Fourth-order Schr\"odinger type operator with singular potentials

In this paper we study the biharmonic operator perturbed by an inverse fourth-order potential. In particular, we consider the operator $A=\Delta^2-V=\Delta^2-c|x|^{-4}$ where $c$ is any constant such that $c<\left(\frac{N(N-4)}{4}\right)^2$. The semigroup generated by $-A$ in $L^2(\mathbb{R}^N)$, $N\geq5$, extrapolates to a bounded holomorphic $C_0$-semigroup on $L^p(\mathbb{R}^N)$ for $p\in [p^{'}_0,p_0]$ where $p_0=\frac{2N}{N-4}$ and $p_0^{'}$ is its dual exponent. Furthermore, we study the boundedness of the Riesz transform $\Delta A^{-1/2}$ on $L^p(\mathbb{R}^N)$ for all $p\in(p_0^{'},2]$

A long and thorny road: Regulatory cooperation under the framework for advancing transatlantic economic integration

When the European Union and the United States agreed on the Framework for Advancing Transatlantic Economic Integration at the EU-US Summit on 30 April 2007, creating the Transatlantic Economic Council (TEC), they praised themselves for opening a new era in transatlantic regulatory cooperation. Transatlantic integration and growth were said to be enhanced and efforts to reduce barriers to transatlantic trade and investment redoubled. However, after two meetings of the TEC with only modest achievements, enthusiasm has faded quickly and finger pointing has begun anew. What went wrong

OR.NET - Approaches for Risk Analysis and Measures of Dynamically Interconnected Medical Devices

Nowadays, it lacks an open, standardized and dynamic interconnection of medical devices. All existing combinations of medical devices consist of isolated solutions with proprietary interfaces, as no common standards for networking and the exchange of data of medical devices exist. This situation leads to confusing operating rooms and inefficient operations. Thus, new strategies need to be developed for the authorization of dynamically interconnected medical devices. Primarily, those concern of an acquisition and methodical adaption of new requirements and risks resulting from this way of interconnection. The approach is to develop a method for a risk analysis for interconnected medical devices, which is structured modular and consists of a risk assessment of the standalone device and a risk analysis for the interconnection considering the risks involved in the transfer of functions. When interconnecting the medical devices the risk analysis of each of the devices is taken and they are compared by a gap analysis. Through this strategy it will be possible to realize a standard-compliant dynamic interconnection of medical products, which would be advantageous both for clinic operators and producers. This paper presents the current situation of the authorization of combined medical devices and proposes a strategy for the risk management of dynamically interconnected medical devices as a substantial part of the authorization

Correction of Optical Aberrations in Elliptic Neutron Guides

Modern, nonlinear ballistic neutron guides are an attractive concept in neutron beam delivery and instrumentation, because they offer increased performance over straight or linearly tapered guides. However, like other ballistic geometries they have the potential to create significantly non-trivial instrumental resolution functions. We address the source of the most prominent optical aberration, namely coma, and we show that for extended sources the off-axis rays have a different focal length from on-axis rays, leading to multiple reflections in the guide system. We illustrate how the interplay between coma, sources of finite size, and mirrors with non-perfect reflectivity can therefore conspire to produce uneven distributions in the neutron beam divergence, the source of complicated resolution functions. To solve these problems, we propose a hybrid elliptic-parabolic guide geometry. Using this new kind of neutron guide shape, it is possible to condition the neutron beam and remove almost all of the aberrations, whilst providing the same performance in beam current as a standard elliptic neutron guide. We highlight the positive implications for a number of neutron scattering instrument types that this new shape can bring.Comment: Presented at NOP2010 Conference in Alpe d'Huez, France, in March 201