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1
Certain aspects of J-statistical supremum and J-statistical infimum of real-valued sequences
Choudhury Chiranjib
Journal of Applied Analysis
|
2023
|
Vol. 29, nr 2
305--312
EN
Over the last few years, numerous researchers have contributed significantly to summability theory by connecting various notions of convergence concepts of sequences. In this paper, we introduce the concepts of J-statistical supremum and J-statistical infimum of a real-valued sequence and study some fundamental features of the newly introduced notions.We also introduce the concept of J-statistical monotonicity and establish the condition under which an J-statistical monotonic sequence is J-statistical convergent. We end up giving a necessary and a sufficient condition for the J-statistical convergence of a real-valued sequence.
2
A study of fuzzy anti-lambda-ideal convergent triple sequence spaces
Idrisi Mohammad Imran, Saini Kavita, Ahmad Mobeen, Aslam Sumaira
Journal of Applied Analysis
|
2023
|
Vol. 29, nr 2
353--358
EN
A class with ambiguous status of its elements by a membership function that assigns to each element a grade in the close interval [0, 1]; Lofti Zadeh introduced this idea into theory as fuzzy sets in the year of 1965. A study of fuzzy anti-normed linear spaces by Kočinac on some topological properties motivated us to work on fuzzy anti-normed triple sequence spaces with respect to ideal by using compact linear operator. Further, we prove some theorems, particularly on convergence and completeness.
3
Content available The Ethos of St. Florian’s knights
Krynicki Jan
Safety & Fire Technology
|
2019
|
Vol. 53, iss. 1
188--196
EN
Objective: The presentation of preliminary considerations on the ethos of the profession of firefighter. Background: In addition to appropriate procedures and standards, the competences of persons who create an institution are an essential element of their good functioning. In the context of the profession of firefighter, which serves an important social mission, axiological competences, which properly condition the effectiveness of all other competences, are taking on particular significance. The shaping of the ethos of duty, which determines its model and aspirations, is their source and point of reference. One should note the important place of valorisation of the ethos of firefighter among the most important factors which build the potential of this profession. The correlation between work and living in accordance with the moral rules of individuals and professional groups is determined by the term “ethos”. This notion became especially important during the dynamic development of knighthood. It became, in a sense, a synonym for a set of moral concepts, attitudes and behaviour. It highlights the unconditional devotion to the undertaken obligations. Ethos is something more than adopting a specific attitude which is highly regarded in moral terms. It approximates something which can be regarded as typical morals of an individual and even more closely resembles the social norm constituting an indicator of average moral behaviour of the members of the group in specific historical circumstances. The level of firefighter’s ethos, therefore, ultimately reflects the level of average moral behaviour of individual representatives of this service. Professional ethos is never shaped over a short period of time. It is often created slowly, with specific effort, by entire generations. One can indicate here an incredibly strong interrelation. Members of a given professional group not only establish the ethos, they are moulded by it into morally adult people through their work and lifestyle. Only by actually becoming involved in the implementation of ethos can one build a model lifestyle, which invariably, in the case of the profession of firefigher, is based on inner strength, courage, sacrifice and professional competence. Conclusions: The effective pursuit of the profession of firefighter must have its axiological foundation. Therefore, shaping the ethos of the knights of St. Florian should be regarded as an important element of the theory and pragmatics of this profession.
PL
Cel: Zaprezentowanie wstępnych rozważań nad etosem zawodu strażaka. Wprowadzenie: Obok właściwych procedur i standardów, zasadniczym elementem dobrego funkcjonowania wszelkich instytucji pozostają kompetencje tworzących je osób. W kontekście profesji strażaka, będącej ważną misją społeczną, szczególnej wagi nabierają kompetencje aksjologiczne, warunkujące właściwie efektywność wszelkich innych. Za ich źródło i punkt odniesienia uznać trzeba kształtowanie etosu służby, określającego jej model i aspiracje. Wśród najważniejszych czynników budujących potencjał zawodu strażaka należy dostrzec też istotne miejsce dla waloryzacji etosu tej służby. Korelacja pracy zawodowej z życiem w zgodzie z zasadami moralnymi jednostek i grup zawodowych odnajduje swój wyznacznik w terminie „etos”. Pojęcie to nabrało szczególnego znaczenia w czasach rozwoju rycerstwa. Stało się poniekąd synonimem zbioru moralnych idei, postaw i zachowań. Podkreśla ono bezwzględną wierność podjętym zobowiązaniom. Etos jest czymś więcej niż przyjęciem określonej, co więcej moralnie wysoko ocenianej postawy. Zbliża się on do czegoś, co można określić typową obyczajowością jednostki, a jeszcze bardziej do normy społecznej stanowiącej wskaźnik przeciętnego postępowania moralnego członków grupy w określonych warunkach dziejowych. Poziom etosu strażaka odzwierciedla więc ostatecznie poziom przeciętnego moralnego postępowania poszczególnych adeptów tej służby. Etos zawodowy nie powstaje nigdy na przestrzeni krótkiego okresu. Nierzadko tworzą go powoli, z określonym wysiłkiem, całe pokolenia. Można w tym miejscu mówić o niezwykle silnej relacji zwrotnej. Nie tylko etos konstytuowany jest przez członków danej grupy zawodowej. Także sami członkowie tej grupy grupa poprzez swoją pracę czy styl życia, są przez niego kształtowani na dojrzałe moralnie osoby. Dopiero dzięki rzeczywistemu zaangażowaniu się w realizację etosu buduje się wzorcowy styl życia, niezmiennie w przypadku zawodu strażaka, oparty na: sile ducha, męstwie, poświęceniu oraz zawodowej kompetencji. Wnioski: Efektywne realizowanie zawodu strażaka musi mieć swoją podbudowę aksjologiczną. Kształtowanie etosu rycerzy św. Floriana uznać należy więc za ważny element teorii i pragmatyki tego zawodu.
