Equivalence Relations and Modular Arithmetic

2010 ◽  
pp. 55-64
Author(s):  
Matthias Beck ◽  
Ross Geoghegan
Keyword(s):  
Modular Arithmetic ◽  
Equivalence Relations

Weakly precomplete equivalence relations in the Ershov hierarchy

2019 ◽  
Vol 58 (3) ◽  
pp. 297-319
Author(s):  
N. A. Bazhenov ◽  
B. S. Kalmurzaev
Keyword(s):  
Equivalence Relations ◽  
Ershov Hierarchy

Equivalence relations among inequalities for some relative operator entropies

Positivity ◽  
2020 ◽  
Vol 24 (5) ◽  
pp. 1503-1518
Author(s):  
Ismail Nikoufar ◽  
Maryam Fazlolahi
Keyword(s):  
Equivalence Relations

Fundamental relations and identities of fuzzy hyperalgebras

2021 ◽  
pp. 1-10
Author(s):  
Narjes Firouzkouhi ◽  
Abbas Amini ◽  
Chun Cheng ◽  
Mehdi Soleymani ◽  
Bijan Davvaz
Keyword(s):  
Universal Algebra ◽  
Equivalence Relation ◽  
Polynomial Function ◽  
Equivalence Relations ◽  
Fundamental Relation ◽  
Term Function ◽  
Biological Phenomena ◽  
Definition Of

Inspired by fuzzy hyperalgebras and fuzzy polynomial function (term function), some homomorphism properties of fundamental relation on fuzzy hyperalgebras are conveyed. The obtained relations of fuzzy hyperalgebra are utilized for certain applications, i.e., biological phenomena and genetics along with some elucidatory examples presenting various aspects of fuzzy hyperalgebras. Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation α i 1 i 2 ∗ on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation α J ∗ on the set of strong identities.

Query Optimization in the Databases Distributed by Means of Product Equivalence Relations

1988 ◽  
Vol 11 (3) ◽  
pp. 241-265
Author(s):  
W. Marek ◽  
C. Rauszer
Keyword(s):  
Query Optimization ◽  
Selection Process ◽  
Distributed Databases ◽  
Optimization Techniques ◽  
Equivalence Relations ◽  
Database Operations ◽  
By Products

In this paper, we address the problem of query optimization in distributed databases. We show that horizontal partitions of databases, generated by products of equivalence relations, induce optimization techniques for the basic database operations (i.e., the selection, projection, and join operators). In the case of selection, our method allows for restriction of the number of blocks to be searched in the selection process and subsequent simplification of the selection formula at each block. For the natural join operation, we propose an algorithm that reduces the computation of fragments. Proofs of the correctness of our algorithms are also included.

An Algorithm Using Modular Arithmetic for the Subset Sum Problem

1990 ◽  
Vol 21 (2) ◽  
pp. 1-10
Author(s):  
Toshiro Tachibana ◽  
Hideo Nakano ◽  
Yoshiro Nakanishi ◽  
Mitsuru Nakao
Keyword(s):  
Modular Arithmetic ◽  
Subset Sum Problem ◽  
Subset Sum

scholarly journals L2-BETTI NUMBERS OF DISCRETE MEASURED GROUPOIDS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1169-1188 ◽  
Author(s):  
ROMAN SAUER
Keyword(s):  
Probability Space ◽  
Betti Numbers ◽  
Free Action ◽  
Countable Group ◽  
Equivalence Relations ◽  
Dimension Theory ◽  
Discrete Groups ◽  
Type Ii ◽  
Orbit Equivalent ◽  
Definition Of

There are notions of L2-Betti numbers for discrete groups (Cheeger–Gromov, Lück), for type II1-factors (recent work of Connes-Shlyakhtenko) and for countable standard equivalence relations (Gaboriau). Whereas the first two are algebraically defined using Lück's dimension theory, Gaboriau's definition of the latter is inspired by the work of Cheeger and Gromov. In this work we give a definition of L2-Betti numbers of discrete measured groupoids that is based on Lück's dimension theory, thereby encompassing the cases of groups, equivalence relations and holonomy groupoids with an invariant measure for a complete transversal. We show that with our definition, like with Gaboriau's, the L2-Betti numbers [Formula: see text] of a countable group G coincide with the L2-Betti numbers [Formula: see text] of the orbit equivalence relation [Formula: see text] of a free action of G on a probability space. This yields a new proof of the fact the L2-Betti numbers of groups with orbit equivalent actions coincide.

Establishing Equivalence Relations Using a Respondent-Type Training Procedure

1996 ◽  
Vol 46 (4) ◽  
pp. 685-706 ◽  
Author(s):  
Geraldine Leader ◽  
Dermot Barnes ◽  
Paul M. Smeets
Keyword(s):  
Equivalence Relations ◽  
Training Procedure

James Cummings and Ernest Schimmerling, editors. Lecture Note Series of the London Mathematical Society, vol. 406. Cambridge University Press, New York, xi + 419 pp. - Paul B. Larson, Peter Lumsdaine, and Yimu Yin. An introduction to Pmax forcing. pp. 5–23. - Simon Thomas and Scott Schneider. Countable Borel equivalence relations. pp. 25–62. - Ilijas Farah and Eric Wofsey. Set theory and operator algebras. pp. 63–119. - Justin Moore and David Milovich. A tutorial on set mapping reflection. pp. 121–144. - Vladimir G. Pestov and Aleksandra Kwiatkowska. An introduction to hyperlinear and sofic groups. pp. 145–185. - Itay Neeman and Spencer Unger. Aronszajn trees and the SCH. pp. 187–206. - Todd Eisworth, Justin Tatch Moore, and David Milovich. Iterated forcing and the Continuum Hypothesis. pp. 207–244. - Moti Gitik and Spencer Unger. Short extender forcing. pp. 245–263. - Alexander S. Kechris and Robin D. Tucker-Drob. The complexity of classification problems in ergodic theory. pp. 265–299. - Menachem Magidor and Chris Lambie-Hanson. On the strengths and weaknesses of weak squares. pp. 301–330. - Boban Veličković and Giorgio Venturi. Proper forcing remastered. pp. 331–362. - Asger ToÖrnquist and Martino Lupini. Set theory and von Neumann algebras. pp. 363–396. - W. Hugh Woodin, Jacob Davis, and Daniel RodrÍguez. The HOD dichotomy. pp. 397–419.

2014 ◽  
Vol 20 (1) ◽  
pp. 94-97
Author(s):  
Natasha Dobrinen
Keyword(s):  
New York ◽  
Set Theory ◽  
Von Neumann Algebras ◽  
Operator Algebras ◽  
Continuum Hypothesis ◽  
London Mathematical Society ◽  
Equivalence Relations ◽  
Classification Problems ◽  
Von Neumann ◽  
Borel Equivalence Relations
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