On the Cauchy problem for non-effectively hyperbolic operators,the Gevrey 5 well-posedness

In this paper, we prove that for non-effectively hyperbolic operators with smooth double characteristics exhibiting a Jordan block of size 4 on the double manifold, the Cauchy problem is well-posed in the Gevrey 5 class, beyond the generic Gevrey class 2 (see, e.g., [5]). Moreover, we show that this value is optimal, due to certain geometric constraints on the Hamiltonian flow of the principal symbol. These results, together with results already proved, give a complete picture of the well-posedness of the Cauchy problem around hyperbolic double characteristics.     

Evolution of two concentrated vortices in a two-dimensional bounded domain

We prove that two initially concentrated vortices with opposite vorticity of an incompressible ideal fluid moving in a two-dimensional bounded domain, remain concentrated during the time. The motion of their centers converges to the solution of the point vortex model with the corresponding initial conditions.     

IDENTIFICATION OF MEMBRANE PROTEINS IMAGED BY ATOMIC FORCE MICROSCOPY USING A TEMPLATE MATCHING ALGORITHM

The atomic force microscope allows to image biological samples in their native environment. But the identification and the topography of individual randomly distributed membrane proteins is still a challenge. We used membranes of isolated vacuoles of barley mesophyll cells. Images at low resolution indicate that vacuoles spontaneously attach, rupture and finally adsorb completely as planar membrane to mica. Height profiles indicate that the membrane at the peripheral boundary exposes the extravacuolar surface to the scanning tip. At molecular resolution a template matching correlation algorithm was used to identify the most abundant membrane protein, the vacuolar H⁺-ATPase by the characteristic extravacuolar head of the transport molecule. The data indicate the possibility to analyse single randomly distributed membrane proteins in their native environment with the knowledge of a suitable template.     

Host-guest-driven copolymerization of tetraphosphonate cavitands

The outstanding complexing properties of tetraphosphonate cavitands towards N‐methylpyridinium salts were exploited to realise a new class of linear and cyclic AABB supramolecular polymers through host–guest interactions. The effectiveness of the selected self‐association processes was tested by ¹H NMR studies, whereas microcalorimetric analyses clarified the binding thermodynamics and revealed the possibility of tuning entropic contributions by acting on the flexibility of the guest linker. Although the formation of linear polymeric chains for a rigid system was demonstrated by X‐ray analysis, the presence of a concentration‐dependent ring–chain equilibrium was indicated by solution viscosity measurements in the case of a very flexible ditopic BB guest co‐monomer.     

Chemically stable anode-supported solid oxide fuel cells based on Y-doped barium zirconate thin films having improved performance

Anode-supported solid oxide fuel cells (SOFCs) based on thin BaZr_0.8Y_0.2O_3 ? δ (BZY) electrolyte films were fabricated by pulsed laser deposition (PLD) on sintered NiO–BZY composite anodes. After in situ reduction of NiO to Ni, the anode substrates became porous, while retaining good adhesion with the electrolyte. A slurry-coated composite cathode made of La_0.6Sr_0.4Co_0.2Fe_0.8O_3 ? δ (LSCF) and BaCe_0.9Yb_0.1O_3 ? δ (BCYb), specifically developed for proton conducting electrolytes, was used to assemble fuel cell prototypes. Depositing by PLD 100 nm thick LSCF porous films onto the BZY thin films was essential to improve the cathode/electrolyte adhesion. A power density output of 110 mW/cm² at 600 °C, the largest reported value for an anode-supported fuel cell based on BZY at this temperature, was achieved. Electrochemical impedance spectroscopy (EIS) measurements were used to investigate the different contributions to the total polarization losses.     

A Mountain Pass-type Theorem for Vector-valued Functions

The mountain pass theorem for scalar functionals is a fundamental result of the minimax methods in variational analysis. In this work we extend this theorem to the class of \(\mathcal{C}^{1}\) functions \(f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{m}\), where the image space is ordered by the nonnegative orthant \(\mathbb{R}_{+}^{m}\). Under suitable geometrical assumptions, we prove the existence of a critical point of f and we localize this point as a solution of a minimax problem. We remark that the considered minimax problem consists of an inner vector maximization problem and of an outer set-valued minimization problem. To deal with the outer set-valued problem we use an ordering relation among subsets of \(\mathbb{R}^{m}\) introduced by Kuroiwa. In order to prove our result, we develop an Ekeland-type principle for set-valued maps and we extensively use the notion of vector pseudogradient.     

Lateral IBIC characterization of single crystal synthetic diamond detectors

In order to evaluate the charge collection efficiency (CCE) profile of single‐crystal diamond devices based on a p‐type/intrinsic/metal configuration, a lateral Ion Beam Induced Charge (IBIC) analysis was performed over their cleaved cross sections using a 2 MeV proton microbeam. CCE profiles in the depth direction were extracted from the cross‐sectional maps at variable bias voltage. IBIC spectra relevant to the depletion region extending beneath the frontal Schottky electrode show a 100% CCE, with a spectral resolution of about 1.5%. The dependence of the width of the high efficiency region from applied bias voltage allows the constant residual doping concentration of the active region to be evaluated. The region where the electric field is absent shows an exponentially decreasing CCE profile, from which it is possible to estimate the diffusion length of the minority carriers by means of a drift–diffusion model. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)