In this work, we compute the representation of mapping class group sphere with [Formula: see text] punctures arising from non-semi-simple TQFT [C. Blanchet, F. Costantino, N. Geer and B. Patureau, Non-semi-simple TQFTs, Reidemeister torsion Kashaev’s invariants, Adv. Math. 301 (2016) 1–78]. We show that it is faithful. Lastly, compare quantum representations punctured spheres in general those b...

Methods are developed for constructing spectral representations of cold (barotropic) neutron-star equations of state. These representations are faithful in the sense that every physical equation of state has a representation of this type and conversely every such representation satisfies the minimal thermodynamic stability criteria required of any physical equation of state. These spectral repr...

A simple axiomatic characterization of the noncommutative Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that every quotient Itô algebra has a faithful representation in a Minkowski space and is canonically decomposed into the orthogonal sum of quantum Brownian (Wiener) algebra and quantum Lévy (Poisson) algebra. In particular,...

In this paper, we present an abstraction refinement approach for model checking safety properties of realtime systems using SAT-solving. We present a faithful embedding of bounded model checking for systems of timed automata into propositional logic with linear arithmetic and prove correctness. With this logical representation, we achieve a linear-size representation of parallel composition and...

This paper claims that causal model theory describes the meaningful information of probability distributions after a factorization. If the minimal factorization of a distribution is incompressible, its Kolmogorov minimal sufficient statistics, the parents lists, can be represented by a directed acyclic graph (DAG). We showed that a faithful Bayesian network is a minimal factorization and that a...

In a previous investigation [1], the author has studied finite groups © of an order g = pgo where p is a prime and go an integer not divisible by p. This work has been continued by H. F. Tuan [51 Let t denote the number of conjugate classes of ® which consist of element of order p. Tuan dealt with the groups ® for which t^2 and which have a faithful representation of degree less than p 1. We sh...

In the reduced free product of C∗–algebras, (A, φ) = (A1, φ1) ∗ (A2, φ2) with respect to faithful states φ1 and φ2, A is purely infinite and simple if A1 is a reduced crossed product B ⋊α,r G for G an infinite group, if φ1 is well behaved with respect to this crossed product decomposition, if A2 6= C and if φ is not a trace. The reduced free product construction for C–algebras was invented inde...