The topological views of a measure space provide deep insights. In this paper, the sigma-set algebraic structure is extended in Hausdorff based on locally compactable neighborhood systems without considering strictly (metrized) Borel variety. null extension gives rise to quasi sigma-semiring sigma-neighborhoods, which are rectifiable view Dieudonné n-space. concepts symmetric signed measure, un...

The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current jμ associated with the global symmetry of the theory, a composite scalar field j, the algebra closes under Poisson brackets. University of Freiburg THEP 91/10 August 1991 ∗Address after September 1, 1991: Department of Mathemati...

The approach to process semantics using quantales and modules is topologized by considering tropological systems whose sets of states are replaced by locales and which satisfy a suitable stability axiom. A corresponding notion of localic suplattice (algebra for the lower powerlocale monad) is described, and it is shown that there are contravariant functors from sup-lattices to localic sup-latic...

Twisted generalized Weyl algebras (TGWAs) A(R,σ,t) are defined over a base ring R by parameters σ and t, where is an n-tuple of automorphisms, t elements in the center R. We show that, for fixed σ, there natural algebra map \(A(R,\sigma ,tt^{\prime })\to A(R,\sigma ,t)\otimes _{R} ,t^{\prime })\). This gives tensor product operation on modules, inducing structure direct sum (over all t) Grothen...

In Arai (An ordinal analysis of a single stable ordinal, submitted) it is shown that an $$\sup _{N<\omega }\psi _{\varOmega _{1}}(\varepsilon _{{\mathbb {S}}+N}+1})$$ upper bound for the proof-theoretic set theory $$\mathsf {KP}\ell ^{r}+(M\prec _{\Sigma _{1}}V)$$ . this paper we show second order arithmetic $$\Sigma ^{1-}_{2}{\mathrm {-CA}}+\Pi ^{1}_{1}{\mathrm {-CA}}_{0}$$ proves wellfoundedn...

We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the pape...

Abstract For a three-dimensional quantum polynomial algebra $A=\mathcal {A}(E,\sigma )$ , Artin, Tate, and Van den Bergh showed that A is finite over its center if only $|\sigma |&lt;\infty $ . Moreover, Artin $E\neq \mathbb P^{2}$ then has fat point module, which plays an important role in noncommutative algebraic geometry; however, the converse not true general. In this paper, we will show mo...

We investigate the mixing coefficients of interval maps satisfying Rychlik’s conditions. A mixing Lasota-Yorke map is reverse φ-mixing. If its invariant density is uniformly bounded away from 0, it is φ-mixing iff all images of all orders are big in which case it is ψ-mixing. Among β-transformations, non-φ-mixing is generic. In this sense, the asymmetry of φ-mixing is natural. §0 Introduction M...

Non linear sigma models on Riemannian symmetric spaces constitute the most general class of classical non linear sigma models which are known to be integrable. Using the the current algebra structure of these models their canonical structure is analysed and it is shown that their non ultralocal fundamental Poisson bracket relation is governed by a field dependent non antisymmetric r-matrix obey...