Tossing a coin is the most elementary Monte-Carlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not capable of imitating a fair coin: pseudo random coins show more ‘‘heads’’ than ‘‘tails.’’ This bias explains the empirically observed failure of some random numbe...

Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo–conformal representation. In special cases, this representation reduces to ordinary– or logarithmic–conformal field theory. There are, however, other cases in which the Green functions differ from those of ordinary– or logarithmic–conformal field theories. This representat...

By including interlocked modules, we showed a modular invariance property of (pseudo) trace functions of modules for a 2-dimensional conformal field theory satisfying C 2-finiteness condition.

A Heyting algebra is supplemented if each element a has dual pseudo-complement $$a^+$$ , and centrally supplement it central. We show that extension in the same variety of algebras as original. use this tool to investigate new type completion arising context algebraic proof theory, so-called hyper-MacNeille completion. MacNeille its extension. This provides an description algebra, allows develo...

In remembrance of our dear colleague Irene Dorfman. Abstract Poisson brackets associated with Lax operators of lattice systems are considered. Linear brackets originate from various r-matrices on the algebra of (pseudo-) shift symbols. Quadratic brackets are investigated which provide Hamiltonian formulations for various reductions of the (modiied) Lattice KP hierarchy.

Modiications of the standard Poisson brackets associated with diierential scattering operators are considered. A linear bracket originates from a non-standard r-matrix on the algebra of pseudo-diierential operators. Two quadratic brackets are investigated which provide Hamiltonian formulations for various reductions of the modiied KP hierarchy.

We introduce a family of factorisable ribbon quasi-Hopf algebras Q(N) for N positive integer: as an algebra, is the semidirect product CZ2 with direct sum Graßmann and Clifford algebra in 2N generators. show that RepQ(N) equivalent to symplectic fermion category SF(N) was computed [54] from conformal blocks corresponding logarithmic field theory. The latter turn conjecturally representations Ve...

A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of exponential weights. Such an algebra with embedded Dirac’s delta distribution induces discrete topology on the basic space. This result is in analogy to Schwartz...

We study the twisted Weyl symbol of metaplectic operators; this requires the definition of an index for symplectic paths related to the Conley–Zehnder index. We thereafter define a metaplectically covariant algebra of pseudo-differential operators acting on functions on symplectic space.