A Counter-Example to the Theorem of Hiemer and Snurnikov

A planar polygonal billiard $\mathcal{P}$ is said to have the finite blocking property if for every pair (O, A) of points in $\mathcal{P}$ there exists a finite number of “blocking” points B ₁,...,B _n such that every billiard trajectory from O to A meets one of the B _i 's. As a counter-example to a theorem of Hiemer and Snurnikov, we construct a family of rational billiards that lack the finite blocking property.     

A difluorosulfide as a Freon-free source of phosphonodifluoromethyl carbanion

The synthesis of difluoromethylphosphonates is becoming difficult due to environmental protective laws restricting the use of HCFCs and CFCs as starting chemicals. To circumvent this limitation, we report the preparation of a thioether as a new source of the lithiodifluoromethylphosphonate. This methodology avoiding the use of HCFCs involves a selective fluorination of sulfide followed by a thiaphilic addition of an organometallic reagent, which offers an alternative route to obtain phosphonodifluoromethyl carbanion. A contrasted reactivity, due to a medium effect, was also noted which allows addition of a wide range of electrophiles including nitroalkenes and DMF to thioethers.     

Size minimization and approximating problems

We consider Plateau type variational problems related to the size minimization of rectifiable currents. We realize the limit of a size minimizing sequence as a stationary varifold and a minimal set. Other examples of functionals to be minimized include the integral over the underlying carrying set of a power q of the multiplicity function, with .Because minimizing sequences may have unbounded mass we make use of a more general object called a rectifiable scan for describing the limit. This concept is motivated by the possibility of recovering a flat chain from a sufficiently large collection of its slices. In case the given boundary is smooth and compact, the limiting scan has finite mass and corresponds to a rectifiable current.Received: 11 February 2002, Accepted: 16 June 2002, Published online: 17 December 2002Mathematics Subject Classification (2000): 49Q15, 28A75Thierry De Pauw: The research of the first author was supported by a Marie Curie fellowship of the European Community program Human Potential under contract HMPF-CT-2001-01235Robert Hardt: The research of the second author was partially supported by NSF grant DMS-0072486     

Magnetic anisotropy in icosahedral cobalt clusters

Magnetic anisotropy has been measured in multiply twinned, icosahedral cobalt clusters. It is found that the low-temperature magnetization of deposited cluster layers is well defined with the Stoner–Wohlfarth model by averaging over clusters with a range of anisotropy energy. Anisotropy energy calculation based on Néel's pair model shows that the icosahedral structure and the layer-by-layer growth of the clusters induce oscillations of the magnetic anisotropy as a function of the filling of the outer surface of the particle. The magnetization measurement at room temperature indicates a weakly correlated cluster glass, as deduced from the approach to saturation that is well described with 2D random anisotropy model.     

Finite-time blowup for a complex Ginzburg–Landau equation with linear driving

In this paper, we consider the complex Ginzburg–Landau equation ${u_t = e^{i\theta} [\Delta u + |u|^\alpha u] + \gamma u}$ on ${\mathbb{R}^N}$ , where ${\alpha > 0,\,\gamma \in \mathbb{R}}$ and ${-\pi /2 < \theta < \pi /2}$ . By convexity arguments, we prove that, under certain conditions on ${\alpha,\theta,\gamma}$ , a class of solutions with negative initial energy blows up in finite time.     

On the transverse vibration of a rubber string

The nearly constant pitch of the sound radiated by a sufficiently stretched rubber cord, a phenomenon observed independently by two experimenters at the turn of the century, is explained analytically for three ideal rubberlike material models. Transverse vibrational frequency data for three kinds of rubber strings, obtained with the aid of a novel laser apparatus, are compared with the analytical results. A numerical scheme is introduced to compute from the experimental data the apparent average number of links in a molecular chain of a rubberlike material from both simple tension and transverse frequency measurements. It is shown that the nearly flat frequency response is a molecular network finite extensibility effect that is controlled by the apparent number of links in a chain of the molecular network structure.     

<Emphasis Type="Italic">J/Ψ</Emphasis>production

For more than 25 yearsJΨ production has helped to sharpen our understanding of QCD. In proton induced reaction some observations are rather well understood while others are still unclear. The current status of the theory ofJΨ production will be sketched, paying special attention to the issues of formation time andJΨ re-interaction in a nuclear medium.     

Synthèse et étude de modèles de NADH à noyaux accolés en série pyrrolo[2,3-b] et [3,2-b]pyridines

Pyrrolo[2,3-b] and [3,2-b]pyridines derivatives, precursors for annealated NADH models have been prepared. Several methods for building a pyridinic annealates ring have been used starting from 2- or 3-aminopyrrole. The corresponding dihydropyridine structure leads to highly reactive NADH models compounds and are very much more stable than common models.