Necessary and sufficient condition for the existence of the one-point time on an oriented set
The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the pro...
Ausführliche Beschreibung
Autor*in: |
Ya.I. Grushka [verfasserIn] |
---|
Format: |
E-Artikel |
---|---|
Sprache: |
Englisch ; Russisch ; Ukrainisch |
Erschienen: |
2019 |
---|
Schlagwörter: |
---|
Übergeordnetes Werk: |
In: Доповiдi Нацiональної академiї наук України - Publishing House "Akademperiodyka", 2019, 8(2019), Seite 9-15 |
---|---|
Übergeordnetes Werk: |
volume:8 ; year:2019 ; pages:9-15 |
Links: |
Link aufrufen |
---|
DOI / URN: |
10.15407/dopovidi2019.08.009 |
---|
Katalog-ID: |
DOAJ008124957 |
---|
LEADER | 01000caa a22002652 4500 | ||
---|---|---|---|
001 | DOAJ008124957 | ||
003 | DE-627 | ||
005 | 20230310004037.0 | ||
007 | cr uuu---uuuuu | ||
008 | 230225s2019 xx |||||o 00| ||eng c | ||
024 | 7 | |a 10.15407/dopovidi2019.08.009 |2 doi | |
035 | |a (DE-627)DOAJ008124957 | ||
035 | |a (DE-599)DOAJdb3c343ea7604ebc86dbbd75e7d4b887 | ||
040 | |a DE-627 |b ger |c DE-627 |e rakwb | ||
041 | |a eng |a rus |a ukr | ||
050 | 0 | |a Q1-390 | |
100 | 0 | |a Ya.I. Grushka |e verfasserin |4 aut | |
245 | 1 | 0 | |a Necessary and sufficient condition for the existence of the one-point time on an oriented set |
264 | 1 | |c 2019 | |
336 | |a Text |b txt |2 rdacontent | ||
337 | |a Computermedien |b c |2 rdamedia | ||
338 | |a Online-Ressource |b cr |2 rdacarrier | ||
520 | |a The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the process of continuous transformations, i.e., they can change their properties, appear or disappear, and disintegrate into several parts or, conversely, several objects can merge into a single one. In addition, the picture of the evolution of a changeable set can depend on the method of observation (that is, on the reference frame). The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. The notion of oriented set is the basic elementary concept of the theory of changeable sets. Oriented sets can be interpreted as the most primitive abstract models of sets of changing objects that evolve within a single (fixed) reference frame. The oriented sets are mathematical objects, in the framework of which one can give the mathematically rigorous definition of the concept of time as a certain mapping from a certain time scale, represented by a linearly ordered set, into the set of simultaneous states of the oriented set. In this paper, the necessary and sufficient condition of the existence of the onepoint time on an oriented set is established. From the intuitive point of view, the onepoint time is the time associated with the evolution of a system consisting of only one object (for example, one material point). Namely, the concept of a quasichain oriented set is introduced, and it is proved that the onepoint time exists on the oriented set, if and only if this oriented set is a quasichain. Using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets. | ||
650 | 4 | |a changeable sets | |
650 | 4 | |a time | |
650 | 4 | |a ordered sets | |
650 | 4 | |a oriented sets | |
653 | 0 | |a Science (General) | |
773 | 0 | 8 | |i In |t Доповiдi Нацiональної академiї наук України |d Publishing House "Akademperiodyka", 2019 |g 8(2019), Seite 9-15 |w (DE-627)66080784X |w (DE-600)2609380-7 |x 2518153X |7 nnns |
773 | 1 | 8 | |g volume:8 |g year:2019 |g pages:9-15 |
856 | 4 | 0 | |u https://doi.org/10.15407/dopovidi2019.08.009 |z kostenfrei |
856 | 4 | 0 | |u https://doaj.org/article/db3c343ea7604ebc86dbbd75e7d4b887 |z kostenfrei |
856 | 4 | 0 | |u http://www.dopovidi-nanu.org.ua/en/archive/2019/8/2 |z kostenfrei |
856 | 4 | 2 | |u https://doaj.org/toc/1025-6415 |y Journal toc |z kostenfrei |
856 | 4 | 2 | |u https://doaj.org/toc/2518-153X |y Journal toc |z kostenfrei |
912 | |a GBV_USEFLAG_A | ||
912 | |a SYSFLAG_A | ||
912 | |a GBV_DOAJ | ||
912 | |a GBV_ILN_11 | ||
912 | |a GBV_ILN_20 | ||
912 | |a GBV_ILN_22 | ||
912 | |a GBV_ILN_23 | ||
912 | |a GBV_ILN_24 | ||
912 | |a GBV_ILN_31 | ||
912 | |a GBV_ILN_39 | ||
912 | |a GBV_ILN_40 | ||
912 | |a GBV_ILN_60 | ||
912 | |a GBV_ILN_62 | ||
912 | |a GBV_ILN_63 | ||
912 | |a GBV_ILN_65 | ||
912 | |a GBV_ILN_69 | ||
912 | |a GBV_ILN_70 | ||
912 | |a GBV_ILN_73 | ||
912 | |a GBV_ILN_74 | ||
912 | |a GBV_ILN_90 | ||
912 | |a GBV_ILN_95 | ||
912 | |a GBV_ILN_100 | ||
912 | |a GBV_ILN_105 | ||
912 | |a GBV_ILN_110 | ||
912 | |a GBV_ILN_138 | ||
912 | |a GBV_ILN_151 | ||
912 | |a GBV_ILN_152 | ||
912 | |a GBV_ILN_161 | ||
912 | |a GBV_ILN_171 | ||
912 | |a GBV_ILN_187 | ||
912 | |a GBV_ILN_213 | ||
912 | |a GBV_ILN_230 | ||
912 | |a GBV_ILN_250 | ||
912 | |a GBV_ILN_281 | ||
912 | |a GBV_ILN_285 | ||
912 | |a GBV_ILN_293 | ||
912 | |a GBV_ILN_370 | ||
912 | |a GBV_ILN_602 | ||
