Natural equivalence

2017 ◽  
pp. 6-23
Keyword(s):  
1999 ◽  
Vol 09 (09) ◽  
pp. 1803-1813 ◽  
Author(s):  
JÉRÔME E. LOS ◽  
ZBIGNIEW H. NITECKI

An automorphism of a graph is edge-transitive if it acts transitively on the set of geometric edges (components of the complement of the vertices), or equivalently, if there is no nontrivial invariant subgraph. Every such automorphism can be embedded as the restriction to an invariant spine of some orientation-preserving periodic homeomorphism of a punctured surface. We find all the edge-transitive graph automorphisms and for each, find a complete list (up to a natural equivalence relation) of the possible ways that it can be embedded in a periodic homeomorphism.


1989 ◽  
Vol 41 (5) ◽  
pp. 830-854 ◽  
Author(s):  
B. Banaschewski ◽  
A. Pultr

A natural approach to topology which emphasizes its geometric essence independent of the notion of points is given by the concept of frame (for instance [4], [8]). We consider this a good formalization of the intuitive perception of a space as given by the “places” of non-trivial extent with appropriate geometric relations between them. Viewed from this position, points are artefacts determined by collections of places which may in some sense by considered as collapsing or contracting; the precise meaning of the latter as well as possible notions of equivalence being largely arbitrary, one may indeed have different notions of point on the same “space”. Of course, the well-known notion of a point as a homomorphism into 2 evidently fits into this pattern by the familiar correspondence between these and the completely prime filters. For frames equipped with a diameter as considered in this paper, we introduce a natural alternative, the Cauchy points. These are the obvious counterparts, for metric locales, of equivalence classes of Cauchy sequences familiar from the classical description of completion of metric spaces: indeed they are decreasing sequences for which the diameters tend to zero, identified by a natural equivalence relation.


2016 ◽  
Vol 81 (4) ◽  
pp. 1225-1254 ◽  
Author(s):  
RUSSELL MILLER ◽  
KENG MENG NG

AbstractWe introduce the notion of finitary computable reducibility on equivalence relations on the domainω. This is a weakening of the usual notion of computable reducibility, and we show it to be distinct in several ways. In particular, whereas no equivalence relation can be${\rm{\Pi }}_{n + 2}^0$-complete under computable reducibility, we show that, for everyn, there does exist a natural equivalence relation which is${\rm{\Pi }}_{n + 2}^0$-complete under finitary reducibility. We also show that our hierarchy of finitary reducibilities does not collapse, and illustrate how it sharpens certain known results. Along the way, we present several new results which use computable reducibility to establish the complexity of various naturally defined equivalence relations in the arithmetical hierarchy.


2020 ◽  
Vol 23 (1) ◽  
pp. 250-266
Author(s):  
Lubna Abd Rahman ◽  
Sulhah Ramli ◽  
Hishomudin Ahmad ◽  
Robiatul Adawiyah Mohd

