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A canonical algebra of open transition systems
[article]

2020
*
arXiv
*
pre-print

Intuitively, this

arXiv:2010.10069v1
fatcat:54c4skobuvcfbnelgmvcpvr4my
*algebra**of**transition**systems*is obtained by adding state to an*algebra**of*predicates, and therefore 𝐒𝐩𝐚𝐧(𝐆𝐫𝐚𝐩𝐡)_∗ is, in this sense, the*canonical*such*algebra*. ... We show that*a*categorical*algebra*for*open**transition**systems*, 𝐒𝐩𝐚𝐧(𝐆𝐫𝐚𝐩𝐡)_∗, also due to Katis, Sabadini and Walters, is the free category with feedback over 𝐒𝐩𝐚𝐧(𝐒𝐞𝐭). ... Span(Graph): an*algebra**of**transition**systems*Span(Graph) [25] is an*algebra**of*"*open**transition**systems*". ...##
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Matrix product states of three families of one-dimensional interacting particle systems

2004
*
Physica A: Statistical Mechanics and its Applications
*

By introducing

doi:10.1016/j.physa.2004.03.009
fatcat:b256eh2jo5f4bkg3bkk5l5wxdu
*a**canonical*ensemble we calculate the*canonical*partition function*of*this model exactly. ... Using the Yang-Lee theory*of*phase*transitions*we spot*a*second-order phase*transition*from*a*power-law to*a*jammed phase. The density profile*of*particles in each phase has also been studied. ... In*open*boundary*systems*, changing the boundary parameters may result in special kinds*of*nonequilibrium phase*transitions*which are called the boundary induced phase*transitions*. ...##
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Shock in a branching–coalescing model with reflecting boundaries

2004
*
Physics Letters A
*

We study the phase

doi:10.1016/j.physleta.2004.01.058
fatcat:b6gtcecrt5aqvh7xl25epriufe
*transitions**of*this model in*a**canonical*ensemble by using the Yang-Lee description*of*the non-equilibrium phase*transitions*. ... Numerical study*of*the*canonical*partition function zeros reveals two second-order phase*transitions*in the*system*. Both*transition*points are determined by the density*of*the particles on the chain. ...*canonical*ensemble for which*a*finite-or infinite-dimensional representation*of*the associate*algebra*exists. ...##
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On the perfection of schemes
[article]

2016
*
arXiv
*
pre-print

We expect the results presented here to be useful in

arXiv:1611.02060v1
fatcat:rprlhmxkjne57js6x4u6dkv5ra
*a*number*of*contexts. For example, several*of*them will be applied in*a*forthcoming paper by the authors. ... This is*a*chiefly expository paper on the subject*of*the title which, in our view, has not received*a*detailed treatment in the literature which is commensurate with its importance. ... (iii) The*transition*morphisms*of*the*system*(F n ) are surjective. ...##
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Numerical study of phase transition in an exclusion model with parallel dynamics

2004
*
Physics Letters A
*

By working in

doi:10.1016/j.physleta.2004.04.021
fatcat:5nm7ft2nuzf5zfncbevgccbyq4
*a**canonical*ensemble, where the total number*of*the particles is being fixed, we find that the model has*a*rather non-trivial phase diagram consisting*of*three different phases which are ... Shocks may evolve in the*system*for special values*of*the reaction parameters. ... In this letter we have investigated the phase*transitions*and shock formation in the ASEP with*open*boundaries and parallel dynamics in*a**canonical*ensemble where the total number*of*particles is kept ...##
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Remarks on modules over deformation quantization algebras
[article]

2004
*
arXiv
*
pre-print

We study an asymptotic version

arXiv:math-ph/0411066v1
fatcat:vigthnso2zgcddn7ju6ayvcale
*of*the Maslov-Hormander construction*of*Lagrangian distributions in terms*of*deformation quantization. ... If M = ∪U α is an*open*cover and*a*coordinate*system*x 1 , . . . , x m is chosen on every completion*of*S[T * M ]) as bundles*of**algebras*. ... On an*open*dense subset, the*transition*functions*of*the type C) can be expressed through the*transition*functions*of*types*A*), B). ...##
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Page 562 of Illinois Journal of Mathematics Vol. 5, Issue 4
[page]

1961
*
Illinois Journal of Mathematics
*

Let F be given by an

*open*covering {U,}*of*X and*transition*functions gij3 Ui n U; — PGL(p — 1) which are regular maps obeying the usual com- patibility condition. ... Let X be quasi-projective, nonsingular, and let (E, X, 2’) be an*algebraic*vector bundle*of*rank p; from it we derive*canonically**a*projective bundle (P(E), X, +) whose fibers r"(x) are the (p — 1)-dimensional ...##
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Page 4545 of Mathematical Reviews Vol. , Issue 82j
[page]

