Infinite Random Geometric Graphs

We introduce a new class of countably infinite random geometric graphs, whose vertices V are points in a metric space, and vertices are adjacent independently with probability p ? (0, 1){p \in (0, 1)} if the metric distance between the vertices is below a given threshold. For certain choices of V as a countable dense set in \mathbbRⁿ{\mathbb{R}^n} equipped with the metric derived from the L _∞-norm, it is shown that with probability 1 such infinite random geometric graphs have a unique isomorphism type. The isomorphism type, which we call GR _n , is characterized by a geometric analogue of the existentially closed adjacency property, and we give a deterministic construction of GR _n . In contrast, we show that infinite random geometric graphs in \mathbbR²{\mathbb{R}^{2}} with the Euclidean metric are not necessarily isomorphic.     

Photoproduction of πmesons from nuclei

Photoproduction of neutral pions from nuclei (carbon, calcium, niobium, lead) has been studied for incident-photon energies from 200 MeV to 800 MeV with the TAPS detector using the Glasgow photon tagging spectrometer at the Mainz MAMI accelerator. Data were obtained for the inclusive photoproduction of neutral pions and the partial channels of quasifree single- , double- , and photoproduction. They have been analyzed in terms of the in-medium behavior of nucleon resonances and the pion-nucleus interaction. They are compared to earlier measurements from the deuteron and to the predictions of a Boltzmann-Uehling-Uhlenbeck (BUU) transport model for photon-induced pion production from nuclei.PACS: 13.60.Le Meson production - 25.20.Lj Photoproduction reactions     

Organoselenium‐substituted poly(p‐phenylenevinylene)

A new type of conjugated polymer, organoselenium substituted poly(p‐phenyleneviny‐ lene) (PPV), was synthesized from the corresponding alkylselenenyl p‐xylylene dibromide via a Gilch route using potassium tert‐butoxide in THF. The p‐xylylene dibromide precursors were synthesized by reacting lithiated bis(methoxymethyl)benzenes with elemental selenium, followed by alkylation of the generated selenolates. As a final demasking step, the bromomethyl functions were liberated by ether cleavage using boron tribromide. Bis‐alkylselenenyl PPV was obtained with an average molecular weight M_w of approximately 300,000 g/mol and with polydispersity M_w/M_n = 2. Due to low solubility, monoalkylselenenyl PPV was obtained with a considerably lower average molecular weight in the proximity of 16,000 g/mol and with a polydispersity slightly larger than 3. Absorption and fluorescence spectroscopy revealed that the bis‐alkylselenenyl PPV is extensively conjugated. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:656–662, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20167     

Ample fields as a basis for possibilistic processes

Ample fields play an important role in possibility theory. These fields of subsets of a universe, which are additionally closed under arbitrary unions, act as the natural domains for possibility measures. A set provided with an ample field is then called an ample space. In this paper we generalise Wang's notions of product ample field and product ample space. We make a topological study of ample spaces and their products, and introduce ample subspaces, extensions and one-point extensions of ample spaces. In this way, a first step towards a mathematical theory of possibilistic processes is made.     

Integral Representation of Invariant Functions

We characterize those positive functions which are invariant for a bounded kernel, and which have a Choquet-type integral representation. Such a representation relies on the wellknown Choquet-type integral representation of measures which are invariant for a kernel. We apply our results to convolution kernels with spread-out measures on second countable locally compact Abelian groups.     

Biased Diffusion with Correlated Noise

The diffusion of hard-core particles subject to a global bias is described by a nonlinear, anisotropic generalization of the diffusion equation with conserved, local noise. Using renormalization group techniques, we analyze the effect of an additional noise term, with spatially long-ranged correlations, on the long-time, long-wavelength behavior of this model. Above an upper critical dimension d _LR, the long-ranged noise is always relevant. In contrast, for d<d _LR, we find a weak noise regime dominated by short-range noise. As the range of the noise correlations increases, an intricate sequence of stability exchanges between different fixed points of the renormalization group occurs. Both smooth and discontinuous crossovers between the associated universality classes are observed, reflected in the scaling exponents. We discuss the necessary techniques in some detail since they are applicable to a much wider range of problems.