912 | |a GBV_ILN_647 | ||
912 | |a GBV_ILN_702 | ||
912 | |a GBV_ILN_2014 | ||
912 | |a GBV_ILN_4012 | ||
912 | |a GBV_ILN_4037 | ||
912 | |a GBV_ILN_4112 | ||
912 | |a GBV_ILN_4125 | ||
912 | |a GBV_ILN_4126 | ||
912 | |a GBV_ILN_4249 | ||
912 | |a GBV_ILN_4305 | ||
912 | |a GBV_ILN_4306 | ||
912 | |a GBV_ILN_4307 | ||
912 | |a GBV_ILN_4313 | ||
912 | |a GBV_ILN_4322 | ||
912 | |a GBV_ILN_4323 | ||
912 | |a GBV_ILN_4324 | ||
912 | |a GBV_ILN_4325 | ||
912 | |a GBV_ILN_4335 | ||
912 | |a GBV_ILN_4338 | ||
912 | |a GBV_ILN_4367 | ||
912 | |a GBV_ILN_4700 | ||
951 | |a AR | ||
952 | |d 8 |j 2019 |h 9-15 |
author_variant |
y g yg |
---|---|
matchkey_str |
article:2518153X:2019----::eesradufcetodtofrheitnefhoeo |
hierarchy_sort_str |
2019 |
callnumber-subject-code |
Q |
publishDate |
2019 |
allfields |
10.15407/dopovidi2019.08.009 doi (DE-627)DOAJ008124957 (DE-599)DOAJdb3c343ea7604ebc86dbbd75e7d4b887 DE-627 ger DE-627 rakwb eng rus ukr Q1-390 Ya.I. Grushka verfasserin aut Necessary and sufficient condition for the existence of the one-point time on an oriented set 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the process of continuous transformations, i.e., they can change their properties, appear or disappear, and disintegrate into several parts or, conversely, several objects can merge into a single one. In addition, the picture of the evolution of a changeable set can depend on the method of observation (that is, on the reference frame). The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. The notion of oriented set is the basic elementary concept of the theory of changeable sets. Oriented sets can be interpreted as the most primitive abstract models of sets of changing objects that evolve within a single (fixed) reference frame. The oriented sets are mathematical objects, in the framework of which one can give the mathematically rigorous definition of the concept of time as a certain mapping from a certain time scale, represented by a linearly ordered set, into the set of simultaneous states of the oriented set. In this paper, the necessary and sufficient condition of the existence of the onepoint time on an oriented set is established. From the intuitive point of view, the onepoint time is the time associated with the evolution of a system consisting of only one object (for example, one material point). Namely, the concept of a quasichain oriented set is introduced, and it is proved that the onepoint time exists on the oriented set, if and only if this oriented set is a quasichain. Using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets. changeable sets time ordered sets oriented sets Science (General) In Доповiдi Нацiональної академiї наук України Publishing House "Akademperiodyka", 2019 8(2019), Seite 9-15 (DE-627)66080784X (DE-600)2609380-7 2518153X nnns volume:8 year:2019 pages:9-15 https://doi.org/10.15407/dopovidi2019.08.009 kostenfrei https://doaj.org/article/db3c343ea7604ebc86dbbd75e7d4b887 kostenfrei http://www.dopovidi-nanu.org.ua/en/archive/2019/8/2 kostenfrei https://doaj.org/toc/1025-6415 Journal toc kostenfrei https://doaj.org/toc/2518-153X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2019 9-15 |
spelling |
10.15407/dopovidi2019.08.009 doi (DE-627)DOAJ008124957 (DE-599)DOAJdb3c343ea7604ebc86dbbd75e7d4b887 DE-627 ger DE-627 rakwb eng rus ukr Q1-390 Ya.I. Grushka verfasserin aut Necessary and sufficient condition for the existence of the one-point time on an oriented set 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the process of continuous transformations, i.e., they can change their properties, appear or disappear, and disintegrate into several parts or, conversely, several objects can merge into a single one. In addition, the picture of the evolution of a changeable set can depend on the method of observation (that is, on the reference frame). The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. The notion of oriented set is the basic elementary concept of the theory of changeable sets. Oriented sets can be interpreted as the most primitive abstract models of sets of changing objects that evolve within a single (fixed) reference frame. The oriented sets are mathematical objects, in the framework of which one can give the mathematically rigorous definition of the concept of time as a certain mapping from a certain time scale, represented by a linearly ordered set, into the set of simultaneous states of the oriented set. In this paper, the necessary and sufficient condition of the existence of the onepoint time on an oriented set is established. From the intuitive point of view, the onepoint time is the time associated with the evolution of a system consisting of only one object (for example, one material point). Namely, the