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  1. 7 Demonstratio Mathematica
  2. 6 Fundamenta Informaticae
  3. 4 Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne
  4. 4 Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
  5. 2 Bulletin of the Section of Logic
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  1. 1 2023
  2. 2 2022
  3. 2 2020
  4. 3 2018
  5. 3 2016
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  1. 1 Abdulwahid A. H.
  2. 1 Almanjahie I. M.
  3. 1 Andrejczuk E.
  4. 1 Atiyah M.
  5. 1 Balcerzyk S.
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1
Content available remote From picture processing to interval diagrams
100%
Kulpa Z.
Prace Instytutu Podstawowych Problemów Techniki PAN
|
2003
|
tom nr 4
1-313
EN
The main aim of the work is the development and presentation of the novel diagrammatic notation for interval algebra and computation developed by the author, and howing its usefulness in some areas of interval algebra. Additionally, as a background for that undertaking, a state of the art survey and partially novel sistematization of basic issues of diagrammatics is attempted, including a unifield framework for relating various subfields and aspects of the pictoral information handling domain.
2
Content available remote On the canonical connection for smooth envelopes
60%
Moreno G.
Demonstratio Mathematica
|
2014
|
tom Vol. 47, nr 2
459--464
EN
A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds, which were proposed in the last decades. Such an operation is indispensable in order to perform differential calculus. A derivation of the enveloping algebra can be restricted to the original one, but it is a delicate question if the the vice–versa can be done as well. In a physical language, this would correspond to the existence of a canonical connection. In this paper, we show an example of an algebra which always possesses such a connection.
3
Content available remote Category approach to R L4 - sets
60%
Biegańska T.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
1998
|
tom Vol. 4
85-88
EN
In this paper Fm going to investigate the subcategory of the category of sets valued by some Heyting algebra. The notion of a Heyting algebra valued set was introduced by Scott [1] in 1972 in his work a the intuitionistic set theory. The categories of Heyting algebra valued sets were investigated and described by D. Higgs in [3] and [4].
4
Content available remote On applications of a functional equation
60%
Smajdor W.
Opuscula Mathematica
|
2001
|
tom Vol. 21
93-99
EN
We characterize the sine function applying the functional equation [formula].
PL
Przedstawiono charakteryzację funkcji sinus za pomocą równania funkcyjnego [wzór].
5
Content available remote Use of computer algebra system for recalculation of the fifth-order aberrations of GRIN media.
60%
Magiera L.
Optica Applicata
|
2001
|
tom Vol. 31, nr 3
545-551
EN
The methodology of calculation of the fifth-order aberrations of gradient-index (GRIN) media by application of computer symbolic calculations (computer algebra) is presented. The software package applied was REDUCE. The results obtained enabled us to correct the results known from the literature. The designed computer program has also been added. A special computer program has also been designed.
6
Content available The projective representations types of finite groups over a ring of formal power series
60%
Klein D.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2009
|
tom Vol. 14
63-73
EN
Let F be a field of characteristic p >0,S=F[[X]],S∗ the unit group of S, and W a subgroup of S ∗. We characterize finite groups depending on a projective (S,W)-representation type. We also give necessary and sufficient conditions for a finite group and its Sylow p-subgroups to be of the same projective (S,W) -representation type.
7
Content available remote Stability of the equation of ring homomorphisms
60%
Ger R.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2007
|
tom Vol. 12
29-35
EN
Let R be a unitary ring and (A,║‧║) stand for a Banach algebra with a unit. In connection with some stability results of R. Badora [1] and D.G. Bourgin [2] concerning the system of two Cauchy functional equations [formula] for mappings f : R→ A, we deal with Hyers-Ulam stability problem for a single equation f(x + y) + f(xy) = f(x) + f(y) + f(x)f(y). The basic question whether or not equation (**) is equivalent to the system (*) has widely been examined by J. Dhombres [3] and the present author in [4] and [5].
8
Content available Liczby algebraiczne i przestępne
60%
Biły B.
MINUT Matematyka i Informatyka na Uczelniach Technicznych
|
2020
|
tom Nr 2
78-83
PL
W artykule przedstawione są definicje liczby algebraicznej i przestępnej, rys historyczny ich wprowadzenia, przykłady oraz niektóre ze znanych twierdzeń dotyczących istnienia pewnych szczególnych liczb przestępnych. Zacytowano twierdzenia Liouville'a oraz twierdzenie Gelfonda-Schneidera. Osobny rozdział poświęcony jest dowodowi przestępności liczby e, który wymaga znajomości rachunku całkowego.
9
Content available Minimalizacja opisów funkcji w algebrze bramek prądowych
57%
Berezowski R.
Zeszyty Naukowe Wydziału Elektroniki i Informatyki Politechniki Koszalińskiej
|
2011
|
tom Nr 3
29--38
PL
W artykule przedstawiono rozwój metod minimalizacji opisów funkcji w algebrze bramek prądowych jakie opracowano w przeciągu ostatnich dwudziestu lat. Technologia bramek prądowych związana jest z koncepcją bramki prądowej zaproponowanej przez prof. Andrzeja Guzińskiego w latach 90 ubiegłego wieku. Wskazane zostaną również kierunki dalszego rozwoju badań nad optymalizacją układów prądowych.
