As usual, we equip an infinite-dimensional separable Hilbert space 2 by such nonzero σ -finite Borel measures which are invariant with respect to everywhere dense vector subspaces and study duality between such measures and Baire category. Section 1 contains constructions of nontrivialσ -finite Borel measures, which are defined in the infinite-dimensional separable Hilbert space 2 and are invar...

In [6], Dehon and the author described two algorithms to classify all geometries Γ of a given group G such that Γ is a firm and residually connected geometry and G acts flag-transitively and residually weakly primitively on Γ. We stated in that paper that these programs were able to classify all geometries with Borel subgroup not equal to the identity of G when G is the Hall-Janko group J2. In ...

Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a disjoint family F ⊆ P (X) of size c, consisting of Borel sets which are not in I . Condition (M) states that there is a Borel function f : X → X with f[{x}] / ∈ ...

Let X and Y be uncountable Polish spaces. A ⊂ X×Y represents a family of sets C provided each set in C occurs as an x-section of A. We say A uniquely represents C provided each set in C occurs exactly once as an xsection of A. A is universal for C if A represents C and every x-section of A is in C. A is uniquely universal for C if it is universal and uniquely represents C. We show that there is...

We have calculated the contributions proportional to β 0 α n+1 s to the longitudinal fragmentation function in ee annihilation to all orders of perturbation theory. We use this result to estimate higher-order perturbative corrections and nonperturbative corrections to the longitudinal cross section σL and discuss the prospects of determining αs from σL. The structure of infrared renormalons in ...

The technique of conformal mappings is applied to enlarge the convergence domain of the Borel series and to accelerate the convergence of Borel-summed Green functions in perturbative QCD. We use the optimal mapping, which takes into account the location of all the singularities of the Borel transform as well as the present knowledge about its behaviour near the first branch points. The determin...

The order dependent mapping method, its convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for Stark effect of the hydrogen atom. We perform a numerical experiment up to the fiftieth order of the perturbation expansion. A simple mapping suggested by the analytic structure and the strong field behavio...

i=1 gijXi, g = (gij) ∈ Gl(n,k)), given any term-ordering< and homogeneous ideal a ⊆ P(n), there exists a non-empty open subset U of Gl(n,k) such that as g ranges in U, gin(a) := in(g(a)) is constant. Moreover, gin(a) is fixed by the group B of upper-triangular invertible matrices, if X1 > · · · > Xn, while gin(a) is fixed by the group B′ of lower-triangular invertible matrices if X1 < · · · < X...