concept of a quasichain oriented set is introduced, and it is proved that the onepoint time exists on the oriented set, if and only if this oriented set is a quasichain. Using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets. changeable sets time ordered sets oriented sets Science (General) In Доповiдi Нацiональної академiї наук України Publishing House "Akademperiodyka", 2019 8(2019), Seite 9-15 (DE-627)66080784X (DE-600)2609380-7 2518153X nnns volume:8 year:2019 pages:9-15 https://doi.org/10.15407/dopovidi2019.08.009 kostenfrei https://doaj.org/article/db3c343ea7604ebc86dbbd75e7d4b887 kostenfrei http://www.dopovidi-nanu.org.ua/en/archive/2019/8/2 kostenfrei https://doaj.org/toc/1025-6415 Journal toc kostenfrei https://doaj.org/toc/2518-153X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2019 9-15 |
allfields_unstemmed |
10.15407/dopovidi2019.08.009 doi (DE-627)DOAJ008124957 (DE-599)DOAJdb3c343ea7604ebc86dbbd75e7d4b887 DE-627 ger DE-627 rakwb eng rus ukr Q1-390 Ya.I. Grushka verfasserin aut Necessary and sufficient condition for the existence of the one-point time on an oriented set 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the process of continuous transformations, i.e., they can change their properties, appear or disappear, and disintegrate into several parts or, conversely, several objects can merge into a single one. In addition, the picture of the evolution of a changeable set can depend on the method of observation (that is, on the reference frame). The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. The notion of oriented set is the basic elementary concept of the theory of changeable sets. Oriented sets can be interpreted as the most primitive abstract models of sets of changing objects that evolve within a single (fixed) reference frame. The oriented sets are mathematical objects, in the framework of which one can give the mathematically rigorous definition of the concept of time as a certain mapping from a certain time scale, represented by a linearly ordered set, into the set of simultaneous states of the oriented set. In this paper, the necessary and sufficient condition of the existence of the onepoint time on an oriented set is established. From the intuitive point of view, the onepoint time is the time associated with the evolution of a system consisting of only one object (for example, one material point). Namely, the concept of a quasichain oriented set is introduced, and it is proved that the onepoint time exists on the oriented set, if and only if this oriented set is a quasichain. Using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets. changeable sets time ordered sets oriented sets Science (General) In Доповiдi Нацiональної академiї наук України Publishing House "Akademperiodyka", 2019 8(2019), Seite 9-15 (DE-627)66080784X (DE-600)2609380-7 2518153X nnns volume:8 year:2019 pages:9-15 https://doi.org/10.15407/dopovidi2019.08.009 kostenfrei https://doaj.org/article/db3c343ea7604ebc86dbbd75e7d4b887 kostenfrei http://www.dopovidi-nanu.org.ua/en/archive/2019/8/2 kostenfrei https://doaj.org/toc/1025-6415 Journal toc kostenfrei https://doaj.org/toc/2518-153X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2019 9-15 |
allfieldsGer |
10.15407/dopovidi2019.08.009 doi (DE-627)DOAJ008124957 (DE-599)DOAJdb3c343ea7604ebc86dbbd75e7d4b887 DE-627 ger DE-627 rakwb eng rus ukr Q1-390 Ya.I. Grushka verfasserin aut Necessary and sufficient condition for the existence of the one-point time on an oriented set 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the process of continuous transformations, i.e., they can change their properties, appear or disappear, and disintegrate into several parts or, conversely, several objects can merge into a single one. In addition, the picture of the evolution of a changeable set can depend on the method of observation (that is, on the reference frame). The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. The notion of oriented set is the basic elementary concept of the theory of changeable sets. Oriented sets can be interpreted as the most primitive abstract models of sets of changing objects that evolve within a single (fixed) reference frame. The oriented sets are mathematical objects, in the framework of which one can give the mathematically rigorous definition of the concept of time as a certain mapping from a certain time scale, represented by a linearly ordered set, into the set of simultaneous states of the oriented set. In this paper, the necessary and sufficient condition of the existence of the onepoint time on an oriented set is established. From the intuitive point of view, the onepoint time is the time associated with the evolution of a system consisting of only one object (for