scholarly journals Classification of fused links

2016 ◽  
Vol 25 (14) ◽  
pp. 1650076 ◽  
Author(s):  
Timur Nasybullov
Keyword(s):  
Symmetric Group ◽  
Equivalence Classes ◽  
One To One ◽  
Text Component

We construct the complete invariant for fused links. It is proved that the set of equivalence classes of [Formula: see text]-component fused links is in one-to-one correspondence with the set of elements of the abelization [Formula: see text] up to conjugation by elements from the symmetric group [Formula: see text].

A CATALOGUE OF ORIENTABLE 3-MANIFOLDS TRIANGULATED BY 30 COLORED TETRAHEDRA

2008 ◽  
Vol 17 (05) ◽  
pp. 579-599 ◽  
Author(s):  
MARIA RITA CASALI ◽  
PAOLA CRISTOFORI
Keyword(s):  
Automatic Generation ◽  
Computational Approach ◽  
Equivalence Classes ◽  
Colored Graphs ◽  
One To One ◽  
Genus Two ◽  
Jsj Decompositions

The present paper follows the computational approach to 3-manifold classification via edge-colored graphs, already performed in [1] (with respect to orientable 3-manifolds up to 28 colored tetrahedra), in [2] (with respect to non-orientable 3-manifolds up to 26 colored tetrahedra), in [3] and [4] (with respect to genus two 3-manifolds up to 34 colored tetrahedra): in fact, by automatic generation and analysis of suitable edge-colored graphs, called crystallizations, we obtain a catalogue of all orientable 3-manifolds admitting colored triangulations with 30 tetrahedra. These manifolds are unambiguously identified via JSJ decompositions and fibering structures. It is worth noting that, in the present work, a suitable use of elementary combinatorial moves yields an automatic partition of the elements of the generated crystallization catalogue into equivalence classes, which turn out to be in one-to-one correspondence with the homeomorphism classes of the represented manifolds.

scholarly journals CLASSIFICATION OF SPARQL QUERIES INTO EQUIVALENCE CLASSES OF RELEVANT QUERIES

2017 ◽  
Vol 8 (9) ◽  
pp. 152-159
Author(s):  
Theodore Andronikos ◽  
Keyword(s):  
Equivalence Classes

Nearnesses and T0-Extensions of Topological Spaces

1983 ◽  
Vol 26 (4) ◽  
pp. 430-437 ◽  
Author(s):  
Alice M. Dean
Keyword(s):  
Topological Space ◽  
Equivalence Classes ◽  
Topological Spaces ◽  
One To One

AbstractIn [3], Reed establishes a bijection between the (equivalence classes of) principal T1-extensions of a topological space X and the compatible, cluster-generated, Lodato nearnesses on X. We extend Reed's result to the T0 case by obtaining a one-to-one correspondence between the principal T0-extensions of a space X and the collections of sets (called “t-grill sets”) which generate a certain class of nearnesses which we call “t-bunch generated” nearnesses. This correspondence specializes to principal T0-compactifications. Finally, we show that there is a bijection between these t-grill sets and the filter systems of Thron [5], and that the corresponding extensions are equivalent.

Rational permutation groups containing a full cycle

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Temha Erkoç ◽  
Utku Yilmaztürk
Keyword(s):  
Symmetric Group ◽  
Proper Subgroup ◽  
Symmetric Groups ◽  
Transitive Permutation Group ◽  
Rational Group ◽  
Prime Degree ◽  
A Finite Group ◽  
Rational Groups ◽  
Complex Characters

AbstractA finite group whose irreducible complex characters are rational valued is called a rational group. Thus, G is a rational group if and only if N G(〈x〉)/C G(〈x〉) ≌ Aut(〈x〉) for every x ∈ G. For example, all symmetric groups and their Sylow 2-subgroups are rational groups. Structure of rational groups have been studied extensively, but the general classification of rational groups has not been able to be done up to now. In this paper, we show that a full symmetric group of prime degree does not have any rational transitive proper subgroup and that a rational doubly transitive permutation group containing a full cycle is the full symmetric group. We also obtain several results related to the study of rational groups.

scholarly journals Irreducible tensor form of three-particle operator for open-shell atoms

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Rytis Juršėnas ◽  
Gintaras Merkelis
Keyword(s):  
Angular Momentum ◽  
Symmetric Group ◽  
Open Shell ◽  
Matrix Elements ◽  
Irreducible Tensor ◽  
Tensor Form ◽  
Momentum Theory ◽  
Recoupling Coefficients ◽  
Particle Operator

AbstractA three-particle operator in a second quantized form is studied systematically and comprehensively. The operator is transformed into irreducible tensor form. Possible coupling schemes, identified by the classes of symmetric group S6, are presented. Recoupling coefficients that make it possible to transform a given scheme into another are produced by using the angular momentum theory combined with quasispin formalism. The classification of the three-particle operator which acts on n = 1, 2,..., 6 open shells of equivalent electrons of atom is considered. The procedure to construct three-particle matrix elements are examined.

