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Wyszukujesz frazę "Smoluk, Antoni" wg kryterium: Autor

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    Wyświetlanie 1-14 z 14
    Tytuł:
    A simple proof of the four-colors theorem
    Autorzy:
    Smoluk, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/421365.pdf
    Data publikacji:
    2016
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    minimum local coloring
    extension of local coloring
    dissecting ring
    simple map
    production of maps
    Opis:
    The paper includes an inductive proof of the four-color theorem. The notions of producing maps and minimum local colorings are applied.
    Źródło:
    Didactics of Mathematics; 2016, 13(17); 35-38
    1733-7941
    Pojawia się w:
    Didactics of Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Invariant approximations
    Autorzy:
    Smoluk, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/747932.pdf
    Data publikacji:
    1981
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
    Opis:
    W artykule uogólniono twierdzenie Meinardusa(1963). Uogólnienie to jest w dwóch kierunkach: po pierwsze, rezygnujemy z konkretnych przestrzeni funkcyjnych na rzecz dowolnych przestrzeni unormowanych i po drugie, podprzestrzeń modeli - elementów aproksymujących - może mieć wymiar dowolny. Operator, ze względu na który badamy niezmienniczość aproksymacji, jest liniowy.
    From the text: "We generalize a theorem of G. Meinardus [Arch. Rational Mech. Anal. 14 (1963), 301–303; MR0156143] in two directions: first, instead of concrete function spaces we consider arbitrary normed spaces and secondly, we deal with the subspace of models-approximating elements-that can be of arbitrary measure. The operator in regard to which we study the invariability of the approximation is linear.''
    Źródło:
    Mathematica Applicanda; 1981, 9, 17
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Remarks on the problem of L. Flatto
    Autorzy:
    Smoluk, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/748360.pdf
    Data publikacji:
    1986
    Wydawca:
    Polskie Towarzystwo Matematyczne
    Tematy:
    Approximation by polynomials
    Opis:
    W pracy tej podajemy proste rozwiązania zadania Flatto(1982) w przypadku gdy dziedzina S jest wypukła w określonym kierunku. Problem Flatto okazuje się szczególnym przypadkiem aproksymacji inwariantnej.
    In this paper a particular solution of the problem of L. Flatto [1] has been given. Namely, the following theorem was proved. If there exists a point (a,b) S such that {a} x T c S, then for any function f C(T) there exists an optimal polynomial g O(f,Pk) such that g C(T).
    Źródło:
    Mathematica Applicanda; 1983, 14, 27
    1730-2668
    2299-4009
    Pojawia się w:
    Mathematica Applicanda
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Tiling by squares, Kirchhoff’s laws and a flow problem in the economy
    Autorzy:
    Maciuk, Arkadiusz
    Smoluk, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/421315.pdf
    Data publikacji:
    2017
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    squarings
    digraph
    Kirchhoff’s laws
    flow problem in the economy
    Opis:
    The problem of tiling by squares was formulated more than one hundred years ago and has been mostly regarded as an interesting mathematical issue in geometry, yet without any special practical associations. In addition to a historical outline of the problem, this paper demonstrates how Smith’s 1940 method using digraphs helps associate an issue linked to two-dimensional dissection or packaging with such economic problems as transportation network planning, researching linkages between suppliers and the like. We also discuss simple perfect squared rectangles whose relevant laws of nature are as yet unknown, according to the principle that elegant scientific structures sooner or later find their equivalents in the real world.
    Źródło:
    Didactics of Mathematics; 2017, 14(18); 33-44
    1733-7941
    Pojawia się w:
    Didactics of Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On maximal social preference
    Autorzy:
    Łyko, Janusz
    Smoluk, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/584937.pdf
    Data publikacji:
    2014
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    of welfare
    2/3 rule
    utylity functions
    Malthus’ increase
    Markov’s matrix
    Opis:
    Mathematics and physics are based on two numbers: Archimedes’ constant = 3,14… and e = 2,71… – Napier’s constant. The former reflects the ratio of the perimeter of a figure to its diameter and maximizes the area, given the diameter. The solutions are the disk and the circle. The latter represents the accumulated capital paid by a bank after one year from investing one unit of money at an annual interest rate of 100% under continuous compounding. The ratio of the disk’s perimeter to its diameter, i.e. , governs omnipresent cyclical motion, whereas Napier’s constant determines natural growth – exponential growth. Nature mixes both kinds of behaviour: there is equilibrium – vortices, and the cobweb model, dynamic growth. Our general remarks are corroborated by the theory of linear differential equations with constant coefficients. Social life – democracy and quality – despite the deceptive chaos of accidental behaviour, is also governed by a beautiful numeral law. This social number is λ = ⅔ whose notation is derived from the Greek meaning crowd, people, assembly. The social number, Łyko’s number, is defined by the fundamental theorem. If each alternative of a maximal relation of a given profile has its frequency in this profile greater than ⅔, then such relation is a group preference. This sufficient condition separates a decisional chaos from a stable economic and voting order – the preference. Also our everyday language makes use of . We distinguish with it upper states – elitist ones, from ordinary standards. The ⅔ rule implies that in each group one third of the population prevails, while the rest are just background actors. The number also appears, a bit of a surprise, in classical theorems of geometry.
