Wave features related to a mathematical model describing pulse transmission in a nerve fibre

In order to describe the signal transmission in a nerve fibre, we consider a non-linear mathematical model which takes into account several dissipative mechanisms. By assuming different orders of magnitude for the relaxation times associated with each of them, we carry out an asymptotic analysis pointing out the wave features in different situations.     

Wave-Like Solutions for a Class of Parabolic Models

A reduction aproach is developed for determining exact solutions of anonlinear second order parabolic PDE. The method in point makes acomplementary use of the leading ideas of the theory of quasilinearhyperbolic systems of first order endowed by differential constraintsand of the techniques providing multiple wave-like solutions ofnonlinear PDEs. The searched solutions exhibit a inherent wave featuresand they are obtained by solving a consistent overdetermined system ofPDEs. Remarkably, in the process it is possible to define nonlinearmodel equations which allow special classes of initial or boundary valueproblems to be solved in a closed form. Within the present reductionapproach exact solutions and model material response functions areobtained for an equation of widespread application in many fields ofinterest.     

A strong form of the quantitative isoperimetric inequality

We give a refinement of the quantitative isoperimetric inequality. We prove that the isoperimetric gap controls not only the Fraenkel asymmetry but also the oscillation of the boundary.     

Weak lower semicontinuity for polyconvex integrals in the limit case

We prove a lower semicontinuity result for polyconvex functionals of the Calculus of Variations along sequences of maps \(u:\Omega \subset \mathbb{R }^n\rightarrow \mathbb{R }^m\) in \(W^{1,m}\) , \(2\le m\le n\) , bounded in \(W^{1,m-1}\) and convergent in \(L^1\) under mild technical conditions but without any extra coercivity assumption on the integrand.     

Constraining dark matter models from a combined analysis of Milky Way satellites with the Fermi Large Area Telescope

Satellite galaxies of the Milky Way are among the most promising targets for dark matter searches in gamma rays. We present a search for dark matter consisting of weakly interacting massive particles, applying a joint likelihood analysis to 10 satellite galaxies with 24 months of data of the Fermi Large Area Telescope. No dark matter signal is detected. Including the uncertainty in the dark matter distribution, robust upper limits are placed on dark matter annihilation cross sections. The 95% confidence level upper limits range from about 10(-26) cm3 s(-1) at 5 GeV to about 5×10(-23) cm3 s(-1) at 1 TeV, depending on the dark matter annihilation final state. For the first time, using gamma rays, we are able to rule out models with the most generic cross section (～3×10(-26) cm3 s(-1) for a purely s-wave cross section), without assuming additional boost factors.     

An analytical strategy for identification of a somatotropin‐like bioactive peptide by ion trap liquid chromatography/electrospray ionization tandem mass spectrometry after immuno‐affinity purification from buffalo serum

The use of growth hormones, such as native and recombinant somatotropins, is forbidden in the European Union (EU), but is legal in the USA. The misuse of recombinant bovine somatotropin in Italy is suspected for enhancing milk production, thanks to its availability on the illegal market. A synthetic bioactive peptide of 27 amino acids derived from bovine somatotropin was successfully tested in France and in southern Italy for scientific purposes, to stimulate milk production, both in cows and buffaloes. This somatotropin‐like peptide (PEP‐ST), suspected for illegal use in southern Italy, was synthesized by linking the 104–113 sequence of bovine somatotropin to the 323–339 sequence of ovalbumin. Herein, a method for detection and identification of the PEP‐ST in buffalo serum is described; our strategy was based on the production of IgG anti‐PEP‐ST, used to synthesize an immuno‐affinity column for peptide purification from buffalo serum, prior to analysis by ion trap liquid chromatography/electrospray ionization tandem mass spectrometry (LC/ESI‐MS/MS). The immuno‐affinity column was successfully used to purify in a single step the bioactive PEP‐ST from buffalo serum samples spiked at 20, 50 and 200 µg/mL for confirmatory analysis. Ion trap LC/ESI‐MS/MS identification was based on detection of a multi‐charged molecular ion and its characteristic fragmentation pattern. No significant matrix interference was observed, accounting for method specificity. We consider this strategy to be a basic approach that could be improved in the perspective of the official control of illegal use of somatotropin and somatotropin‐like compounds in buffalo breeding. Copyright © 2009 John Wiley & Sons, Ltd.     

Higher integrability of the gradient and dimension of the singular set for minimisers of the Mumford–Shah functional

The paper is concerned with the higher regularity properties of the minimizers of the Mumford–Shah functional. It is shown that, near to singular points where the scaled Dirichlet integral tends to 0, the discontinuity set is close to an Almgren area minimizing set. As a byproduct, the set of singular points of this type has Hausdorff dimension at most N-2, N being the dimension of the ambient space. Assuming higher integrability of the gradient this leads to an optimal estimate of the Hausdorff dimension of the full singular set. Received: 5 July 2001 / Accepted: 29 November 2001 / Published online: 23 May 2002     

Optimal control for Multi-Conjugate Adaptive Optics

Classic adaptive optics (AO) is now a proven technique that provides a closed loop real time correction of the turbulence. It is generally based on simple and efficient control algorithms. The next AO generation (Multi-Conjugate AO (MCAO) in its various forms and Extreme AO (XAO)) will require more sophisticated control approaches, especially in the case of wide field AO. We present here the concepts behind optimal control. The advantages compared to more standard approaches are stressed. A first experimental validation is presented. To cite this article: C. Petit et al., C. R. Physique 6 (2005).