example, one material point). Namely, the concept of a quasichain oriented set is introduced, and it is proved that the onepoint time exists on the oriented set, if and only if this oriented set is a quasichain. Using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets. changeable sets time ordered sets oriented sets Science (General) In Доповiдi Нацiональної академiї наук України Publishing House "Akademperiodyka", 2019 8(2019), Seite 9-15 (DE-627)66080784X (DE-600)2609380-7 2518153X nnns volume:8 year:2019 pages:9-15 https://doi.org/10.15407/dopovidi2019.08.009 kostenfrei https://doaj.org/article/db3c343ea7604ebc86dbbd75e7d4b887 kostenfrei http://www.dopovidi-nanu.org.ua/en/archive/2019/8/2 kostenfrei https://doaj.org/toc/1025-6415 Journal toc kostenfrei https://doaj.org/toc/2518-153X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2019 9-15 |
allfieldsSound |
10.15407/dopovidi2019.08.009 doi (DE-627)DOAJ008124957 (DE-599)DOAJdb3c343ea7604ebc86dbbd75e7d4b887 DE-627 ger DE-627 rakwb eng rus ukr Q1-390 Ya.I. Grushka verfasserin aut Necessary and sufficient condition for the existence of the one-point time on an oriented set 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the process of continuous transformations, i.e., they can change their properties, appear or disappear, and disintegrate into several parts or, conversely, several objects can merge into a single one. In addition, the picture of the evolution of a changeable set can depend on the method of observation (that is, on the reference frame). The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. The notion of oriented set is the basic elementary concept of the theory of changeable sets. Oriented sets can be interpreted as the most primitive abstract models of sets of changing objects that evolve within a single (fixed) reference frame. The oriented sets are mathematical objects, in the framework of which one can give the mathematically rigorous definition of the concept of time as a certain mapping from a certain time scale, represented by a linearly ordered set, into the set of simultaneous states of the oriented set. In this paper, the necessary and sufficient condition of the existence of the onepoint time on an oriented set is established. From the intuitive point of view, the onepoint time is the time associated with the evolution of a system consisting of only one object (for example, one material point). Namely, the concept of a quasichain oriented set is introduced, and it is proved that the onepoint time exists on the oriented set, if and only if this oriented set is a quasichain. Using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets. changeable sets time ordered sets oriented sets Science (General) In Доповiдi Нацiональної академiї наук України Publishing House "Akademperiodyka", 2019 8(2019), Seite 9-15 (DE-627)66080784X (DE-600)2609380-7 2518153X nnns volume:8 year:2019 pages:9-15 https://doi.org/10.15407/dopovidi2019.08.009 kostenfrei https://doaj.org/article/db3c343ea7604ebc86dbbd75e7d4b887 kostenfrei http://www.dopovidi-nanu.org.ua/en/archive/2019/8/2 kostenfrei https://doaj.org/toc/1025-6415 Journal toc kostenfrei https://doaj.org/toc/2518-153X Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2019 9-15 |
language |
English Russian Ukrainian |
source |
In Доповiдi Нацiональної академiї наук України 8(2019), Seite 9-15 volume:8 year:2019 pages:9-15 |
sourceStr |
In Доповiдi Нацiональної академiї наук України 8(2019), Seite 9-15 volume:8 year:2019 pages:9-15 |
format_phy_str_mv |
Article |
institution |
findex.gbv.de |
topic_facet |
changeable sets time ordered sets oriented sets Science (General) |
isfreeaccess_bool |
true |
container_title |
Доповiдi Нацiональної академiї наук України |
authorswithroles_txt_mv |
Ya.I. Grushka @@aut@@ |
publishDateDaySort_date |
2019-01-01T00:00:00Z |
hierarchy_top_id |
66080784X |
id |
DOAJ008124957 |
language_de |
englisch russisch ukrainisch |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">DOAJ008124957</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230310004037.