10
On cancellative congruences for semigroups
57%
Macedońska O.
|
|
tom z. 84
171-176
EN
Given a semigroup identity u = v. We describe a smallest normal subgroup N in a free group F, such that F / N contains a relatively free cancellative semigroup which satisfies the identity u = v.
PL
Niech u = v oznacza tożsamość półgrupową. Rozpatrujemy najmniejszą podgrupę normalną N w grupie wolnej F, taką że F / N zawiera relatywnie wolną półgrupę skracalną, spełniającą tożsamość u = v.
11
Content available remote Vznik formalismu a nové pojetí vědy
57%
Sousedík P. , Svoboda D.
Filosofický časopis (Philosophical Journal)
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2015
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tom 63
|
nr 3, Special No: Sedmkrát z logiky a metodologie vědy
39-60
EN
According to formalism a mathematician is not concerned with mysterious meta-physical entities but with mathematical symbols themselves. Mathematical entities, on this view, become mere sensible signs. However, the price that has to be paid for this move looks to be too high. Mathematics, which is nowadays considered to be the queen of the sciences, thus turns out to be a content-less game. That is why it seems too absurd to regard numbers and all mathematical entities as mere symbols. T e aim of our paper is to show the reasons that have led some philosophers and mathemati¬cians to accept the view that mathematical terms in a proper sense do not refer to anything and mathematical propositions do not have any real content. At the same time we want to explain how formalism helped to overcome the traditional concept of science.
12
Content available remote Edward Sąsiada (1924-1999)
57%
Balcerzyk S. , Kamiński B.
|
|
tom [Z] 37
145-152
13
Content available remote Matematyka w XX wieku
57%
Atiyah M.
|
|
tom [Z] 39
47-63
14
Content available Applications of Algebra in Logic and Computer Science – the Past and the Future
57%
Grygiel J.
Bulletin of the Section of Logic
|
2018
|
tom 47
|
nr 1
EN
We present the history of the conference Applications of Algebra in Logic and Computer Science, whose twenty-third edition will be held in March, 2019. At the end we outline some plans for the future.
15
Content available remote Anzelm Iwanik (1946-1998)
57%
Byczkowski T. , Downarowicz T. , Lipecki Z. , Romanowicz Z.
Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne
|
1999
|
tom [Z] 35
191-200
16
Content available remote Początki toruńskiej algebry
57%
Simson D.
Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne
|
1999
|
tom [Z] 35
1-9
17
Content available remote Order-theoretic Trees : Monadic Second-order Descriptions and Regularity
57%
Courcelle B.
|
2022
|
tom Vol. 186, nr 1-4
89--120
EN
An order-theoretic forest is a countable partial order such that the set of elements larger than any element is linearly ordered. It is an order-theoretic tree if any two elements have an upper-bound. The order type of a branch can be any countable linear order. Such generalized infinite trees yield convenient definitions of the rank-width and the modular decomposition of countable graphs. We define an algebra based on only four operations that generate up to isomorphism and via infinite terms these order-theoretic trees and forests. We prove that the associated regular objects, those defined by regular terms, are exactly the ones that are the unique models of monadic second-order sentences.
18
Content available Application of geogebra for teaching mathematics
57%
Majerek D.
Advances in Science and Technology. Research Journal
|
2014
|
tom Vol. 8, nr 24
51--54
EN
This paper shows how GeoGebra can be helpful in teaching mathematics. GeoGebra is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. It can be used for active and problem oriented teaching and fosters mathematical experiments and discoveries both in classroom and at home. In this work we show the sketch of using the above-mentioned software to build, solve and illustrate mathematical problems.
19
Content available Bayer Noise symmetric functions and some combinatorial algebraic structures
51%
Abdulwahid A. H. , Elamami E.
Journal of Mathematics and Applications
|
2023
|
tom Vol. 46
115--148
EN
Symmetric functions play a crucial role in classifying representations of symmetric groups, and they are largely involved with combinatorial algebras and graph theory. Bayer filter technique is largely applied in most of the professional digital cameras due to the fact that it is a low-cost, and it allows photosensors not only to capture the intensity of light, but also to record the wavelength of light as well. Using Bayer Pattern, we introduce the Bayer Noise symmetric functions and the Bayer Noise Schur functions, and we study some combinatorial structures on the Bayer Noise modules. We study the connection between Bayer Noise symmetric functions and other bases for the algebra of symmetric functions, and we explicitly calculate special cases over a fixed commutative ring k. We also study the compatibility of such algebraic and coalgebraic structures.
20
Content available Automatic search of rational self-equivalences
51%
Stępień L. , Stępień M. R.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2018
|
tom Vol. 23
67--74
EN
Two Witt rings that are not strongly isomorphic (i.e., two Witt rings over two fields that are not Witt equivalent) have different groups of strong automorphisms. Therefore, the description of a group of strong automorphisms is different for almost every Witt ring, which requires the use various tools in proofs. It is natural idea to use computers to generate strong automorphisms of the Witt rings, which is especially effective in the case of the finitely generated Witt rings, where a complete list of strong automorphisms can be created. In this paper we present the algorithm that was used to generate strong automorphisms from the infinite group of strong automorphisms of the Witt ring of rational numbers W(Q).
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