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

Stephen D. Bartlett
2003 arXiv   pre-print
This framework provides 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.  ... 
arXiv:quant-ph/0302063v1 fatcat:wmmpkrr6pvgepj7pmezw5s3to4

A note on the boundary representation of a continuous spatial semigroup of $*$-endomorphisms of $\mathcal{B}(\mathcal{H})$

Alexis Alevras
1995 Proceedings of the American Mathematical Society  
We prove that the equivalence class 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¿?  ... 
doi:10.1090/s0002-9939-1995-1277086-6 fatcat:ew75b2y7dfakzegb3johvcdgvi

Power graphs: A survey
English

Jemal Abawajy, Andrei Kelarev, Morshed Chowdhury
2013 Electronic Journal of Graph Theory and Applications  
This article gives 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.  ... 
doi:10.5614/ejgta.2013.1.2.6 fatcat:tgvssnqcfndilhnsxfaluevgqq

Breakable Semihypergroups

Dariush Heidari, Irina Cristea
2019 Symmetry  
In this paper, we introduce and characterize the breakable semihypergroups, 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  ... 
doi:10.3390/sym11010100 fatcat:3kgilyhzarb7pjhpa4ajfxrqum

Inverse $*$-semigroups $*$-generated by families of isometries

Wacław Szyma{ński
1990 Proceedings of the American Mathematical Society  
Both results follow from the special behavior 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.  ... 
doi:10.1090/s0002-9939-1990-0982408-2 fatcat:ua2jietzf5c7ffl5oikkr6yfga

Application Of Jessen's Type Inequality For Positive C0-Semigroup Of Operators

Gul I Hina Aslam, Matloob Anwar
2015 Journal of Statistical Science and Application  
Moreover, 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  ... 
doi:10.17265/2328-224x/2015.78.003 fatcat:sp4ks4ngqrbbjfwlgrnrtesnee

Interplay of Simple and Selfadjoint-Ideal Semigroups in B(H) [article]

Sasmita Patnaik, Gary Weiss
2019 arXiv   pre-print
The study 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  ... 
arXiv:1806.01272v2 fatcat:5ejkbbex2ncazdhxepbakoo77q

Polyadic Analogs of Direct Product

Steven Duplij
2022 Universe  
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  ...  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.  ... 
doi:10.3390/universe8040230 fatcat:xqsncyscsfehnk4ddo6zxhgyai

Locally commutative power semigroups and counting factors of words

Jorge Almeida
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.  ... 
doi:10.1016/0304-3975(93)90227-k fatcat:objrlnjwnfgrnehjanhsqwtwky

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.  ... 

Polyadic analogs of direct product [article]

Steven Duplij
2022 arXiv   pre-print
For polyadic 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  ... 
arXiv:2201.08479v1 fatcat:4vo4gjpgcrev5deusukhxqouh4

Spectral and Asymptotic Properties of Contractive Semigroups on Non-Hilbert Spaces [article]

Jochen Glück
2016 arXiv   pre-print
We analyse C_0-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".  ... 
arXiv:1410.2502v2 fatcat:ennfsrug3ngddnattmzuffzinq

NUMERICAL AND GRAPHICAL RESULTS OF FINITE SYMMETRIC INVERSE (I_{n}) AND FULL (T_{n}) TRANSFORMATION SEMIGROUPS

R. Kehinde, O. H. Abdulazeez
2021 FUDMA Journal of Sciences  
We 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 .  ... 
doi:10.33003/fjs-2020-0404-501 fatcat:ordri746mjdghf7rrlfnyxj3y4

The q-theory of finite semigroups: history and mathematics [article]

Stuart W. Margolis
2014 arXiv   pre-print
This paper is 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  ... 
arXiv:1409.2308v2 fatcat:f6awhe4vjbg5jmxobgrtj3sifi
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