Al-Quran adalah teks suci yang mengandungi ciri-ciri linguistik dan retorik yang adakalanya menjangkau kemampuan aspek semantik untuk menerangkannya. Sifat Allah merupakan istilah khusus Al-Quran yang tidak dapat diterjemahkan hanya dengan melihat makna semantik semata-mata, kerana mengandungi makna khusus yang merujuk kepada sifat Ketuhanan. Dalam fenomena seperti ini, penterjemah disaran menggunakan pendekatan pragmatik yang menafsirkan makna ujaran dan menyampaikan maklumat berdasarkan konteks ayat untuk memberi pemahaman yang jelas tentang makna sebenar ujaran tersebut kepada pembaca bahasa sasaran, agar dapat mencapai tahap kerelevanan optimum. Kajian ini bertujuan mengkaji terjemahan salah satu sifat Allah dalam Al-Quran, Baseer untuk melihat sama ada terjemahannya mencapai kerelevanan optimum atau sebaliknya. Teori Relevan (TR) yang lazimnya diaplikasi dalam bidang komunikasi dijadikan landasan teori untuk menganalisis terjemahan perkataan Baseer dalam surah al-Isra’ untuk melihat bagaimana makna Baseer dinyatakan dalam teks terjemahan al-Quran yang dipilih iaitu teks terjemahan Al-Quran terkenal dalam bahasa Inggeris oleh Abdel Haleem, Pickthall dan George Sale. Kajian ini menunjukkan bahawa terdapat perbezaan dalam terjemahan sifat Baseer antara tiga teks sasaran. Sekiranya dilihat dari sudut Teori Relevan pula, kebanyakan terjemahannya tidak mencapai kerelevanan optimum, kerana makna yang diberikan oleh penterjemah tidak menyokong makna yang dimaksudkan oleh sifat Allah. This study aims to investigate the translation of one of the Devine Attributes in Quran, the word Baseer whether its translation achieves optimal relevance or otherwise. It employed a qualitative method using content analysis technique based on Relevance Theory, which is basically applied in communication field, in analyzing the translation of the word 'baseer' in surah al-Isra’ to investigate how the meaning of Baseer is rendered in in three well-known Quran translations in English language by Abdel Haleem, Pickthall and George Sale. This study shows that there are differences in the translation of Baseer among the three target texts. If viewed from the point of Relevance Theory, most of its translations do not achieve optimal relevance, because the meanings given by the translators do not support the meaning meant by the nature of Allah. This indicates that absolute equivalence could never been achieved when translating specific words of the Quran and in this study, the translation of Devine Attributes sometimes does not achieve optimal relevance. Therefore, the translator may select the closest natural equivalence of the meaning of the attribute.


Author(s):  
P. M. Edwards

AbstractA natural equivalence θ on the lattice of congruences λ(S) of a semigroup S is studied. For any eventually regular semigroup S, it is shown that θ is a congruence, each θ-class is a complete sublattice of λ(S) and the maximum element in each θ-class is determined. 1980 Mathematics subject classification (Amer. Math. Soc.): 20 M 10.


2014 ◽  
Vol 36 (2) ◽  
pp. 470-513 ◽  
Author(s):  
ALFREDO COSTA ◽  
BENJAMIN STEINBERG

We prove that the Karoubi envelope of a shift—defined as the Karoubi envelope of the syntactic semigroup of the language of blocks of the shift—is, up to natural equivalence of categories, an invariant of flow equivalence. More precisely, we show that the action of the Karoubi envelope on the Krieger cover of the shift is a flow invariant. An analogous result concerning the Fischer cover of a synchronizing shift is also obtained. From these main results, several flow equivalence invariants—some new and some old—are obtained. We also show that the Karoubi envelope is, in a natural sense, the best possible syntactic invariant of flow equivalence of sofic shifts. Another application concerns the classification of Markov–Dyck and Markov–Motzkin shifts: it is shown that, under mild conditions, two graphs define flow equivalent shifts if and only if they are isomorphic. Shifts with property ($\mathscr{A}$) and their associated semigroups, introduced by Wolfgang Krieger, are interpreted in terms of the Karoubi envelope, yielding a proof of the flow invariance of the associated semigroups in the cases usually considered (a result recently announced by Krieger), and also a proof that property ($\mathscr{A}$) is decidable for sofic shifts.


Author(s):  
Bijan Davvaz ◽  
Wieslaw A. Dudek

The notion of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of the notion of fuzzy sets. In this paper, we apply the concept of intuitionistic fuzzy sets toHv-rings. We introduce the notion of an intuitionistic fuzzyHv-ideal of anHv-ring and then some related properties are investigated. We state some characterizations of intuitionistic fuzzyHv-ideals. Also we investigate some natural equivalence relations on the set of all intuitionistic fuzzyHv-ideals of anHv-ring.


2010 ◽  
Vol 20 (07) ◽  
pp. 901-922 ◽  
Author(s):  
BRIAN A. DAVEY ◽  
JANE G. PITKETHLY

We investigate when a finite algebra admits only a finite number of compatible relations (modulo a natural equivalence). This finiteness condition is closely related to others in the literature, and arises naturally in duality theory. We find necessary conditions for a finite algebra to admit only finitely many compatible relations, as well as a family of examples of such algebras.


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