Self-assembly of fullerene-rich nanostructures with a stannoxane core

Fullerene derivatives bearing a carboxylic acid function undergo self-assembly with n-butylstannonic acid (nBuSn(O)OH) to produce fullerene-rich nanostructures with a stannoxane core in almost quantitative yields.     

Influence of deposition conditions on the optical properties of erbium-doped yttrium oxide films grown by aerosol-UV assisted MOCVD

Erbium-doped Y₂O₃ films were prepared by aerosol-UV assisted metal-organic chemical vapour deposition (MOCVD) at 410 °C. The effects of humidity of carrier gas and UV-assistance on their structure and optical properties were investigated on the as-deposited and thermal annealed films using infrared spectroscopy, X-ray diffraction and transmission electron microscopy. It was found that the as-deposited Er:Y₂O₃ films crystallise in the Y₂O₃ cubic structure and present a very low organic contamination when the deposition takes place under high air humidity and, even better, with UV-assistance. After annealing, two different structural phases are observed corresponding to the cubic and the monoclinic structures of Y₂O₃. The Er³⁺ luminescence analysed in the visible and IR regions, shows the classical green transitions. The best optical properties were obtained with as-deposited and annealed Er:Y₂O₃ films grown under high air humidity with UV-assistance. Under such deposition conditions, ⁴I_13/2 lifetimes was found to be 3.07 and 6.1 ms for films annealed at 800 and 1000 °C, respectively, and up-conversion phenomena were underlined. This indicates that the deposition conditions, in particular air humidity, play an important role in the luminescent properties even after annealing.     

Use of ram extruder as a combined rheo-tribometer to study the behaviour of high yield stress fluids at low strain rate

We propose in this work to provide an efficient and simple extruder device able to evaluate the rheological and tribological behaviour of high yield stress fluids, such as extrudible materials. An extruder able to measure simultaneously both the friction force acting on the extruder wall and the total extrusion force is developed. Based on previous studies, an efficient and accurate method of data analysis is then proposed and applied in order to obtain both a flow curve and a tribological law. Experimental tests are performed on soft modelling clay, kaolin paste and cement-based materials. Results are compared to conventional rheometry measurements. This comparison helps to evaluate the accuracy of the proposed experimental device and procedure.     

On Well-Posedness of 2D Dissipative Quasi-Geostrophic Equation in Critical Mixed Norm Lebesgue Spaces

We establish local and global well-posedness of the 2D dissipative quasi-geostrophic equation in critical mixed norm Lebesgue spaces. The result demonstrates the persistence of the anisotropic behavior of the initial data under the evolution of the 2D dissipative quasi-geostrophic equation. The phenomenon is a priori nontrivial due to the nonlocal structure of the equation. Our approach is based on Kato's method using Picard's iteration, which can be adapted to the multi-dimensional case and other nonlinear non-local equations. We develop time decay estimates for solutions of fractional heat equation in mixed norm Lebesgue spaces that could be useful for other problems.     

Regularity of Inhomogeneous Quasi-Linear Equations on the Heisenberg Group

We establish Hölder continuity of the horizontal gradient of weak solutions to quasi-linear $p$-Laplacian type non-homogeneous equations in the Heisenberg Group.     

A fractional isoperimetric problem in the Wiener space

We introduce a notion of fractional perimeter in an abstract Wiener space and show that half-spaces are the only volume-constrained minimisers.     

ESTIMATION OF PARAMETERS IN A CLOSED PYGMY POPULATION IN CAMEROON

Inspired by Kouakep [16], we consider in this note a wellposed model with differential susceptibility and infectivity adding continuous age structure to an ODE model for a Baka pygmy group in the East of Cameroon(Africa).Assuming a very low contribution of carriers to infection compared to acute infection, we estimate a probability p(a)(to develop symptomatic Hepatitis B state at age a) and acute carriers' transmission rate. The value R_0= 2:67 1 of the basic reproduction number estimated from data in the east of Cameroon confirms that HBV is endemic in the Baka pygmy group.     

A free boundary problem for the Laplacian with a constant Bernoulli-type boundary condition

We study a free boundary problem for the Laplace operator, where we impose a Bernoulli-type boundary condition. We show that there exists a solution to this problem. We use A. Beurling’s technique, by defining two classes of sub- and super-solutions and a Perron argument. We try to generalize here a previous work of A. Henrot and H. Shahgholian. We extend these results in different directions.     

Reaction-Diffusion Equations in Homogeneous Media: Existence,Uniqueness and Stability of Travelling Fronts

The goal of this survey is to describe the construction and some qualitative properties of particular global solutions of certain reaction-diffusion equations. These solutions are known as travelling fronts (or travelling waves) and play an important role in the long-time behaviour of the solutions of the parabolic system. We will mainly focus on the existence of travelling wave solutions and their stability. We will also give some standard tools in elliptic and parabolic theory, which are of general interest.     

Functionalization and Rearrangement of Spirocyclohexadienyl Oxindoles: Experimental and Theoretical Investigations

The preparation and functionalization of spirocyclohexa‐2,5‐diene oxindoles is described. The spirocyclic core of the title compounds was installed by using a SmI₂‐mediated cyclization of aryl iodobenzamides. Epoxidation with CF₃CO₃H was then carried out and was shown to occur with a high level of diastereocontrol: the reagent approaches the diene moiety syn to the amide group, which is likely to be as a consequence of hydrogen bonding between the amide C?O bond and the peracid hydrogen. Carbanionic functionalization of the spirocyclohexa‐2,5‐diene oxindoles was then examined, leading to an unprecedented rearrangement of the strained spiro system into dearomatized phenanthridinones. Upon treatment with lithium diisopropylamide (LDA) at ?40 °C, the dienes rearranged to provide a phenanthridinone lithium enolate intermediate that was trapped by electrophiles including alkyl halides and aldehydes. Interestingly, alkylation and hydroxyalkylation occurred with different regiocontrol. DFT calculations were performed that rationalize the observed skeleton rearrangement, emphasizing the role of LDA/diisopropylamine in this rearrangement. The proposed mechanism thus relies on a thermodynamically driven diisopropylamine‐mediated proton transfer with the cleavage of the diene–amide C?O bond as the key step.