Let A ⊆ R be a set definable in an o-minimal expansion S of the real field, A′ ⊆ R be its projection, and assume that the non-empty fibers Aa ⊆ R n are compact for all a ∈ A′ and uniformly bounded. If L is the Hausdorff limit of a sequence of fibers Aai , we give an upper-bound for the Betti numbers bk(L) in terms of definable sets explicitly constructed from a generic fiber Aa. In particular, ...

In this paper, we establish the necessary and sufficient condition for an equivalence relation ρ on S-act A endowed with a topology such that A/ρ becomes Hausdorff topological S-act. Also, show if A1 A2 be two S-acts, then any homomorphism ϕ : → A2, A1/ ker is only ϕ-saturated continuous. Moreover, congruences θ1 θ2 topology, ∩ congruence mapping A/θ1 × A/θ2, defined by ϕ(a) = (aθ1, aθ2), all ∈...

The notion of fuzzy s-prime filters of a bounded BCK-algebra is introduced.We discuss the relation between fuzzy s-prime filters and fuzzy prime filters. By the fuzzy s-prime filters of a bounded commutative BCK-algebra X, we establish a fuzzy topological structure on X. We prove that the set of all fuzzy s-prime filters of a bounded commutative BCK-algebra forms a topological space. Moreover, ...

We look at invariance of a.e. boundary condition spectral behavior under perturbations, W ; of half-line, continuum or discrete Schrödinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported W ’s to suitable short-range W : We also discuss invariance of the local Hausdorff dimension of spectral measures under such perturbations. r 2002 Elsevier Science (USA). All...

We obtain for any spin, s, the Hausdorff dimension, hi, for fractional spin particles and we discuss the connection between this number, hi, and the Chern-Simons potential. We also define the topological invariants, Ws, in terms of the statistics of these particles. PACS numbers: 11.90+t

The dynamical discrete web (DDW), introduced in recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter s. The evolution is by independent updating of the underlying Bernoulli variables indexed by discrete space-time that define the discrete web at any fixed s. In this paper, we study ...

Spacetime is modelled a s a fractal subset of R". Analysis on homogeneous sets with non-integer Hausdorff dimension is applied to the low-order perturbative renormalisation of quantum electrodynamics. This new regularisation method implements the Dirac matrices and tensors in R4 without difficulties, is gauge invariant, covariant and differs from dimensional regularisation in some aspects.