4
Content available remote Universal sets for ideals
Cieślak A., Michalski M.
Bulletin of the Polish Academy of Sciences. Mathematics
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2018
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Vol. 66, no. 2
157--166
EN
We consider the notion of universal sets for ideals. We show that there exist universal sets of minimal Borel complexity for classical ideals like the null subsets of 2ω and the meager subsets of any Polish space, and demonstrate that the existence of such sets is helpful in establishing some facts about the real line in generic extensions. We also construct universal sets for E, the σ-ideal generated by closed null subsets of 2ω, and for some ideals connected with forcing notions: the Kσ subsets of ωω and the Laver ideal. We also consider Fubini products of ideals and show that there are Σ03 universal sets for N[symbol]M and M[symbol]N.
5
Content available remote Every Filter is Homeomorphic to Its Square
Medini A., Zdomskyy L.
Bulletin of the Polish Academy of Sciences. Mathematics
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2016
|
Vol. 64, no. 1
63--67
EN
We show that every filter F on ω, viewed as a subspace of 2ω, is homeomorphic to F2. This generalizes a theorem of van Engelen, who proved that this holds for Borel filters.
6
Content available remote Some classes of ideal convergent difference sequence spaces of fuzzy numbers defined by Orlicz function
Hazarika B
Fasciculi Mathematici
|
2014
|
Nr 52
45--63
EN
An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In [25], Kostyrko et. al introduced the concept of ideal convergence as a sequence (xk) of real numbers is said to be I-convergent to a real number l, if for each Ɛ > 0 the set {k N : |xk - l| > Ɛ} belongs to I. In this article we introduce the concept of ideal convergent sequence of fuzzy numbers using difference operator and Orlicz functions and study their basic facts. Also we investigate the different algebraic and topological properties of these classes of sequences.
7
Content available remote Rough I-convergence
Dündar E., Çakan C.
Demonstratio Mathematica
|
2014
|
Vol. 47, nr 3
638--651
EN
In this work, using the concept of I-convergence and using the concept of rough convergence, we introduced the notion of rough I-convergence and the set of rough I-limit points of a sequence and obtained two rough I-convergence criteria associated with this set. Later, we proved that this set is closed and convex. Finally, we examined the relations between the set of I-cluster points and the set of rough I-limit points of a sequence.
8
On the Riesz space properties of the space of real statistically convergent sequences
Sencimen T. T, Pehlivan S
Journal of Applied Analysis
|
2013
|
Vol. 19, nr 1
31--39
EN
In this paper, we investigate some Riesz space (vector lattice) properties of the space of real statistically convergent sequences. We prove that this space is an order dense Riesz subspace of the linear space of all real sequences, but it is not an ideal.
9
Content available remote On asymmetric I and I∗-divergence
Ghosal S., Pal S. K.
Demonstratio Mathematica
|
2013
|
Vol. 46, nr 1
137--147
EN
In this paper we introduce and study the concepts of I-divergence and I∗-divergence of sequences as well as double sequences in an asymmetric metric spaces. We investigate the interrelationship between I-divergence and I∗-divergence and show that they are equivalent under some condition and prove some basic properties of these concepts.
10
Content available remote Dzieje miasta przyszłości
Motak M.
Czasopismo Techniczne. Architektura
|
2012
|
R. 109, z. 1-A/1
523--533
PL
Problemy przyszłości miasta i miasta przyszłości były rozważane od dawna. Stały się zatem już także zagadnieniem historycznym. Niniejszy artykuł jest próbą krótkiego przedstawienia poglądów zawartych w wybranych opracowaniach i projektach dotyczących miasta przyszłości, powstałych w sześciu kolejnych okresach w przeszłości. Są to: 1. Renesans, ok. 1400–1600 (z uwzględnieniem wpływu okresu antycznego); 2. Barok, ok. 1600–1800; 3. Rozwój przemysłu, ok. 1800–1920; 4. Modernizm, ok. 1920–1980; 5. Totalitaryzm, 1933–1956; 6. Współczesność, po 1980. Poszczególne teorie zostały skonfrontowane z efektami realizacyjnymi osiągniętymi przy stosowaniu ich założeń.
