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

2017
*
Lecture Notes in Computer Science
*

These algebras play

doi:10.1007/978-3-319-57418-9_9
fatcat:c7rkwlaclffatmyqmydcsqvrem
*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*. ...##
###
Cyclic Extensions of Order Varieties

2008
*
Electronical Notes in Theoretical Computer Science
*

It is known that the problem

doi:10.1016/j.entcs.2008.04.057
fatcat:qezsnojbyzgu3n3cnvrnbcxzi4
*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. ...##
###
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

2022
*
Electronic Proceedings in Theoretical Computer Science
*

Purely formal logical result

doi:10.4204/eptcs.358.16
fatcat:fxu7pdsu65hblddifjzptuw6hi
*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 ...##
###
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

1957
*
Proceedings of the American Mathematical Society
*

The notion

doi:10.2307/2032693
fatcat:t72lqb6afzfe7o3v36grdwl3su
*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*). ...##
###
Invariants of the Anti-Automorphisms of a Group
[chapter]

1990
*
The Collected Works of J. Richard Büchi
*

The notion

doi:10.1007/978-1-4613-8928-6_13
fatcat:j7gydo5xjjaqdmm2ghtc76o5ee
*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*). ...##
###
Invariants of the anti-automorphisms of a group

1957
*
Proceedings of the American Mathematical Society
*

The notion

doi:10.1090/s0002-9939-1957-0095891-5
fatcat:lptmxr5op5dzhn6tqcji2m7vcm
*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*). ...##
###
Ternary monolayers as DNA recognition interfaces for direct and sensitive electrochemical detection in untreated clinical samples

2011
*
Biosensors & bioelectronics
*

Detection

doi:10.1016/j.bios.2011.02.004
pmid:21377347
pmcid:PMC3065524
fatcat:ohf7bivmjrgxvdupqths2j7pbe
*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 ...##
###
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

2021
*
Special Matrices
*

We combine matrix theory and graph theory methods to give

doi:10.1515/spma-2020-0128
fatcat:xirjdr3epzggnmmyspxg7iwafu
*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. ...##
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Borane Polyhedra as Building Blocks for Unknown but Potentially Isolatable New Molecules – Extensions based on Computations of the Known B18H22 Isomers

2013
*
Croatica Chemica Acta
*

We have also derived two new

doi:10.5562/cca2304
fatcat:kye5it6p7fegfjzddeol225gku
*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 ...##
###
From Binary Groups to Terminal Rings

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. ...

##
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Labeled binary planar trees and quasi-Lie algebras

2006
*
Algebraic and Geometric Topology
*

We study the natural map eta between

doi:10.2140/agt.2006.6.935
fatcat:mkime5bjynaarktxbk2ovodrt4
*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 . ...
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