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A canonical algebra of open transition systems [article]

Elena Di Lavore, Alessandro Gianola, Mario Román, Nicoletta Sabadini, Paweł Sobociński
2020 arXiv   pre-print
Intuitively, this 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".  ... 
arXiv:2010.10069v1 fatcat:54c4skobuvcfbnelgmvcpvr4my

Matrix product states of three families of one-dimensional interacting particle systems

Farhad H Jafarpour
2004 Physica A: Statistical Mechanics and its Applications  
By introducing 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.  ... 
doi:10.1016/j.physa.2004.03.009 fatcat:b256eh2jo5f4bkg3bkk5l5wxdu

Shock in a branching–coalescing model with reflecting boundaries

Farhad H Jafarpour
2004 Physics Letters A  
We study the phase 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.  ... 
doi:10.1016/j.physleta.2004.01.058 fatcat:b6gtcecrt5aqvh7xl25epriufe

On the perfection of schemes [article]

Alessandra Bertapelle, Cristian D. Gonzalez-Aviles
2016 arXiv   pre-print
We expect the results presented here to be useful in 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.  ... 
arXiv:1611.02060v1 fatcat:rprlhmxkjne57js6x4u6dkv5ra

Numerical study of phase transition in an exclusion model with parallel dynamics

Farhad H. Jafarpour
2004 Physics Letters A  
By working in 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  ... 
doi:10.1016/j.physleta.2004.04.021 fatcat:5nm7ft2nuzf5zfncbevgccbyq4

Remarks on modules over deformation quantization algebras [article]

Ryszard Nest, Boris Tsygan
2004 arXiv   pre-print
We study an asymptotic version 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).  ... 
arXiv:math-ph/0411066v1 fatcat:vigthnso2zgcddn7ju6ayvcale

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  ... 

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  ... 

Towards categorical models for fairness: fully abstract presheaf semantics of SCCS with finite delay

Thomas T. Hildebrandt
2003 Theoretical Computer Science  
case 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.  ... 
doi:10.1016/s0304-3975(01)00247-x fatcat:6xf54tqzyjbqnfkdtkafyn32yu

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.  ... 

Remarks on Modules over Deformation Quantization Algebras

R. Nest, B. Tsygan
2004 Moscow Mathematical Journal  
We study the Maslov theory 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.  ... 
doi:10.17323/1609-4514-2004-4-4-911-940 fatcat:q6doh4i4rrdqbivs442npig7cq

A Fully Abstract Presheaf Semantics of SCCS with Finite Delay

Thomas Troels Hildebrandt
1999 BRICS Report Series  
, which are 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.  ... 
doi:10.7146/brics.v6i28.20097 fatcat:vkyv3lsmhfgt5a6nhangm7s7x4

A Fully Abstract Presheaf Semantics of SCCS with Finite Delay

Thomas T. Hildebrandt
1999 Electronical Notes in Theoretical Computer Science  
special case 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.  ... 
doi:10.1016/s1571-0661(05)80311-1 fatcat:tnqelgzmlfdfbjpcch4gywop5m

Gerbes on quantum groups [article]

Jouko Mickelsson
2003 arXiv   pre-print
We discuss an approach to quantum gerbes over quantum groups in terms 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).  ... 
arXiv:math/0308235v1 fatcat:ry3nervf5bdhll2p2wsh3bjbti

Computation of Composition Functions and Invariant Vector Fields in Terms of Structure Constants of Associated Lie Algebras

Alexey A. Magazev, Vitaly V. Mikheyev, Igor V. Shirokov
2015 Symmetry, Integrability and Geometry: Methods and Applications  
Methods 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.  ... 
doi:10.3842/sigma.2015.066 fatcat:wviz756sjna6rn7hirqgpj2vii
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