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Semigroup techniques for the efficient classical simulation of optical quantum information
[article]

2003
*
arXiv
*
pre-print

This framework provides

arXiv:quant-ph/0302063v1
fatcat:wmmpkrr6pvgepj7pmezw5s3to4
*a**powerful*tool for assessing the capabilities and limitations*of*performing quantum information processing tasks*using*current experimental techniques. ...*a*theorem for the efficient classical simulation*of**operations*within this framework. ... Conclusions*Semigroup*techniques provide*a**powerful*tool for constructing and assessing new quantum information protocols*using*quantum optics. ...##
###
A note on the boundary representation of a continuous spatial semigroup of $*$-endomorphisms of $\mathcal{B}(\mathcal{H})$

1995
*
Proceedings of the American Mathematical Society
*

We prove that the equivalence class

doi:10.1090/s0002-9939-1995-1277086-6
fatcat:ew75b2y7dfakzegb3johvcdgvi
*of*the boundary representation na <%*of*an iso-*semigroup**a*is independent*of*the intertwining*semigroup**of*isometries %. ... We are making*use**of*the following result: Theorem (*Powers*and Price [5] ). ... Let*a*bean E^-*semigroup**of*3 § (%f), and suppose that 1¿ and S? are*two*strongly continuous intertwining*semigroups**of*isometries. Then the*two*boundary representations na^ and na¿? ...##
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Power graphs: A survey

English

2013
*
Electronic Journal of Graph Theory and Applications
*

English

This article gives

doi:10.5614/ejgta.2013.1.2.6
fatcat:tgvssnqcfndilhnsxfaluevgqq
*a*survey*of*all results on the*power*graphs*of*groups and*semigroups*obtained in the literature. ... The authors would like to thank*two*referees for helpful reports. ... The authors are grateful to Brian Curtin, Gholam Reza Pourgholi and Igor Shparlinski for comments and lists*of*typographical corrections to the manuscript. ...##
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Breakable Semihypergroups

2019
*
Symmetry
*

In this paper, we introduce and characterize the breakable semihypergroups,

doi:10.3390/sym11010100
fatcat:3kgilyhzarb7pjhpa4ajfxrqum
*a*natural generalization*of*breakable*semigroups*, defined by*a*simple property: every nonempty subset*of*them is*a*subsemihypergroup ... breakable*semigroups*. ... Another characterization*of*these*semigroups*is given by Tamura and Shafer [2] ,*using*the associated*power**semigroup*, i.e.,*a**semigroup*S is breakable if and only if its*power**semigroup*P * (S) is idempotent ...##
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Inverse $*$-semigroups $*$-generated by families of isometries

1990
*
Proceedings of the American Mathematical Society
*

Both results follow from the special behavior

doi:10.1090/s0002-9939-1990-0982408-2
fatcat:ua2jietzf5c7ffl5oikkr6yfga
*of*inverse »-*semigroups*»-generated by analytic Toeplitz*operators*. ...*power**of*another one, consists*of*partial isometries, then it is singly »-generated. ... Now S*(V, W) is an inverse*semigroup*, because it is*a*»-*semigroup*consisting*of*partial isometries-*use**a*result*of*Duncan-Paterson quoted in §1. ...##
###
Application Of Jessen's Type Inequality For Positive C0-Semigroup Of Operators

2015
*
Journal of Statistical Science and Application
*

Moreover,

doi:10.17265/2328-224x/2015.78.003
fatcat:sp4ks4ngqrbbjfwlgrnrtesnee
*a*Dresher's type inequality for*two*-parameter family*of*means, is also proved. ... In this note, we present few results*of*this inequality, yielding Hölder's Type and Minkowski's type inequalities for corresponding*semigroup*. ... , we prove*a*Hölder's type inequality for positive 0 C -*semigroup**of**operators*, assuming the fractional*powers**of*elements in Banach algebra exist. is*a**semigroups**of*positive linear*operators*satisfying ...##
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Interplay of Simple and Selfadjoint-Ideal Semigroups in B(H)
[article]

2019
*
arXiv
*
pre-print

The study

arXiv:1806.01272v2
fatcat:5ejkbbex2ncazdhxepbakoo77q
*of*SI*semigroups*involves solving certain*operator*equations in the*semigroups*.*A*central theme*of*this paper is to study when and when not SI is equivalent to simple. ... We characterize those SI*semigroups*S singly generated by T, for T*a*normal*operator*and for T*a*rank one*operator*. ...*A*connection we found between the notion*of*SI*semigroup*and*power*partial isometry is: For T*a*normal nonselfadjoint*operator*, S(T, T * ) is*a*selfadjoint-ideal*semigroup*if and only if T is*a**power*partial ...##
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Polyadic Analogs of Direct Product

