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Relation Algebras, Idempotent Semirings and Generalized Bunched Implication Algebras [chapter]

Peter Jipsen
2017 Lecture Notes in Computer Science  
These algebras play a role similar to representable relation algebras, and we identify a finitely-based variety of cyclic involutive GBI-algebras that includes all weakening relation algebras.  ...  Extending a result of Chajda and Länger, we show that involutive residuated lattices are determined by a pair of dually isomorphic idempotent semirings on the same set, and this result also applies to  ...  of binary relations.  ... 
doi:10.1007/978-3-319-57418-9_9 fatcat:c7rkwlaclffatmyqmydcsqvrem

Cyclic Extensions of Order Varieties

Pierre Ille, Paul Ruet
2008 Electronical Notes in Theoretical Computer Science  
It is known that the problem of telling whether a cyclic order is included in some cycle is NP-complete. We show that the same question for order varieties, a special class of cyclic orders, is in L.  ...  For this, we relate the entropy relation between partial orders to the forcing relation of graph theory.  ...  Cyclic orders [13, 15] are ternary relations with the property that when a point in the support is fixed (focussed on), the induced binary relation is a partial (binary) order.  ... 
doi:10.1016/j.entcs.2008.04.057 fatcat:qezsnojbyzgu3n3cnvrnbcxzi4

Page 8226 of Mathematical Reviews Vol. , Issue 2003k [page]

2003 Mathematical Reviews  
It is noted that all semilattices that admit a diagram (semilattice diagram of unions) of a fixed form define a completely definite class of complete semi- groups of binary relations.  ...  The au- thors believe that in order to study complete semigroups of binary relations, it is natural to highlight a semilattice diagram of unions of a definite form and consider the class of semigroups  ... 

Cyclic Negations and Four-valuedness

Oleg Grigoriev, Dmitry Zaitsev
2022 Electronic Proceedings in Theoretical Computer Science  
Purely formal logical result of our study consists in axiomatizing the logics of defined matrices as the systems of binary consequence relation and proving correctness and completeness theorems for these  ...  In particular we consider a representation of so called square root of negation within this four valued semantics as an operation which acts like a cycling negation.  ...  According to [13] , the first appearance of a cyclic negation in four valued framework can be found in [17] , while [13] itself deals with the property of functional completeness for the expansions  ... 
doi:10.4204/eptcs.358.16 fatcat:fxu7pdsu65hblddifjzptuw6hi

Page 7 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
In this paper we describe a binary composition operation, the anti-join, which combines a pair of clutters 4 and & to give a new clutter &.  ...  In fact, it has the property that the blocker of the clutter & obtained by join- ing two clutters A and Y% is the anti-join of the blockers of 7% and .%.  ... 

Invariants of the Anti-Automorphisms of a Group

J. Richard Buchi, Jesse B. Wright
1957 Proceedings of the American Mathematical Society  
The notion of an anti-automorphism applies to any algebraic system A = (A, •) consisting of a set A and a binary operation x-y.  ...  The automorphisms and anti-automorphisms of a group A constitute the group of automorphisms of the relation a(x, y, z) : xy = z\/ yx = z i.e., the relation a is a characterizing invariant for Gi(A).  ... 
doi:10.2307/2032693 fatcat:t72lqb6afzfe7o3v36grdwl3su

Invariants of the Anti-Automorphisms of a Group [chapter]

J. Richard Büchi, Jesse B. Wright
1990 The Collected Works of J. Richard Büchi  
The notion of an anti-automorphism applies to any algebraic system A = (A, •) consisting of a set A and a binary operation x-y.  ...  The automorphisms and anti-automorphisms of a group A constitute the group of automorphisms of the relation a(x, y, z) : xy = z\/ yx = z i.e., the relation a is a characterizing invariant for Gi(A).  ... 
doi:10.1007/978-1-4613-8928-6_13 fatcat:j7gydo5xjjaqdmm2ghtc76o5ee

Invariants of the anti-automorphisms of a group

J. Richard B{üchi, Jesse B. Wright
1957 Proceedings of the American Mathematical Society  
The notion of an anti-automorphism applies to any algebraic system A = (A, •) consisting of a set A and a binary operation x-y.  ...  The automorphisms and anti-automorphisms of a group A constitute the group of automorphisms of the relation a(x, y, z) : xy = z\/ yx = z i.e., the relation a is a characterizing invariant for Gi(A).  ... 
doi:10.1090/s0002-9939-1957-0095891-5 fatcat:lptmxr5op5dzhn6tqcji2m7vcm

