Covering relation in the language of mono-unary algebras with at most one constant symbol

1989 ◽  
Vol 26 (2) ◽  
pp. 143-148 ◽  
Author(s):  
Cornelia Kalfa
Keyword(s):  
Constant Symbol ◽  
Covering Relation

Multiplication complexe et équivalence élémentaire dans le langage des corps (Complex multiplication and elementary equivalence in the language of fields)

2002 ◽  
Vol 67 (2) ◽  
pp. 635-648
Author(s):  
Xavier Vidaux
Keyword(s):  
Function Fields ◽  
Complex Multiplication ◽  
Closed Field ◽  
Constant Symbol ◽  
Endomorphism Rings ◽  
Modular Invariant ◽  
Elementary Equivalence ◽  
Algebraically Closed Field

AbstractLet K and K′ be two elliptic fields with complex multiplication over an algebraically closed field k of characteristic 0. non k-isomorphic, and let C and C′ be two curves with respectively K and K′ as function fields. We prove that if the endomorphism rings of the curves are not isomorphic then K and K′ are not elementarily equivalent in the language of fields expanded with a constant symbol (the modular invariant). This theorem is an analogue of a theorem from David A. Pierce in the language of k-algebras.

Variable Precision Rough Set Model Based on Covering Relation and Uncertainty Measure

2013 ◽  
Vol 694-697 ◽  
pp. 2856-2859
Author(s):  
Mei Yun Wang ◽  
Chao Wang ◽  
Da Zeng Tian
Keyword(s):  
Rough Set ◽  
Uncertainty Measure ◽  
Probabilistic Measure ◽  
Covering Relation ◽  
Practical Applications ◽  
Variable Precision ◽  
Model Based ◽  
Equivalent Relation ◽  
Proposed Model ◽  
Variable Precision Rough Set

The variable precision probabilistic rough set model is based on equivalent relation and probabilistic measure. However, the requirements of equivalent relation and probabilistic measure are too strict to satisfy in some practical applications. In order to solve the above problem, a variable precision rough set model based on covering relation and uncertainty measure is proposed. Moreover, the upper and lower approximation operators of the proposed model are given, while the properties of the operators are discussed.

scholarly journals A New Rapid Incremental Algorithm for Constructing Concept Lattices

Information ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 78 ◽  
Author(s):  
Jingpu Zhang ◽  
Ronghui Liu ◽  
Ligeng Zou ◽  
Licheng Zeng
Keyword(s):  
Formal Concept Analysis ◽  
Concept Lattice ◽  
Incremental Algorithm ◽  
Formal Context ◽  
Formal Concept ◽  
Concept Lattices ◽  
Covering Relation ◽  
Canonical Generator ◽  
Lattice Construction ◽  
Time And Space Complexity

Formal concept analysis has proven to be a very effective method for data analysis and rule extraction, but how to build formal concept lattices is a difficult and hot topic. In this paper, an efficient and rapid incremental concept lattice construction algorithm is proposed. The algorithm, named FastAddExtent, is seen as a modification of AddIntent in which we improve two fundamental procedures, including fixing the covering relation and searching the canonical generator. The proposed algorithm can locate the desired concept quickly by adding data fields to every concept. The algorithm is depicted in detail, using a formal context to show how the new algorithm works and discussing time and space complexity issues. We also present an experimental evaluation of its performance and comparison with AddExtent. Experimental results show that the FastAddExtent algorithm can improve efficiency compared with the primitive AddExtent algorithm.

-fuzzy covering relation

2007 ◽  
Vol 158 (22) ◽  
pp. 2456-2465 ◽  
Author(s):  
Branimir Šešelja
Keyword(s):  
Covering Relation

scholarly journals Ordered Structures and Projections

2008 ◽  
Vol 2008 ◽  
pp. 1-6
Author(s):  
M. Yazi
Keyword(s):  
Order Relation ◽  
Linear Representation ◽  
Chain Condition ◽  
Ordered Structures ◽  
Dimensional Vector Space ◽  
Covering Relation ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
The Family ◽  
Usual Order

We associate a covering relation to the usual order relation defined in the set of all idempotent endomorphisms (projections) of a finite-dimensional vector space. A characterization is given of it. This characterization makes this order an order verifying the Jordan-Dedekind chain condition. We give also a property for certain finite families of this order. More precisely, the family of parts intervening in the linear representation of diagonalizable endomorphism, that is, the orthogonal families forming a decomposition of the identity endomorphism.

