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1
Content available remote On objective and subjective difficulties in understanding the notions of the least upper bound and the greatest lower bound
100%
Jędrzejewski J.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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tom Vol. 12
245-248
EN
The notion of the least upper bound (the greatest lower bound) of a subset of real numbers is discussed from different points of view and some difficulties of this notion are presented.
2
Content available Some Remarks of Different Aggregation Modes Applications Within the Framework of Intuitionistic Fuzzy Weights
100%
Tikhonenko-Kędziak A. , Kurkowski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2016
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tom Vol. 21
145--159
EN
In the classical intuitionistic fuzzy sets theory it is known, that the use of all aggregation modes is not always possible, because of the lack of definition of raising intuitionistic fuzzy values to the intuitionistic fuzzy power. The main aim of this work is to introduct an operation of raising of intuitionistic fuzzy values to an intuitionistic fuzzy power,which does not require conversion to intuitionistic fuzzy values. Additionally, we will present a heuristic method of raising an intuitionistic fuzzy values to the intuitionistic fuzzy power and consideration about its properties.
3
Content available remote Remarks on connectivity and I-connectivity
100%
Jędrzejewski J. , Kowalczyk S.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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tom Vol. 12
49-54
4
Content available remote Some remarks on definition of the absolute value of a real number
100%
Major J. , Powązka Z.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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tom Vol. 12
283-288
EN
The article presents a didactic proposition of introducing the definition of the absolute value of a real number.
5
Content available remote On I-limit superior and I-limit inferior of sequences of fuzzy numbers
84%
Sen M.
Fasciculi Mathematici
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2010
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tom Nr 43
139-145
EN
In this article we introduce the notions of I-limit superior and I-limit inferior for sequences of fuzzy real numbers . We prove fuzzy analogue of some results on I-limit superior and I-limit inferior for real sequences.
6
Content available remote Transient analysis in 1st order electrical circuits in violation of commutation laws
67%
Kukharchuk V. V. , Pavlov S. V. , Katsyv S. S. , Koval A. M. , Holodiuk V. S. , Lysyi M. V. , Kotyra A. , Mamyrbaev O. , Kalabayeva A.
Przegląd Elektrotechniczny
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2021
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tom R. 97, nr 9
26--29
EN
The paper considers the usage of non-standard analysis mathematical apparatus to solve some non-trivial problems of electrical engineering theory. The axiomatics of non-standard analysis makes it possible to simplify the transient analysis in the 1st order electrical circuits in violation of the commutation laws. Examples of solving such problems are given.
PL
W artykule rozważono zastosowanie aparatu matematycznego analizy niestandardowej do rozwiązywania niektórych nietrywialnych zadań z teorii elektrotechniki. Aksjomatyka analizy niestandardowej pozwala na uproszczenie analizy stanów nieustalonych w obwodach elektrycznych I rzędu z naruszeniem praw komutacji. Podane są przykłady rozwiązywania takich przypadków.
7
Content available remote Representations of reals in reverse mathematics
67%
Hirst J. L.
Bulletin of the Polish Academy of Sciences. Mathematics
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2007
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tom Vol. 55, no 4
303-316
EN
Working in the framework of reverse mathematics, we consider representations of reals as rapidly converging Cauchy sequences, decimal expansions, and two sorts of Dedekind cuts. Converting single reals from one representation to another can always be carried out in RCA[sub]0. However, the conversion process is not always uniform. Converting infinite sequences of reals in some representations to other representations requires the use of WKU[sub]0 or ACA[sub]0.
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