Detecting Non-Triviality of Virtual Links

2003 ◽  
Vol 12 (06) ◽  
pp. 781-803 ◽  
Author(s):  
Teruhisa Kadokami
Keyword(s):  
Equivalence Classes ◽  
Geometric Method ◽  
Virtual Link ◽  
Virtual Knot ◽  
Stable Equivalence ◽  
Link Diagrams ◽  
Virtual Links ◽  
Algebraic Invariants ◽  
One To One

J. S. Carter, S. Kamada and M. Saito showed that there is one to one correspondence between the virtual Reidemeister equivalence classes of virtual link diagrams and the stable equivalence classes of link diagrams on compact oriented surfaces. Using the result, we show how to obtain the supporting genus of a projected virtual link by a geometric method. From this result, we show that a certain virtual knot which cannot be judged to be non-trivial by known algebraic invariants is non-trivial, and we suggest to classify the equivalence classes of projected virtual links by using the supporting genus.

Translation semantic variability: How semantic relatedness affects learning of translation-ambiguous words

2016 ◽  
Vol 20 (4) ◽  
pp. 783-794 ◽  
Author(s):  
JENNIFER BRACKEN ◽  
TAMAR DEGANI ◽  
CHELSEA EDDINGTON ◽  
NATASHA TOKOWICZ
Keyword(s):  
Language Learning ◽  
Word Learning ◽  
Ambiguous Word ◽  
Semantic Relatedness ◽  
Continuous Measure ◽  
Unique Variance ◽  
Ambiguous Words ◽  
One To One ◽  
Dichotomous Classification

Translations often do not align directly across languages, and indirect mappings reduce the accuracy of language learning. To facilitate examination of this issue, we developed a new continuous measure for quantifying the semantic relatedness of words with more than one translation (hereafter translation-ambiguous words). Participants rated the similarity of each translation to every other translation, yielding a Translation Semantic Variability (TSV) score, ranging from 1.00 (unrelated) to 7.00 (related). Then, we determined how relatedness between translations affects translation-ambiguous word learning from German to English. German words with low TSV scores were recognized as translations more slowly and less accurately than German words with high TSV scores. TSV explains unique variance beyond the previously-used dichotomous classification of words as form vs. meaning ambiguous. We propose that the relatedness of the translation alternatives influences learning because it affects the ease with which a one-to-one mapping can be established between form and meaning.

AN ALGEBRAIC THEORY FOR REGULAR LANGUAGES OF FINITE AND INFINITE WORDS

1993 ◽  
Vol 03 (04) ◽  
pp. 447-489 ◽  
Author(s):  
THOMAS WILKE
Keyword(s):  
Algebraic Theory ◽  
Algebraic Approach ◽  
Regular Languages ◽  
Cantor Space ◽  
Infinite Words ◽  
Finite Semigroups ◽  
Borel Hierarchy ◽  
Algebraic Description ◽  
One To One

An algebraic approach to the theory of regular languages of finite and infinite words (∞-languages) is presented. It extends the algebraic theory of regular languages of finite words, which is based on finite semigroups. Their role is taken over by a structure called right binoid. A variety theorem is proved: there is a one-to-one correspondence between varieties of ∞-languages and pseudovarieties of right binoids. The class of locally threshold testable languages and several natural subclasses (such as the class of locally testable languages) as well as classes of the Borel hierarchy over the Cantor space (restricted to regular languages) are investigated as examples for varieties of ∞-languages. The corresponding pseudovarieties of right binoids are characterized and in some cases defining equations are derived. The connections with the algebraic description and classification of regular languages of infinite words in terms of finite semigroups are pointed out.

scholarly journals A classification of intersection type systems

2002 ◽  
Vol 67 (1) ◽  
pp. 353-368
Author(s):  
M. W. Bunder
Keyword(s):  
Type Systems ◽  
Equivalence Classes ◽  
Type Assignment ◽  
Emptiness Problem ◽  
Intersection Types

AbstractThe first system of intersection types. Coppo and Dezani [3], extended simple types to include intersections and added intersection introduction and elimination rules ((ΛI ) and (ΛE) ) to the type assignment system. The major advantage of these new types was that they were invariant under β-equality, later work by Barendregt, Coppo and Dezani [1], extended this to include an (η) rule which gave types invariant under βη-reduction.Urzyczyn proved in [6] that for both these systems it is undecidable whether a given intersection type is empty. Kurata and Takahashi however have shown in [5] that this emptiness problem is decidable for the sytem including (η). but without (ΛI).The aim of this paper is to classify intersection type systems lacking some of (ΛI), (ΛE) and (η), into equivalence classes according to their strength in typing λ-terms and also according to their strength in possessing inhabitants.This classification is used in a later paper to extend the above (un)decidability results to two of the five inhabitation-equivalence classes. This later paper also shows that the systems in two more of these classes have decidable inhabitation problems and develops algorithms to find such inhabitants.

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