Complete types and the natural numbers

1973 ◽  
Vol 38 (3) ◽  
pp. 413-415
Author(s):  
Julia F. Knight
Keyword(s):  
Complete Theory ◽  
Elementary Extension ◽  
Constant Symbol ◽  
Natural Numbers ◽  
Complete Type

In this paper it is shown that, for any complete type Σ omitted in the structure , or in any expansion of having only countably many relations and operations, there is a proper elementary extension of (or of ) which omits Σ. This result (which was announced in [2]) is used to answer a question of Malitz on complete -sentences. The result holds also for countable families of types.A type is a countable set of formulas with just the variable υ free. A structure is said to omit a type Σ if no element of satisfies all of the formulas of Σ. For example, omits the type Σω = {υ ≠ n: n ∈ ω}, since n fails to satisfy υ ≠ n. (Here n is the constant symbol standing for n.)A type Σ is said to be complete with respect to a theory T if the set of sentences T ∪ Σ(e) generates a complete theory, where Σ(e) is the result of replacing υ by the new constant e in all of the formulas of Σ. The type Σω is clearly not complete with respect to Th(). (For any structure Th(), Th() is the set of all sentences true in .)

scholarly journals Alignments, crossings, cycles, inversions, and weak Bruhat order in permutation tableaux of type $B$

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Soojin Cho ◽  
Kyoungsuk Park
Keyword(s):  
Bruhat Order ◽  
Type B ◽  
Coxeter System ◽  
Covering Relation ◽  
Signed Permutations ◽  
Weak Bruhat Order ◽  
International Audience

International audience Alignments, crossings and inversions of signed permutations are realized in the corresponding permutation tableaux of type $B$, and the cycles of signed permutations are understood in the corresponding bare tableaux of type $B$. We find the relation between the number of alignments, crossings and other statistics of signed permutations, and also characterize the covering relation in weak Bruhat order on Coxeter system of type $B$ in terms of permutation tableaux of type $B$. De nombreuses statistiques importantes des permutations signées sont réalisées dans les tableaux de permutations ou ”bare” tableaux de type $B$ correspondants : les alignements, croisements et inversions des permutations signées sont réalisés dans les tableaux de permutations de type $B$ correspondants, et les cycles des permutations signées sont comprises dans les ”bare” tableaux de type $B$ correspondants. Cela nous mène à relier le nombre d’alignements et de croisements avec d’autres statistiques des permutations signées, et aussi de caractériser la relation de couverture dans l’ordre de Bruhat faible sur des systèmes de Coxeter de type $B$ en termes de tableaux de permutations de type $B$.

scholarly journals Fast Möbius Inversion in Semimodular Lattices and ER-labelable Posets

10.37236/5998 ◽  
2016 ◽  
Vol 23 (3) ◽  
Author(s):  
Petteri Kaski ◽  
Jukka Kohonen ◽  
Thomas Westerbäck
Keyword(s):  
General Algorithm ◽  
Arithmetic Operations ◽  
Covering Relation ◽  
Möbius Inversion ◽  
Semimodular Lattices ◽  
Möbius Transforms ◽  
Finite Posets ◽  
Geometric Lattices

We consider the problem of fast zeta and Möbius transforms in finite posets, particularly in lattices. It has previously been shown that for a certain family of lattices, zeta and Möbius transforms can be computed in $O(e)$ elementary arithmetic operations, where $e$ denotes the size of the covering relation. We show that this family is exactly that of geometric lattices. We also extend the algorithms so that they work in $e$ operations for all semimodular lattices, including chains and divisor lattices. Finally, for both transforms, we provide a more general algorithm that works in $e$ operations for all ER-labelable posets.

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