A hypercyclic finite rank perturbation of a unitary operator

A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space \H are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.Comment: published in Mathematische Annale

Measuring order in the isotropic packing of elastic rods

The packing of elastic bodies has emerged as a paradigm for the study of macroscopic disordered systems. However, progress is hampered by the lack of controlled experiments. Here we consider a model experiment for the isotropic two-dimensional confinement of a rod by a central force. We seek to measure how ordered is a folded configuration and we identify two key quantities. A geometrical characterization is given by the number of superposed layers in the configuration. Using temporal modulations of the confining force, we probe the mechanical properties of the configuration and we define and measure its effective compressibility. These two quantities may be used to build a statistical framework for packed elastic systems.Comment: 4 pages, 5 figure

Finite-distance singularities in the tearing of thin sheets

We investigate the interaction between two cracks propagating in a thin sheet. Two different experimental geometries allow us to tear sheets by imposing an out-of-plane shear loading. We find that two tears converge along self-similar paths and annihilate each other. These finite-distance singularities display geometry-dependent similarity exponents, which we retrieve using scaling arguments based on a balance between the stretching and the bending of the sheet close to the tips of the cracks.Comment: 4 pages, 4 figure

Impact of pump phase modulation on system performance of fibre-optical parametric amplifiers

Bit error rate induced in a parametric amplifier has been measured with a 10 Gbit=s line rate. It is shown experimentally that the phase modulation of the pump distorts the mark level of the channel and may cause system penalty. Different phase modulation schemes have been compared

Impact of pump OSNR on noise figure for fiber-optical parametric amplifiers

Electrical measurements of the noise figure of a fiberoptical parametric amplifier are presented and compared with optical measurements. The transfer of pump noise by four-wave mixing was clearly demonstrated. A numerical model was developed to simulate the transfer of pump noise and validated by these measurements. Using this model, we determine, for practical systems, a minimum required pump optical signal-to-noise ratio of 65 dB

Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems

Nigerian scam e-mails and the charms of capital

So-called '419' or 'advance-fee' e-mail frauds have proved remarkably successful. Global losses to these scams are believed to run to billions of dollars. Although it can be assumed that the promise of personal gain which these e-mails hold out is part of what motivates victims, there is more than greed at issue here. How is it that the seemingly incredible offers given in these unsolicited messages can find an audience willing to treat them as credible? The essay offers a speculative thesis in answer to this question. Firstly, it is argued, these scams are adept at exploiting common presuppositions in British and American culture regarding Africa and the relationships that are assumed to exist between their nations and those in the global south. Secondly, part of the appeal of these e-mails lies in the fact that they appear to reveal the processes by which wealth is created and distributed in the global economy. They thus speak to their readers’ attempts to map or conceptualise the otherwise inscrutable processes of that economy. In the conclusion the essay looks at the contradictions in the official state response to this phenomena

Spectral and spatial shaping of a laser-produced ion beam for radiation-biology experiments

International audience; The study of radiation biology on laser-based accelerators is most interesting due to the unique irradiation conditions they can produce, in terms of peak current and duration of the irradiation. In this paper we present the implementation of a beam transport system to transport and shape the proton beam generated by laser-target interaction for in vitro irradiation of biological samples. A set of four permanent magnet quadrupoles is used to transport and focus the beam, efficiently shaping the spectrum and providing a large and relatively uniform irradiation surface. Real time, absolutely calibrated, dosimetry is installed on the beam line, to enable shot-to-shot control of dose deposition in the irradiated volume. Preliminary results of cell sample irradiation are presented to validate the robustness of the full system

On the Bohr inequality

The Bohr inequality, first introduced by Harald Bohr in 1914, deals with finding the largest radius $r$, $0<r<1$, such that $\sum_{n=0}^\infty |a_n|r^n \leq 1$ holds whenever $|\sum_{n=0}^\infty a_nz^n|\leq 1$ in the unit disk $\mathbb{D}$ of the complex plane. The exact value of this largest radius, known as the \emph{Bohr radius}, has been established to be $1/3.$ This paper surveys recent advances and generalizations on the Bohr inequality. It discusses the Bohr radius for certain power series in $\mathbb{D},$ as well as for analytic functions from $\mathbb{D}$ into particular domains. These domains include the punctured unit disk, the exterior of the closed unit disk, and concave wedge-domains. The analogous Bohr radius is also studied for harmonic and starlike logharmonic mappings in $\mathbb{D}.$ The Bohr phenomenon which is described in terms of the Euclidean distance is further investigated using the spherical chordal metric and the hyperbolic metric. The exposition concludes with a discussion on the $n$-dimensional Bohr radius

Military business and the business of the military

Contrary to dominant approaches that locate the causes for military entrepreneurialism in eastern Democratic Republic of the Congo predominantly in criminal military elites, this article highlights the importance of the Congolese military’s (FARDC) civilian context for understanding military revenue-generation. It analyses how the latter is shaped by structures of domination, signification and legitimisation that drive and are driven by the FARDC’s governance, private protection and security practices. It argues that these practices contribute to bestowing a degree of legitimacy on both the FARDC’s position of power and some of its revenue-generation activities. Furthermore, by emphasising that the FARDC’s regulatory and protection practices are partly the product of popular demands and the routine actions of civilians, the article contends that the causes of military revenue-generation are co-located in the military’s civilian environment. In this manner, it offers a more nuanced conceptualisation of military entrepreneurialism, thus opening up new perspectives on policy interventions in this area