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230225s2019 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.15407/dopovidi2019.08.009</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)DOAJ008124957</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DOAJdb3c343ea7604ebc86dbbd75e7d4b887</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield><subfield code="a">rus</subfield><subfield code="a">ukr</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">Q1-390</subfield></datafield><datafield tag="100" ind1="0" ind2=" "><subfield code="a">Ya.I. Grushka</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Necessary and sufficient condition for the existence of the one-point time on an oriented set</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the process of continuous transformations, i.e., they can change their properties, appear or disappear, and disintegrate into several parts or, conversely, several objects can merge into a single one. In addition, the picture of the evolution of a changeable set can depend on the method of observation (that is, on the reference frame). The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. The notion of oriented set is the basic elementary concept of the theory of changeable sets. Oriented sets can be interpreted as the most primitive abstract models of sets of changing objects that evolve within a single (fixed) reference frame. The oriented sets are mathematical objects, in the framework of which one can give the mathematically rigorous definition of the concept of time as a certain mapping from a certain time scale, represented by a linearly ordered set, into the set of simultaneous states of the oriented set. In this paper, the necessary and sufficient condition of the existence of the onepoint time on an oriented set is established. From the intuitive point of view, the onepoint time is the time associated with the evolution of a system consisting of only one object (for example, one material point). Namely, the concept of a quasichain oriented set is introduced, and it is proved that the onepoint time exists on the oriented set, if and only if this oriented set is a quasichain. Using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">changeable sets</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">time</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">ordered sets</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">oriented sets</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Science (General)</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">Доповiдi Нацiональної академiї наук України</subfield><subfield code="d">Publishing House "Akademperiodyka", 2019</subfield><subfield code="g">8(2019), Seite 9-15</subfield><subfield code="w">(DE-627)66080784X</subfield><subfield code="w">(DE-600)2609380-7</subfield><subfield code="x">2518153X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:8</subfield><subfield code="g">year:2019</subfield><subfield code="g">pages:9-15</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.15407/dopovidi2019.08.009</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doaj.org/article/db3c343ea7604ebc86dbbd75e7d4b887</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://www.dopovidi-nanu.org.ua/en/archive/2019/8/2</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/1025-6415</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2518-153X</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_DOAJ</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_138</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_171</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_250</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_281</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_647</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4367</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">8</subfield><subfield code="j">2019</subfield><subfield code="h">9-15</subfield></datafield></record></collection>
|
callnumber-first |
Q - Science |
author |
Ya.I. Grushka |
spellingShingle |
Ya.I. Grushka misc Q1-390 misc changeable sets misc time misc ordered sets misc oriented sets misc Science (General) Necessary and sufficient condition for the existence of the one-point time on an oriented set |
authorStr |
Ya.I. Grushka |
ppnlink_with_tag_str_mv |
@@773@@(DE-627)66080784X |
format |
electronic Article |
delete_txt_mv |
keep |
author_role |
aut |
collection |
DOAJ |
remote_str |
true |
callnumber-label |
Q1-390 |
illustrated |
Not Illustrated |
issn |
2518153X |
topic_title |
Q1-390 Necessary and sufficient condition for the existence of the one-point time on an oriented set changeable sets time ordered sets oriented sets |
topic |
misc Q1-390 misc changeable sets misc time misc ordered sets misc oriented sets misc Science (General) |
topic_unstemmed |
misc Q1-390 misc changeable sets misc time misc ordered sets misc oriented sets misc Science (General) |
topic_browse |
misc Q1-390 misc changeable sets misc time misc ordered sets misc oriented sets misc Science (General) |
format_facet |
Elektronische Aufsätze Aufsätze Elektronische Ressource |
format_main_str_mv |
Text Zeitschrift/Artikel |
carriertype_str_mv |
cr |
hierarchy_parent_title |
Доповiдi Нацiональної академiї наук України |
hierarchy_parent_id |
66080784X |
hierarchy_top_title |
Доповiдi Нацiональної академiї наук України |
isfreeaccess_txt |
true |