2022
*
Universe
*

We propose

doi:10.3390/universe8040230
fatcat:xqsncyscsfehnk4ddo6zxhgyai
*a*generalization*of*the external direct product concept to polyadic algebraic structures which introduces novel properties in*two*ways: the arity*of*the product can differ from that*of*the constituents ... For polyadic*semigroups*and groups we introduce*two*external products: (1) the iterated direct product, which is componentwise but can have an arity that is different from the multipliers and (2) the hetero ... Conflicts*of*Interest: The authors declare no conflict*of*interest. ...##
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Locally commutative power semigroups and counting factors of words

1993
*
Theoretical Computer Science
*

*A*formal equality rc = p between

*two*implicit

*operations*

*of*the same arity is called

*a*pseudoidentity. An identity is

*a*formal equality between

*two*explicit

*operations*

*of*the same arity. ... This paper deals with

*power*pseudovarieties consisting

*of*locally commutative

*semigroups*.

*Two*types

*of*

*powers*

*of*minimal nonpermutative pseudovarieties are locally commutative. ...

##
###
Page 4228 of Mathematical Reviews Vol. , Issue 92h
[page]

1992
*
Mathematical Reviews
*

*A*finite

*semigroup*S is called

*power*commutative if for any

*two*elements x,y in S, some

*power*

*of*xy is equal to

*a*

*power*

*of*yx. ...

*A*variety

*of*bands with

*two*nullary

*operations*added is universal if and only if it contains either the variety

*of*semilattices

*of*left zero seimgroups or the variety

*of*semilattices

*of*right zero

*semigroups*...

##
###
Page 8440 of Mathematical Reviews Vol. , Issue 2003k
[page]

2003
*
Mathematical Reviews
*

*operators*related to the infinitesimal generator

*of*the

*semigroup*, for example, fractional

*powers*

*of*the generator. ... Soc. (3) 29 (1974), 557-576; MR 50 #14364] developed some techniques

*using*Fourier and Laplace transforms to treat fractional

*powers*

*of*generators

*of*equicontin- uous

*semigroups*. Jazar [Proc. Amer. ...

##
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Polyadic analogs of direct product
[article]

2022
*
arXiv
*
pre-print

For polyadic

arXiv:2201.08479v1
fatcat:4vo4gjpgcrev5deusukhxqouh4
*semigroups*and groups we introduce*two*external products: 1) the iterated direct product which is componentwise, but can have arity different from the multipliers; 2) the hetero product (*power*... We propose*a*generalization*of*the external direct product concept to polyadic algebraic structures which introduces novel properties in*two*ways: the arity*of*the product can differ from that*of*the constituents ... Let G p4q " @ G | µ p4q D be*a*4-ary*semigroup*, then we can construct its ternary associative cubic hetero*power*G 1p3q " @ G 1 | µ 1p3q D*using*the associative quivers with one intact element and*two*...##
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Spectral and Asymptotic Properties of Contractive Semigroups on Non-Hilbert Spaces
[article]

2016
*
arXiv
*
pre-print

We analyse C_0-

arXiv:1410.2502v2
fatcat:ennfsrug3ngddnattmzuffzinq
*semigroups**of*contractive*operators*on real-valued L^p-spaces for p = 2 and on other classes*of*non-Hilbert spaces. ... For example, we can show that*a*contractive and eventually norm continuous C_0-*semigroup*on*a*real-valued L^p-space automatically converges strongly if p ∈{1,2,∞}. ... During his work on this article, the author was supported by*a*scholarship*of*the "Landesgraduiertenförderung Baden-Württemberg". ...##
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NUMERICAL AND GRAPHICAL RESULTS OF FINITE SYMMETRIC INVERSE (I_{n}) AND FULL (T_{n}) TRANSFORMATION SEMIGROUPS

2021
*
FUDMA Journal of Sciences
*

We

doi:10.33003/fjs-2020-0404-501
fatcat:ordri746mjdghf7rrlfnyxj3y4
*used*an effective methodology and valid combinatorial results to generalize the total work done, the average work done and*powers**of*each*of*the transformation*semigroups*. ... full transformation*semigroup**of*degree , as well as their respective*powers*for*a*given fixed time in space. ... INTRODUCTION*A**semigroup*is*a*pair ( , where is*a*nonempty set and is an associative binary*operation*on . ...##
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The q-theory of finite semigroups: history and mathematics
[article]

2014
*
arXiv
*
pre-print

This paper is

arXiv:1409.2308v2
fatcat:f6awhe4vjbg5jmxobgrtj3sifi
*a*historical and mathematical review*of*the book, "The q-theory*of*Finite*Semigroups*" by John Rhodes and Benjamin Steinberg. ... They*use*this to improve unpublished results*of*Fox and Rhodes [17] on the Krohn-Rhodes complexity*of*the*power**semigroup**of*the powersemigroup P (S)*of**a*finite*semigroup*S. ... An important example*of*an*operator*that does not satisfy the generalized Malcev condition is the well studied*operator*that sends*a*pseudovariety V to the pseudovariety PowV generated by the*power**semigroups*...
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