Ternary monolayers as DNA recognition interfaces for direct and sensitive electrochemical detection in untreated clinical samples

Susana Campuzano, Filiz Kuralay, M. Jesús Lobo-Castañón, Martin Bartošík, Kedar Vyavahare, Emil Paleček, David A. Haake, Joseph Wang
2011 Biosensors & bioelectronics  
Detection of specific DNA sequences in clinical samples is a key goal of studies on DNA biosensors and gene chips.  ...  Such genosensing relies on a new ternary interface involving hexanedithiol (HDT) co-immobilized with the thiolated capture probe (SHCP) on gold surfaces, followed by the incorporation of 6-mercapto-1-hexanol  ...  Acknowledgements Financial support from the National Institutes of Health (Award U01 AI075565) is gratefully  ... 
doi:10.1016/j.bios.2011.02.004 pmid:21377347 pmcid:PMC3065524 fatcat:ohf7bivmjrgxvdupqths2j7pbe

Page 2088 of Mathematical Reviews Vol. , Issue 88d [page]

1988 Mathematical Reviews  
As a tool of the investigation we use the canon- ical anti-isomorphism between Arm(U) and the lattice of closure systems on U.” 88d:68013 68P15 Krentel, Mark W. (1-CRNL-C) A note on the transaction backout  ...  The first method is based on the formulation of con- straints in terms of inclusions of some binary relations associated with the database.  ... 

Page 4458 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
See also «01023. 95h:04002 04A05 Hansson, Sven Ove (S-UPPS-Q; Uppsala) A note on anti-cyclic properties of complete binary relations. (English summary) Rep. Math. Logic No.27 (1993), 41-44 (1994).  ...  A short notation is introduced for investigating connected binary relations, and rules for manipulations are formulated.  ... 

Linear transformations of tropical matrices preserving the cyclicity index

Alexander Guterman, Elena Kreines, Carsten Thomassen
2021 Special Matrices  
We combine matrix theory and graph theory methods to give a complete characterization of the surjective linear transformations of tropical matrices that preserve the cyclicity index.  ...  We show that there are non-surjective linear transformations that preserve the cyclicity index and we leave it open to characterize those.  ...  The research of the rst and the second authors is nancially supported by RSF Project N. 17-11-01124. The third author is supported by Independent Research Fund Denmark, 8021-002498 AlgoGraph.  ... 
doi:10.1515/spma-2020-0128 fatcat:xirjdr3epzggnmmyspxg7iwafu

Borane Polyhedra as Building Blocks for Unknown but Potentially Isolatable New Molecules – Extensions based on Computations of the Known B18H22 Isomers

Josep M. Oliva, Juanjo Rué, John D. Kennedy, Vladimir R. Rosenfeld
2013 Croatica Chemica Acta  
We have also derived two new cyclic structures based on the condensation of borane pentagonal pyramids and bipyramids.  ...  The concatenation of polyhedral borane molecules is also considered from a mathematical point of view. (  ...  VRR acknowledges a visiting collaboration with Professor Douglas Klein at Galveston. JMO is greatly indebted to Professor Douglas Klein for showing comprehensive aspects of the  ... 
doi:10.5562/cca2304 fatcat:kye5it6p7fegfjzddeol225gku

From Binary Groups to Terminal Rings

Stuart D. Scott
2021 Mathematica Pannonica  
One of the main theorems of this paper occurs in section five where it is shown that a binary group V is a P0(V) ring module if, and only if, it is a rather restricted form of non-associative ring.  ...  Binary groups are a meaningful step up from non-associative rings and nearrings. It makes sense to study them in terms of their nearrings of zero-fixing polynomial maps.  ...  A property of some minimal ideals of a binary group was brie y touched on at the end of section six.  ... 
doi:10.1556/314.2021.00013 fatcat:h3tvoy62dzgqxbzu2bjpowbyj4

Labeled binary planar trees and quasi-Lie algebras

Jerome Levine
2006 Algebraic and Geometric Topology  
We study the natural map eta between a group of binary planar trees whose leaves are labeled by elements of a free abelian group H and a certain group D(H) derived from the free Lie algebra over H.  ...  Both of these groups arise in several different topological contexts. The map eta is known to be an isomorphism over Q, but not over Z.  ...  We now have defined a retraction r W V n ! W n satisfying properties (1)-(3). To complete the proof we need to show that r induces a map L 0 n .H / ! W n .  ... 
doi:10.2140/agt.2006.6.935 fatcat:mkime5bjynaarktxbk2ovodrt4
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