familylinks_str_mv |
(DE-627)66080784X (DE-600)2609380-7 |
title |
Necessary and sufficient condition for the existence of the one-point time on an oriented set |
ctrlnum |
(DE-627)DOAJ008124957 (DE-599)DOAJdb3c343ea7604ebc86dbbd75e7d4b887 |
title_full |
Necessary and sufficient condition for the existence of the one-point time on an oriented set |
author_sort |
Ya.I. Grushka |
journal |
Доповiдi Нацiональної академiї наук України |
journalStr |
Доповiдi Нацiональної академiї наук України |
callnumber-first-code |
Q |
lang_code |
eng rus ukr |
isOA_bool |
true |
recordtype |
marc |
publishDateSort |
2019 |
contenttype_str_mv |
txt |
container_start_page |
9 |
author_browse |
Ya.I. Grushka |
container_volume |
8 |
class |
Q1-390 |
format_se |
Elektronische Aufsätze |
author-letter |
Ya.I. Grushka |
doi_str_mv |
10.15407/dopovidi2019.08.009 |
title_sort |
necessary and sufficient condition for the existence of the one-point time on an oriented set |
callnumber |
Q1-390 |
title_auth |
Necessary and sufficient condition for the existence of the one-point time on an oriented set |
abstract |
The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the process of continuous transformations, i.e., they can change their properties, appear or disappear, and disintegrate into several parts or, conversely, several objects can merge into a single one. In addition, the picture of the evolution of a changeable set can depend on the method of observation (that is, on the reference frame). The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. The notion of oriented set is the basic elementary concept of the theory of changeable sets. Oriented sets can be interpreted as the most primitive abstract models of sets of changing objects that evolve within a single (fixed) reference frame. The oriented sets are mathematical objects, in the framework of which one can give the mathematically rigorous definition of the concept of time as a certain mapping from a certain time scale, represented by a linearly ordered set, into the set of simultaneous states of the oriented set. In this paper, the necessary and sufficient condition of the existence of the onepoint time on an oriented set is established. From the intuitive point of view, the onepoint time is the time associated with the evolution of a system consisting of only one object (for example, one material point). Namely, the concept of a quasichain oriented set is introduced, and it is proved that the onepoint time exists on the oriented set, if and only if this oriented set is a quasichain. Using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets. |
abstractGer |
The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the process of continuous transformations, i.e., they can change their properties, appear or disappear, and disintegrate into several parts or, conversely, several objects can merge into a single one. In addition, the picture of the evolution of a changeable set can depend on the method of observation (that is, on the reference frame). The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. The notion of oriented set is the basic elementary concept of the theory of changeable sets. Oriented sets can be interpreted as the most primitive abstract models of sets of changing objects that evolve within a single (fixed) reference frame. The oriented sets are mathematical objects, in the framework of which one can give the mathematically rigorous definition of the concept of time as a certain mapping from a certain time scale, represented by a linearly ordered set, into the set of simultaneous states of the oriented set. In this paper, the necessary and sufficient condition of the existence of the onepoint time on an oriented set is established. From the intuitive point of view, the onepoint time is the time associated with the evolution of a system consisting of only one object (for example, one material point). Namely, the concept of a quasichain oriented set is introduced, and it is proved that the onepoint time exists on the oriented set, if and only if this oriented set is a quasichain. Using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets. |
abstract_unstemmed |
