Polyazomethines derived from polynuclear dihydroxyquinones and siloxane diamines

New polyazomethines have been synthesized based on polynuclear dihydroxy quinones (5,8-dihydroxy-1,4-naphthoquinone and 1,4-dihydroxyanthraquinone) and siloxane diamines differing by the siloxane sequence length (1,3-bis(3-aminopropyl)tetramethyldisiloxane and α,ω-bis(3-aminopropyl)oligodimethylsiloxane having about 12 siloxane units/sequence). The structures were verified by spectral analyses. Solubility tests, GPC and viscosity measurements were performed. Some properties of the resulted polymers were investigated by thermal (TGA and DSC), electrical, spectral (UV-Vis) and electrochemical (differential pulse voltammetry) methods.     

Cumulative plasmon field enhancement in finite metal particle chains

The dramatic field enhancement at the extremity of finite chains of strongly coupled gold nanoparticles illuminated under total internal reflection is investigated numerically. We demonstrate that high enhancement factors can be achieved by exploiting the in-plane forward scattering of the particles, with geometries achievable by state-of-the-art lithographic techniques.     

Fluid mechanics in rectangular cavities — analytical model and numerics

We present an analytical model of Stokes creeping flows in rectangular cavities. In the model, the fluid normal velocity at the wall is zero, while the fluid tangential velocity at the wall differs from the wall velocity. Numerical work is used to validate some of the ideas generated from this realizable model.     

Characterisation and evaluation of the environmental impact on historical parchments by differential scanning calorimetry

Our recent developments concerning the assessment of parchments deterioration using DSC are reported. Measurements performed on samples in excess water conditions, in static air and gas flow provided qualitative and quantitative information on parchment ageing and deterioration at microscopic and mesoscopic level, when assembly of fibres/fibrils is weakened, partially and eventually completely lost, and at molecular level, when triple helix uncoiling occurs. A damage ranking scale based on a large collection of DSC parameters obtained by investigating artificially aged samples was set up. Deconvolution of the DSC thermal denaturation peaks in excess water enabled evaluating and discriminating stability of parchments with similar damage levels. Further experimental evidences such as softening of the crystalline fraction of collagen, thermal-oxidation and collagen gelatinisation were detected by DSC measurements in gas flow and static air, and related to specific deterioration patterns. DSC measurement of wet samples provided an objective and reliable method for evaluating parchment shrinkage temperature overcoming the limitations of conventional methods.     

Molybdic Acid-Catalysed Isomerization of D-Ribulose and D-Xylulose to the Corresponding 2-C-(Hydroxymethyl)-D-Tetroses

ABSTRACT

2-C-(Hydroxymethyl)-D-erythrose (2) and 2-C-(hydroxymethyl)-D-threose (4) have been stereospecifically synthesized in one-step by a molybdic acid-catalysed isomerization reaction from respective D-xylulose (1) and D-ribulose (3). In the case of interconversion of 1 to 2, the content of the 2-C-branched chain tetrose in the equilibrium mixture can be doubled if boric acid is present in the reaction mixture in addition to the catalyst.     

Prescribing the Jacobian in critical spaces

We consider the Sobolev space $X = W^{s,p} \left( {\mathbb{S}^m ;\mathbb{S}^{k - 1} } \right)$ . We prove the existence of a robust distributional Jacobian Ju for u ∈ X, provided sp ≥ k ? 1; this generalizes a result of Bourgain, Brezis, and the second author [10] dealing with the case m = k. We identify the image of the map X ? u ? Ju in the critical case sp = k ? 1. This extends a result of Alberti, Baldo, and Orlandi [2] for s = 1 and p = k ? 1. We also present a new, analytical, dipole construction method.     

Existence of critical points with semi-stiff boundary conditions for singular perturbation problems in simply connected planar domains

Let Ω   be a smooth bounded simply connected domain in R²${\mathbb{R}}^2$. We investigate the existence of critical points of the energy _Eε(u)=1/2_∫Ω|∇u|²+1/(4ε²)_∫Ω(1−|u|²)²$E_{\epsilon }(u)=1/2{\int }_{\Omega }{|\mathrm{\nabla }u|}^2+1/(4{\epsilon }^2){\int }_{\Omega }{(1-{|u|}^2)}^2$, where the complex map u has modulus one and prescribed degree d on the boundary. Under suitable nondegeneracy assumptions on Ω, we prove existence of critical points for small ε. More can be said when the prescribed degree equals one. First, we obtain existence of critical points in domains close to a disk. Next, we prove that critical points exist in “most” of the domains.