    Źródło:
    Mathematical Economics; 2014, 10(17); 33-52
    1733-9707
    Pojawia się w:
    Mathematical Economics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Vortices and complex numbers
    Autorzy:
    Maciuk, Arkadiusz
    Smoluk, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/584918.pdf
    Data publikacji:
    2015
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    complex number
    vortex
    Opis:
    The paper emphasizes that complex numbers are objects with their equivalents commonly occurring in nature. Just like real numbers measure lengths in a physical world, complex numbers measure vortices observed in nature. The spiral orbits in this paper are exponential spirals (also called logarithmic spirals). A vortex is identified by determining a complex number that generates it. To determine this number, we need two snap-reading observations that provide the argument of a complex number, while the ratio of radiuses – the modulus of a complex number. Therefore, we also deal with the area of a complex number. Complex numbers involve a meaningful description of the laws of nature, i.e. of vortices and of equilibrium.
    Źródło:
    Mathematical Economics; 2015, 11(18); 77-88
    1733-9707
    Pojawia się w:
    Mathematical Economics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Partitions and branching processes
    Autorzy:
    Maciuk, Arkadiusz
    Smoluk, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/584949.pdf
    Data publikacji:
    2015
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    partition
    branching process
    Sacała’s line
    tree (dendrite)
    Opis:
    A partition, i.e. a division of a finite set into nonempty subsets, is a simple and essential concept of quantitatively understanding the reality. A partition of a number n is a decreasing sequence of natural numbers whose sum equals n. Greater numbers are seen only in terms of the union of partitions. The most important processes such as stochastic processes of branching processes can be expressed most simply using the language of partitions. By means of partitions any Sacała’s line defines a wide class of related quasibranching processes which are more general than Markov processes. Didactically such an approach is extremely useful.
    Źródło:
    Mathematical Economics; 2015, 11(18); 69-76
    1733-9707
    Pojawia się w:
    Mathematical Economics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A golden ratio as a generalization of the 2/3 rule of Janusz Łyko
    Autorzy:
    Maciuk, Arkadiusz
    Smoluk, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/584963.pdf
    Data publikacji:
    2018
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    golden number
    problem of group choice
    2/3 rule
    Opis:
    A golden ratio has been applied since ancient times in many areas, starting with architecture and art, and nowadays in modern financial markets and contemporary physics. This paper defines a golden rule in a set of preferences, generalizing the problem of group choice and the 2/3 rule of Łyko by means of a golden number corresponding to the ratio of lengths of sides in a golden rectangle.
    Źródło:
    Mathematical Economics; 2018, 14(21); 31-36
    1733-9707
    Pojawia się w:
    Mathematical Economics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The mirror of science
    Autorzy:
    Biernacki, Marek
    Smoluk, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/585017.pdf
    Data publikacji:
    2018
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    mathematics
    science
    faith
    Opis:
    Mathematics is a family of theories; there is an interpretation of every science of the physical world in the corresponding mathematical structure. Hence, mathematics is the mirror of science in its entirety.
    Źródło:
    Mathematical Economics; 2018, 14(21); 5-18
    1733-9707
    Pojawia się w:
    Mathematical Economics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Two proofs of Stokes’ theorem in new clothes
    Autorzy:
    Maciuk, Arkadiusz
    Smoluk, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/421369.pdf
    Data publikacji:
    2015
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    Stokes’ theorem
    Sacała’s column
    additivity of integration
    Opis:
    The paper presents two proofs of Stokes’ theorem that are intuitively simple and clear. A manifold, on which a differential form is defined, is reduced to a three-dimensional cube, as extending to other dimensions is straightforward. The first proof reduces the integral over a manifold to the integral over a boundary, while the second proof extends the integral over a boundary to the integral over a manifold. A new idea consists in the definition of Sacała’s line that inspired the authors to taking a different look at the proof of Stokes’ theorem.
    Źródło:
    Didactics of Mathematics; 2015, 12(16); 85-92
    1733-7941
    Pojawia się w:
    Didactics of Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Number three as a law of science. In praise of number three
    Autorzy:
    Maciuk, Arkadiusz
    Smoluk, Antoni
    Powiązania:
    https://bibliotekanauki.pl/articles/421393.pdf
    Data publikacji:
    2016
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    perception of natural numbers
    three-valued logic
    test exams
    Opis:
    Comprehension of nature, in the simplest and quickest fashion, boils down to the differentiation of three states. This is probably related to the psychological fact that the human mind grasps only natural numbers from zero to three and the other numbers it calculates. We live in a divalent world created by Aristotle. However not everything can be reduced to two categories: “yes” and “no”, because Nature is abundant. The principle of continuity which facilitates understanding is in natural conflict with the binary description of the world. Ever since the times of Aristotle it has been normal to use in science a description of the world that is reduced to two states: “true” and “false”. In nature it is more obvious to distinguish three states: low-medium-high or negative-neutral-positive, etc. Man embraces at a single glance sets of three elements at most, and more numerous sets are divided into parts. Binary logic may have a negative impact on the process of teaching and examinations, especially if the tests are used.
    Źródło:
    Didactics of Mathematics; 2016, 13(17); 25-34
    1733-7941
    Pojawia się w:
    Didactics of Mathematics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-14 z 14

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