Filament sets, aposyndesis, and the decomposition theorem of Jones

Applications of the work introduced by the authors in a recent article, Filament sets and homogeneous continua, are given to aposyndesis and local connectedness. The aposyndetic decomposition theorem of Jones is generalized to spaces with the property of Kelley.

     

A continuous decomposition of the Menger curve into pseudo-arcs

It is proved that the Menger universal curve admits a continuous decomposition into pseudo-arcs with the quotient space homeomorphic to .

     

Plasticity as the Γ-limit of a Nonlinear Dislocation Energy with Mixed Growth

We consider a model for straight parallel edge dislocations with a nonlinear elastic energy with mixed growth. By means of Γ-convergence we show that the suitably rescaled energy converges to a strain-gradient plasticity model. As a tool we proof a generalized rigidity estimate which bounds the distance of a field with non-vanishing curl to a specific rotation by the distance to all rotations. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Nash approximation of complex analytic sets in Runge domains

We prove that every complex analytic set X in a Runge domain Ω   can be approximated by Nash sets on any relatively compact subdomain _Ω0${\Omega }_0$ of Ω. Moreover, for every Nash subset Y of Ω   with Y⊂X$Y\subset X$, the approximating sets can be chosen so that they contain Y∩_Ω0$Y\cap {\Omega }_0$. As a consequence, we derive a necessary and sufficient condition for a complex analytic set X to admit a Nash approximation which coincides with X along its arbitrary given subset.     

Automorphisms of endomorphism semigroups of reflexive digraphs

A reflexive digraph is a pair (X, ρ), where X is an arbitrary set and ρ is a reflexive binary relation on X. Let End (X, ρ) be the semigroup of endomorphisms of (X, ρ). We determine the group of automorphisms of End (X, ρ) for: digraphs containing an edge not contained in a cycle, digraphs consisting of arbitrary unions of cycles such that cycles of length ≥2 are pairwise disjoint, and some circulant digraphs (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The converse theorem for Minkowski's inequality

Let (Ω, Σ, μ) be a measure space and ?, ψ : (0, ∞) → (0, ∞) some bijective functions. Suppose that the functional _?,ψ defined on class of μ-integrable simple functions χ : Ω → [0, ∞), μ({? : χ(?) > 0} > 0, by the formula

     

On amenability of two-generator groups

A discrete group G is amenable if there exists a finitely additive probability measure on G which is invariant under left translations and is defined on all subsets of G. It is proved that if the group is generated by two elements and is amenable then there are words being relators whose most of the consecutive pairs of the letters belong to a certain four-element set of pairs. This fact is applied to reproving non-amenability of a braid group. The same group provides an example showing that such type of condition is not su?cient for amenabilty.     

Natural bound in Kwiecinski's criterion for flatness

Kwiecinski has proved a geometric criterion for flatness: A morphism of germs of analytic spaces is not flat if and only if its fibre power has a vertical component, for some . We show how to bound using Hironaka's local flattener: If is not flat, then has a vertical component, where is the minimal number of generators of the ideal in of the flattener of .

     

Eta physics at threshold

The production of - and -mesons in elementary nucleon-nucleon collisions has been investigated at the synchrotrons CELSIUS, COSY and SATURNE. The high-quality proton beam with low emittance and small momentum spread permits to study the creation of these mesons very close to the kinematical threshold, where --due to the rapid growth of the phase space volume-- the total cross-section increases by orders of magnitude over a few MeV range of the excess energy. The magnitude and energy dependence of the total cross-section as well as the occupation distribution of the phase space serve as observables for investigating the mechanisms underlying the production processes and the interaction of mesons with nucleons. The precise data on the and creation via the reactions allowed to settle the general features of the - and -meson production and revealed the sensitivity of the mentioned observables to the nucleon-nucleon-meson final-state interaction. The particular production properties, like for example, the determination of the dominating exchange processes which lead to the excitation of the S ₁₁ nucleon isobar in the case of creation, must be established by confrontation with other observables. The present status of this investigation with an emphasis on the results of the COSY-11 Collaboration is briefly presented. The available data are interpreted in view of the production mechanism and the meson-nucleon interaction.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.60.Le Meson production - 13.75.-n Hadron-induced low- and intermediate-energy reactions and scattering (energy GeV) - 13.85.Lg Total cross sections - 25.40.-h Nucleon-induced reactions