A Note on the analytic solutions of the Camassa–Holm equation

In this Note we are concerned with the well-posedness of the Camassa–Holm equation in analytic function spaces. Using the Abstract Cauchy–Kowalewski Theorem we prove that the Camassa–Holm equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic, belongs to $H^s(\mathbb{R})$ with $s>3/2$, $6u_0{6}_{L^1}<\infty$ and $u_0?u_{0xx}$ does not change sign, we prove that the solution stays analytic globally in time. To cite this article: M.C. Lombardo et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

A Universal Cassette-Based System for the Dissolution of Solid Targets

Cyclotron-based radionuclides production by using solid targets has become important in the last years due to the growing demand of radiometals, e.g., ⁶⁸Ga, ⁸⁹Zr, ^43/47Sc, and ^52/54Mn. This shifted the focus on solid target management, where the first fundamental step of the radiochemical processing is the target dissolution. Currently, this step is generally performed with commercial or home-made modules separated from the following purification/radiolabelling modules. The aim of this work is the realization of a flexible solid target dissolution system to be easily installed on commercial cassette-based synthesis modules. This would offer a complete target processing and radiopharmaceutical synthesis performable in a single module continuously. The presented solid target dissolution system concept relies on an open-bottomed vial positioned upon a target coin. In particular, the idea is to use the movement mechanism of a syringe pump to position the vial up and down on the target, and to exploit the heater/cooler reactor of the module as a target holder. All the steps can be remotely controlled and are incorporated in the cassette manifold together with the purification and radiolabelling steps. The performance of the device was tested by processing three different irradiated targets under different dissolution conditions.     

Switching of fluorescence mediated by a peroxynitrite-glutathione redox reaction in a porous silicon nanoreactor

A nanostructured porous silicon chip functionalized with dichlorofluorescein is employed as a nanoreactor to respond to Reactive Oxygen Species (ROS) and to real-time studying redox reactions.     

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper, we investigate the asymptotic validity of boundary-layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl’s boundary-layer solution to Navier-Stokes solutions with different Reynolds numbers. We show how Prandtl’s solution develops a finite-time separation singularity. On the other hand, the Navier-Stokes solutions are characterized by the presence of two distinct types of viscous-inviscid interactions that can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover, we apply the complex singularity-tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective.     

Bioconjugate functionalization of thermally carbonized porous silicon using a radical coupling reaction

The high stability of Salonen's thermally carbonized porous silicon (TCPSi) has attracted attention for environmental and biochemical sensing applications, where corrosion-induced zero point drift of porous silicon-based sensor elements has historically been a significant problem. Prepared by the high temperature reaction of porous silicon with acetylene gas, the stability of this silicon carbide-like material also poses a challenge--many sensor applications require a functionalized surface, and the low reactivity of TCPSi has limited the ability to chemically modify its surface. This work presents a simple reaction to modify the surface of TCPSi with an alkyl carboxylate. The method involves radical coupling of a dicarboxylic acid (sebacic acid) to the TCPSi surface using a benzoyl peroxide initiator. The grafted carboxylic acid species provides a route for bioconjugate chemical modification, demonstrated in this work by coupling propylamine to the surface carboxylic acid group through the intermediacy of pentafluorophenol and 1-ethyl-3-[3-dimethylaminopropyl]carbodiimide hydrochloride (EDC). The stability of the carbonized porous Si surface, both before and after chemical modification, is tested in phosphate buffered saline solution and found to be superior to either hydrosilylated (with undecylenic acid) or thermally oxidized porous Si surfaces.     

Thermodynamics of azurin folding

The role played by the metal ion in thermodynamics of azurin folding was addressed by studying the thermal denaturation of the apo-form by differential scanning calorimetry (DSC), and by comparing the results with data concerning the holo protein. The thermal unfolding experiments showed that at 25°C the presence of metal ion increases the thermodynamic stability of azurin by 24 kJ mol⁻¹. A comparison between the unfolding and the copper binding free energies allow us to assert that the unfolded polypeptide chain binds copper and subsequently folds into native holo azurin, being this the thermodynamically most favourable process in driving azurin folding.     

Non-classical Velocity Statistics in Counterflow Quantum Turbulence

In this work we analyse the statistical distribution of turbulent superfluid velocity components in a He II counterflow channel, via two-dimensional numerical simulations presented in past studies. The Probability Density Functions (PDFs) of the superfluid velocity components are investigated at lengthscales smaller than the average intervortex spacing, for varying vortex densities and different wall-normal distances. The results obtained confirm the non-classical signature of quantum turbulence already observed in past numerical studies.     

A direct method to find solutions of some type of coupled Korteweg-de Vries equations using hyperelliptic functions of genus two

We suggest how one can obtain exact solutions of some type of coupled Korteweg-de Vries equations by means of hyperelliptic functions of genus two.