EN
The future of the city and the city of the future have been considered for a long time. Therefore they have become historic problems, too. This article is an attempt of presenting the views from the selected research and projects concerning the city of the future, which were created in six consecutive periods in the past. They are: 1. Renaissance period, ca. 1400–1600 (including Ancient Roman impact); 2. Baroque period, ca. 1600–1800; 3. Industrial period, ca. 1800–1920; 4. Modernism, ca. 1920–1980; 5. Totalitarianism, 1933–1956; 6. Contemporary period, since 1980. The particular theories have been confronted with the effects achieved by the application of the given principles.
11
Content available remote On monoids of injective partial selfmaps almost everywhere the identity
Chuchman I., Gutik O.
Demonstratio Mathematica
|
2011
|
Vol. 44, nr 4
699-722
EN
In this paper we study the semigroup (…) of injective partial selfmaps almost everywhere the identity of a set of infinite cardinality (…). We describe the Green relations on (…), all (two-sided) ideals and all congruences of the semigroup (…). We prove that every Hausdorff hereditary Baire topology (…) such that (…) is a semitopological semigroup is discrete and describe the closure of the discrete semigroup (…) in a topological semigroup. Also we show that for an infinite cardinal (…) the discrete semigroup (…) does not embed into a compact topological semigroup and construct two non-discrete Hausdorff topologies turning (…) into a topological inverse semigroup.
12
Content available remote Normal pseudo-BCK-algebras
Dymek G.
Commentationes Mathematicae
|
2011
|
Vol. 51, [Z] 1
99-107
EN
A normal pseudo-BCK-algebra X is an algebra in which every subalgebra of X is an ideal of X. Characterizations of normal pseudo-BCK-algebras are given.
13
Content available remote Unconditional convergence in lattice groups with respect to ideals
Boccuto A., Dimitriou X., Papanastassiou N.
Commentationes Mathematicae
|
2010
|
Vol. 50, [Z] 2
161-174
EN
We deal with unconditional convergence of series and some special classes of subsets of N.
14
Content available remote On maximal ideals of pseudo MV-algebras
Dymek G., Walendziak A.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2007
|
Vol. 47, [Z] 1
117-126
15
Content available remote Implications and equivalences in orthomodular lattices
Hyčko M.
Demonstratio Mathematica
|
2005
|
Vol. 38, nr 4
777--792
EN
The present article describes a method for checking the validity of implications or equivalences in the free orthomodular lattice on two generators and in the F(a, b, c1,..., cn), which is the free orthomodular lattice generated by the elements a, 6, ci,... Cn, where the elements ci, i = 1,..., n are central in it. The structure of the previous lattices is described in [3] and [1]. The method presented is based on comparing the elements that are assigned to each expression on both sides of an implication or an equivalence. It gives a necessary condition for the implication or equivalence of arbitrary positive statements (a combination of identities and logical connectives AND and OR) to hold. When the conclusion part is an identity or a conjunction of identities, these conditions become also sufficient.
16
Content available remote Ideał żołnierza w polskich przysięgach wojskowych
Wajda A.
Wiedza Obronna
|
2002
|
nr 3
126--130
17
Content available remote Order algebras
Chajda I., Halaš R.
Demonstratio Mathematica
|
2002
|
Vol. 35, nr 1
1-10
EN
To every ordered set with a greatest element is assigned an order algebra, a Hilbert algebra occuring in intuicionistic logic. We prove some basic properties of order algebras and characterize their ideals and congruences. We introduce a concept of (relative) annihilator and show that it is a (relative) pseudocomplement in the lattice of all ideals.
18
Content available remote Meanders in orthoposets and QMV algebras
Dvurečenskij A., Pulmannova S., Salvati S.
Demonstratio Mathematica
|
2001
|
Vol. 34, nr 1
1-11
EN
The notion of a meander of an ideal in lattices is generalized in two directions: to ideals in orthoposets and to ideals in QMV-algebras, and used to a characterization of subclasses of the above structures, namely Boolean orthoposets and QMV-algebras m which every ideal is closed under perspectivity, and to a characterization of Riesz ideals in orthoposets and perspectivity closed ideals in QMV algebras.
19
Content available remote On ideals, filters and weak distributivity in generalized Boolean Quasirings
Kaleta J.
Demonstratio Mathematica
|
2000
|
Vol. 33, nr 2
231-241
EN
In this paper a theory of ideals and filters m some kind of ring-like structures, namely in generalized Boolean quasirings (GBQRs), is presented. We refer to weak distributivity in GBQRs, too.
20
Content available remote Commutative BCK-algebras with product
Dvurecenskij A.
Demonstratio Mathematica
|
2000
|
Vol. 33, nr 1
1-19
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