution for the Dirichlet problem provided that the weights are bounded. Furthermore, under this assumption the solution belongs to the Sobolev space $W₀^{1,p}(Ω)$.
    Źródło:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2014, 34, 1; 89-103
    1509-9407
    Pojawia się w:
    Discussiones Mathematicae, Differential Inclusions, Control and Optimization
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the solvability of Dirichlet problem for the weighted p-Laplacian
    Autorzy:
    Szlachtowska, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/255957.pdf
    Data publikacji:
    2012
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    p-Laplacian
    weak solutions
    solvability
    Opis:
    The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted ρ-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces.
    Źródło:
    Opuscula Mathematica; 2012, 32, 4; 775-781
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The $L^p$ solvability of the Dirichlet problems for parabolic equations
    Autorzy:
    Tao, Xiang Xing
    Powiązania:
    https://bibliotekanauki.pl/articles/1206127.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    parabolic equation
    $L^p$ solvability
    Dirichlet problems
    Lip(1,1/2) cylinder
    Opis:
    For two general second order parabolic equations in divergence form in Lip(1,1/2) cylinders, we give a criterion for the preservation of $L^p$ solvability of the Dirichlet problems.
    Źródło:
    Studia Mathematica; 2000, 139, 1; 69-80
    0039-3223
    Pojawia się w:
    Studia Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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