The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the process of continuous transformations, i.e., they can change their properties, appear or disappear, and disintegrate into several parts or, conversely, several objects can merge into a single one. In addition, the picture of the evolution of a changeable set can depend on the method of observation (that is, on the reference frame). The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. The notion of oriented set is the basic elementary concept of the theory of changeable sets. Oriented sets can be interpreted as the most primitive abstract models of sets of changing objects that evolve within a single (fixed) reference frame. The oriented sets are mathematical objects, in the framework of which one can give the mathematically rigorous definition of the concept of time as a certain mapping from a certain time scale, represented by a linearly ordered set, into the set of simultaneous states of the oriented set. In this paper, the necessary and sufficient condition of the existence of the onepoint time on an oriented set is established. From the intuitive point of view, the onepoint time is the time associated with the evolution of a system consisting of only one object (for example, one material point). Namely, the concept of a quasichain oriented set is introduced, and it is proved that the onepoint time exists on the oriented set, if and only if this oriented set is a quasichain. Using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets. |
collection_details |
GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_138 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 |
title_short |
Necessary and sufficient condition for the existence of the one-point time on an oriented set |
url |
https://doi.org/10.15407/dopovidi2019.08.009 https://doaj.org/article/db3c343ea7604ebc86dbbd75e7d4b887 http://www.dopovidi-nanu.org.ua/en/archive/2019/8/2 https://doaj.org/toc/1025-6415 https://doaj.org/toc/2518-153X |
remote_bool |
true |
ppnlink |
66080784X |
callnumber-subject |
Q - General Science |
mediatype_str_mv |
c |
isOA_txt |
true |
hochschulschrift_bool |
false |
doi_str |
10.15407/dopovidi2019.08.009 |
callnumber-a |
Q1-390 |
up_date |
2024-07-03T16:06:54.290Z |
_version_ |
1803574642517999616 |
fullrecord_marcxml |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">DOAJ008124957</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230310004037.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">230225s2019 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.15407/dopovidi2019.08.009</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)DOAJ008124957</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DOAJdb3c343ea7604ebc86dbbd75e7d4b887</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield><subfield code="a">rus</subfield><subfield code="a">ukr</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">Q1-390</subfield></datafield><datafield tag="100" ind1="0" ind2=" "><subfield code="a">Ya.I. Grushka</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Necessary and sufficient condition for the existence of the one-point time on an oriented set</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">The subject of this article is closely related to the theory of changeable sets. The mathematically rigorous theory of changeable sets was constructed in 2012. From an intuitive point of view, the changeable sets are sets of objects which, unlike elements of ordinary (static) sets, can be in the process of continuous transformations, i.e., they can change their properties, appear or disappear, and disintegrate into several parts or, conversely, several objects can merge into a single one. In addition, the picture of the evolution of a changeable set can depend on the method of observation (that is, on the reference frame). The main motivation for the introduction of changeable sets was the sixth Hilbert problem, that is, the problem of mathematically rigorous formulation of the fundamentals of theoretical physics. The notion of oriented set is the basic elementary concept of the theory of changeable sets. Oriented sets can be interpreted as the most primitive abstract models of sets of changing objects that evolve within a single (fixed) reference frame. The oriented sets are mathematical objects, in the framework of which one can give the mathematically rigorous definition of the concept of time as a certain mapping from a certain time scale, represented by a linearly ordered set, into the set of simultaneous states of the oriented set. In this paper, the necessary and sufficient condition of the existence of the onepoint time on an oriented set is established. From the intuitive point of view, the onepoint time is the time associated with the evolution of a system consisting of only one object (for example, one material point). Namely, the concept of a quasichain oriented set is introduced, and it is proved that the onepoint time exists on the oriented set, if and only if this oriented set is a quasichain. Using the obtained result, the problem of describing all possible images of linearly ordered sets is solved. This problem naturally arises in the theory of ordered sets.