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1
Content available On some inclusion in the set theory
Ochab Justyna, Ulaszek Marcin
Journal of Mathematics and Applications
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2022
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Vol. 45
129--132
EN
This note contains the proof of an inclusion in the set theory. In that proof we use only basic laws appearing in the set theory. More precisely, using some basic laws of the set theory we provide the proof of an inclusion which is applied in the proof of certain theorem of the classical measure theory. The presented paper has an elementary character. Only the basic tools of the set theory are involved.
2
Content available remote On existence of the support of a Borel measure
Kozarzewski P. A.
Demonstratio Mathematica
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2018
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Vol. 51, nr 1
76--84
EN
We present arguments showing that the standard notion of the support of a probabilistic Borel measure is not well defined in every topological space. Our goal is to create a "very inseparable" space and to show the existence of a family of closed sets such that each of them is of full measure, but their intersection is empty. The presented classic construction is credited to Jean Dieudonné and dates back to 1939. We also propose certain, up to our best knowledge, new simplifications.
3
Content available remote Efficient similarity measures for texts matching
Akinwale A., Niewiadomski A.
Journal of Applied Computer Science
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2015
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Vol. 23, nr 1
7--28
EN
Calculation of similarity measures of exact matching texts is a critical task in the area of pattern matching that needs a great attention. There are many existing similarity measures in literature but the best methods do not exist for closeness measurement of two strings. The objective of this paper is to explore the grammatical properties and features of generalized n-gram matching technique of similarity measures to find exact text in electronic computer applications. Three new similarity measures have been proposed to improve the performance of generalized n-gram method. The new methods assigned high values of similarity measures and performance to price with low values of running time. The experiment with the new methods demonstrated that they are universal and very useful in words that could be derived from the word list as a group and retrieve relevant medical terms from database . One of the methods achieved best correlation of values for the evaluation of subjective examination.
4
Content available remote Some remarks of Jan Śleszyński regarding foundations of mathematics of Stanisław Leśniewski
Obojska L.
Czasopismo Techniczne. Nauki Podstawowe
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2015
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Y. 112, iss. 2-NP
235--245
EN
Jan Śleszyński, a great mathematician, is considered a pioneer of Polish logic; however, he was not connected with the famous Warsaw School of Logic (WSL). He believed that his mission was a critical evaluation of work of other logicians in the field of foundations of mathematics and proof theory. Among his writings we find several notes regarding the work of Stanisław Leśniewski (the co-founder of the WSL) and his collective set theory. These remarks are the subject of investigation of the presented paper.
PL
Jan Śleszyński, wielki matematyk, uważany jest za pioniera polskiej logiki, chociaż nie był związany ze słynną Warszawską Szkołą Logiki (WSL). Śleszyński uważał, że jego misją była krytyczna ocena prac dotyczących podstaw matematyki oraz teorii dowodu autorstwa innych logików. Wśród jego zapisków znajdujemy między innymi uwagi dotyczące teorii zbiorów kolektywnych Stanisława Leśniewskiego, współzałożyciela WSL. Uwagi te są przedmiotem analizy niniejszego artykułu.
5
Content available remote O kształtowaniu się intuicyjnej koncepcji zbioru Stanisława Leśniewskiego
Miszczyński R.
Kwartalnik Historii Nauki i Techniki
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2013
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R. 58, nr 3
99--119
EN
The first vague definitions of a set (Cantor, Dedekind, Hausdorfi) described it as bringing certain objects together. However, in the set theory there appeared some objects which did not originate in this way, for example the empty set. The disadvantages of this theory were clearly revealed in Russell’s antinomy. According to Leśniewski, the con tradictions will disappear when the concept of a set is based on intuition. Therefore, the distributive concept was replaced with the collective one: the relation of the element to the set is based on the relation between the part and the whole. In the new theory, the empty set no longer exists - the non-intuitive distinction between an object and the set composed of this object, disappears. These features allow to prevent Russell’s antinomy.
6
Content available remote Wykorzystanie teorii zbiorów do badania konfiguracji organizacyjnych
Kwiotkowska A.
Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska
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2010
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z. 53
163-175
PL
Badania konfiguracji organizacyjnych obejmują rozpatrywanie wielowymiarowych układów koncepcyjnie odrębnych cech charakterystycznych, które zazwyczaj występują razem. W artykule do badania konfiguracji organizacyjnych proponuje się wykorzystanie teorii zbiorów traktujących konfiguracje jak różne typy przypadków. Celem artykułu jest określenie istoty konfiguracji organizacyjnych oraz wskazanie praktycznych aspektów wykorzystania teorii zbiorów do badania konfiguracji organizacyjnych.
EN
The research of organizational configurations includes the investigation of multidimensional systems conceptually distinct characteristics, which usually occur together. In the article, to the research of organizational configurations was proposed to use set-theory as treating different types of configurations of the cases. The aim of this paper is to define the essence of organizational configurations and the indication of the practical aspects of using set-theory to the research the organizational configuration.
7
Content available remote Analysis of GO composition of gene clusters by using multiattribute decision rules
Gruca A.
Biocybernetics and Biomedical Engineering
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2008
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Vol. 28, no. 4
21-32
EN
In this paper, a novel method for characterizing the Gene Ontology (GO) composition of the gene clusters on basis of the decision rules is presented. The rules are expressed as logical functions of the Gene Ontology terms which are interpreted as binary attributes. A new method for evaluating the quality of decision rules based on statistical significance is developed. The presented approach is applied to the well-known data set and the results are compared with the results obtained by other authors.
8
Ernst Schroder's algebra of logic
Gruszecki Lech
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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2004
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z. 27 [212]
25-28
EN
In this article a short outline of Ernst Schroder's methods in logic is presented.
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