1982
*
Mathematical Reviews
*

by

*a*linear representation*system*(*a**canonical**system*here is quasireachable and distinguishable, not necessarily reachable) and any two*canonical*realizations*of*the same input/response map are isomorphic ... He also defines*a*notion*of**canonical**system*(reachable + distinguishable corresponding to the usual concepts*of*reachable and observable) and shows that two*canonical*realizations*of*an input/response ...##
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Towards categorical models for fairness: fully abstract presheaf semantics of SCCS with finite delay

2003
*
Theoretical Computer Science
*

case

doi:10.1016/s0304-3975(01)00247-x
fatcat:6xf54tqzyjbqnfkdtkafyn32yu
*of*the general*transition**systems**of*Hennessy and Stirling. ... We give*a*concrete representation*of*the presheaf model as*a*category*of*generalised synchronisation trees and show that it is core ective in*a*category*of*generalised*transition**systems*, which are*a*special ...*open*map within the category*of*generalised*transition**systems*. ...##
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Page 2746 of Mathematical Reviews Vol. , Issue 87e
[page]

1987
*
Mathematical Reviews
*

The authors develop

*a**canonical*statistical description for*systems*with nonabelian symmetries. ... Then the associated Hilbert space, representation*of*the*algebra*and the unitary operators*of*time translation are obtained. However, the relation to the first approach is left*open*. ...##
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Remarks on Modules over Deformation Quantization Algebras

2004
*
Moscow Mathematical Journal
*

We study the Maslov theory

doi:10.17323/1609-4514-2004-4-4-911-940
fatcat:q6doh4i4rrdqbivs442npig7cq
*of**canonical*operator and the Hörmander theory*of*distributions given by oscillatory integrals from the point*of*view*of*deformation quantization. ... Sternin for*a*masterful exposition*of*the theory*of**canonical*operator. We are grateful to D. Arinkin,*A*. Beilinson, R. Bezrukavnikov, P. Bressler, V. Drinfeld, K. Fukaya, D. Gaitsgori,*A*. ... We believe that most*of*the contents*of*the paper is well known to experts in some form. ...##
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A Fully Abstract Presheaf Semantics of SCCS with Finite Delay

1999
*
BRICS Report Series
*

, which are

doi:10.7146/brics.v6i28.20097
fatcat:vkyv3lsmhfgt5a6nhangm7s7x4
*a*special case*of*the general*transition**systems*<br />*of*Hennessy and Stirling. ... We give*a*concrete representation<br />*of*the presheaf model as*a*category*of*generalised synchronisation<br />trees and show that it is coreflective in*a*category*of*generalised*transition*<br />*systems*... and thus comes with*a**canonical*notion*of**open*maps. ...##
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A Fully Abstract Presheaf Semantics of SCCS with Finite Delay

1999
*
Electronical Notes in Theoretical Computer Science
*

special case

doi:10.1016/s1571-0661(05)80311-1
fatcat:tnqelgzmlfdfbjpcch4gywop5m
*of*the general*transition**systems**of*Hennessy and Stirling. ... We give*a*concrete representation*of*the presheaf model as*a*category*of*generalised synchronisation trees and show that it is coreflective in*a*category*of*generalised*transition**systems*, which are*a*... and thus comes with*a**canonical*notion*of**open*maps. ...##
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Gerbes on quantum groups
[article]

2003
*
arXiv
*
pre-print

We discuss an approach to quantum gerbes over quantum groups in terms

arXiv:math/0308235v1
fatcat:ry3nervf5bdhll2p2wsh3bjbti
*of*q-deformation*of**transition*functions for*a*loop group bundle. The case*of*the quantum group SUq(2) is treated in some detail. ... This means that the*transition*functions are loops in*a*group*of*matrices with entries in the Hopf*algebra*SU q (n). ... There is*a**canonical*central extension 1 → S 1 → U (H) → P U (H) → 1*of*the projective unitary group which gives*a**canonical*complex line bundle L over P U (H). ...##
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Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras

2015
*
Symmetry, Integrability and Geometry: Methods and Applications
*

Methods

doi:10.3842/sigma.2015.066
fatcat:wviz756sjna6rn7hirqgpj2vii
*of*construction*of*the composition function, left- and right-invariant vector fields and differential 1-forms*of**a*Lie group from the structure constants*of*the associated Lie*algebra*are proposed ... Moreover, it is proven that the*transition*function from the first*canonical*coordinates to the second*canonical*coordinates can be found by quadratures. ... Acknowledgements Authors greatly appreciate the cooperation*of*the editors and referees who put decent effort and amount*of*time to improve the content and style*of*the paper. ...
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