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">changeable sets</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">time</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">ordered sets</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">oriented sets</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Science (General)</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">In</subfield><subfield code="t">Доповiдi Нацiональної академiї наук України</subfield><subfield code="d">Publishing House "Akademperiodyka", 2019</subfield><subfield code="g">8(2019), Seite 9-15</subfield><subfield code="w">(DE-627)66080784X</subfield><subfield code="w">(DE-600)2609380-7</subfield><subfield code="x">2518153X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:8</subfield><subfield code="g">year:2019</subfield><subfield code="g">pages:9-15</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.15407/dopovidi2019.08.009</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doaj.org/article/db3c343ea7604ebc86dbbd75e7d4b887</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://www.dopovidi-nanu.org.ua/en/archive/2019/8/2</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/1025-6415</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="u">https://doaj.org/toc/2518-153X</subfield><subfield code="y">Journal toc</subfield><subfield code="z">kostenfrei</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_DOAJ</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_11</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_20</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_22</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_23</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_24</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_31</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_39</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_40</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_60</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_62</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_63</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_65</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_69</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_73</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_74</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_90</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_95</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_100</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_105</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_110</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_138</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_151</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_152</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_161</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_171</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_187</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_213</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_230</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_250</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_281</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_285</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_293</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_370</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_602</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_647</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_702</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_2014</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4012</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4037</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4112</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4125</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4126</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4249</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4305</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4306</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4307</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4313</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4322</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4323</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4324</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4325</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4335</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4338</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4367</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_4700</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">8</subfield><subfield code="j">2019</subfield><subfield code="h">9-15</subfield></datafield></record></collection>
|
score |
7.4008236 |