Fock representations of quantum fields with generalized statistics

We develop a rigorous framework for constructing Fock representations of quantum fields obeying generalized statistics. The main features of these representations are investigated. Various aspects of the underlying mathematical structure are illustrated by means of explicit examples.     

Effect of SiO2 on relaxation phenomena and mechanism of ion conductivity of [Nafion/(SiO2)x] composite membranes

This report describes a study of the effect of SiO2 nanopowders on the mechanism of ionic motion and interactions taking place in hybrid inorganic-organic membranes based on Nafion. Five nanocomposite membranes of the formula [Nafion/(SiO2)x] with SiO2 ranging from 0 to 15 wt % were prepared by a solvent casting procedure. TG measurements demonstrated that the membranes are thermally stable up to 170 degrees C but with the loss water it changes the cluster environments and changes the conductivity properties. MDSC investigations in the 90-300 degrees C temperature range revealed the presence of three intense overlapping endothermal peaks indicated as I, II, and III. Peak I measures the order-disorder molecular rearrangement in hydrophilic polar clusters, II corresponds to the endothermic decomposition of -SO3 groups, and III describes the melting process in microcrystalline regions of hydrophobic fluorocarbon domains of the Nafion moiety. ESEM with EDAX measurements revealed that the membranes are homogeneous materials with smooth surfaces. DMA studies allowed us to measure two relaxation modes. The mechanical relaxation detected at ca. 100 degrees C is attributed to the motion of cluster aggregates of side chains and is diagnostic for R-SO3H...SiO2 nanocluster interactions. DMA disclosed that at SiO2/-SO3H (psi) molar ratios lower than 1.9, the oxoclusters act to restrict chain mobility of hydrophobic domains of Nafion and the dynamics inside polar cages of [Nafion/(SiO2)x] systems; at psi higher than 1.9, the oxoclusters reduce the cohesiveness of hydrophilic polar domains owing to a reduction in the density of cross-links. FT-IR and FT-Raman studies of the [Nafion/(SiO2)x] membranes indicated that the fluorocarbon chains of Nafion hydrophobic domains assume the typical helical conformation structure with a D(14pi/15) symmetry. These analyses revealed four different species of water domains embedded inside polar cages and their interconnecting channels: (a) bulk water [(H2O)n]; (b) water solvating the oxonium ions directly interacting with sulfonic acid groups [H3O+...SO3(-)-].(H2O)n; (c) water aggregates associated with H3O+ ions [H3O+.(H2O)n]; and (d) low associated water species in dimer form [(H2O)2]. The conductivity mechanism and relaxation events were investigated by broadband dielectric spectroscopy (BDS). [Nafion/(SiO2)x] nanocomposite membranes were found to possess two different molecular relaxation phenomena which are associated with the alpha-relaxation mode of PTFE-like fluorocarbon domains and the beta-relaxation mode of acid side groups of the Nafion component. Owing to their strong coupling, both these relaxation modes are diagnostic for the interactions between the polar groups of the Nafion host polymer and the (SiO2)x oxoclusters and play a determining role in the conductivity mechanism of the membranes. The studies support the proposal that long-range proton charge transfer in [Nafion/(SiO2)x] composites takes place due to a mechanism involving exchange of the proton between the four water domains. This latter proton transfer occurs owing to a subsequent combination of domain intersections resulting from the water domain fluctuations induced by the molecular relaxation events of host Nafion polymer.     

A new semifield of order 2

In [G. Lunardon, Semifields and linear sets of PG(1,q^t), Quad. Mat., Dept. Math., Seconda Univ. Napoli, Caserta (in press)], G. Lunardon has exhibited a construction method yielding a theoretical family of semifields of order q²ⁿ,n>1 and n odd, with left nucleus F_qⁿ, middle and right nuclei both F_q² and center F_q. When n=3 this method gives an alternative construction of a family of semifields described in [N.L. Johnson, G. Marino, O. Polverino, R. Trombetti, On a generalization of cyclic semifields, J. Algebraic Combin. 26 (2009), 1-34], which generalizes the family of cyclic semifields obtained by Jha and Johnson in [V. Jha, N.L. Johnson, Translation planes of large dimension admitting non-solvable groups, J. Geom. 45 (1992), 87-104]. For n>3, no example of a semifield belonging to this family is known.In this paper we first prove that, when n>3, any semifield belonging to the family introduced in the second work cited above is not isotopic to any semifield of the family constructed in the former. Then we construct, with the aid of a computer, a semifield of order 2¹⁰ belonging to the family introduced by Lunardon, which turns out to be non-isotopic to any other known semifield.     

A One-Pot Entry to a Novel 3-H-benzo[d]pyrazolo[1,5-b]isothiazole Ring System

Summary The phosphorus ylide obtained from the reaction between 2-aminobenzo[d]isothiazol-3-one and dimethyl acetylenedicarboxylate in the presence of triphenylphosphine undergoes a smooth intramolecular Wittig-type reaction to produce, in a one-pot reaction, 3-H-benzo[d]pyrazolo[1,5-b]isothiazole-2,3a-dicarboxylic acid dimethyl ester, a novel functionalized heterocyclic compound.     

New degree bounds for polynomial threshold functions

A real multivariate polynomial p(x ₁, …, x _n ) is said to sign-represent a Boolean function f: {0,1} ⁿ →{−1,1} if the sign of p(x) equals f(x) for all inputs x∈{0,1} ⁿ . We give new upper and lower bounds on the degree of polynomials which sign-represent Boolean functions. Our upper bounds for Boolean formulas yield the first known subexponential time learning algorithms for formulas of superconstant depth. Our lower bounds for constant-depth circuits and intersections of halfspaces are the first new degree lower bounds since 1968, improving results of Minsky and Papert. The lower bounds are proved constructively; we give explicit dual solutions to the necessary linear programs.     

Shape reconstruction of metallic objects from intensity scattered field data only

We address an inverse scattering problem using only amplitude information of the scattered field. In particular, we are concerned with the reconstruction of the shape of a metallic planar obstacle, located in a known plane (aperture plane), starting from the knowledge of the intensity of the scattered field over two measurement planes in near zone and parallel to the aperture plane, when a single-frequency incident plane wave is exploited. The formulation of the inverse scattering problem is given under the physical optics approximation, and thus the resulting phase retrieval problem is quadratic. This allows us to apply some phase retrieval techniques already developed for antenna diagnostics. Reconstruction results with synthetic data indicate the feasibility of the proposed approach.     

Hardware-in-the-loop simulation of wave energy converters based on dielectric elastomer generators

Dielectric elastomer generators (DEGs) are soft electrostatic generators based on low-cost electroactive polymer materials. These devices have attracted the attention of the marine energy community as a promising solution to implement economically viable wave energy converters (WECs). This paper introduces a hardware-in-the-loop (HIL) simulation framework for a class of WECs that combines the concept of the oscillating water columns (OWCs) with the DEGs. The proposed HIL system replicates in a laboratory environment the realistic operating conditions of an OWC/DEG plant, while drastically reducing the experimental burden compared to wave tank or sea tests. The HIL simulator is driven by a closed-loop real-time hydrodynamic model that is based on a novel coupling criterion which allows rendering a realistic dynamic response for a diversity of scenarios, including large scale DEG plants, whose dimensions and topologies are largely different from those available in the HIL setup. A case study is also introduced, which simulates the application of DEGs on an OWC plant installed in a mild real sea laboratory test-site. Comparisons with available real sea-test data demonstrated the ability of the HIL setup to effectively replicate a realistic operating scenario. The insights gathered on the promising performance of the analysed OWC/DEG systems pave the way to pursue further sea trials in the future.