Non-Liouville numbers and a Theorem of Hörmander

It is shown in this paper that Theorem 1 of [G. H. Meisters, “Translation-invariant linear forms and a formula for the Dirac measure,” J. Functional Analysis 8 (1971), 173–188] can be deduced from a very general result of Lars Hörmander, namely, Theorem 1 of “Generators for some rings of analytic functions” [Bull. Amer. Math. Soc.73 (1967), 943–949]. However, Hörmander's theorem is evidently not applicable in several other cases where Meisters'-type results have been obtained (e.g., Theorem 1 of G.H. Meisters and Wolfgang M. Schmidt, “Translation-invariant linear forms on L²(G) for compact abelian groups G,” J. Functional Analysis11 (1972), 407–424).     

Circular dichroism of helical structures using semiempirical methods

A general semiempirical scheme has been elaborated to simulate circular dichroism (CD) spectra of supramolecular systems. This approach adopts the analytical method of Beck and Hohlneicher [Theor. Chem. Acc. 101, 297 (1999).] to evaluate the one- and two-center integrals over Slater atomic orbitals. The performance of the method, employing INDO/S and CNDO/S semiempirical parametrizations, has been assessed by considering (i) the effect of the size of the singly excited states manifold, (ii) the origin invariance, and (iii) comparisons with the experimental and other theoretical spectra of several helicenes as well as pyridine-pyrimidine oligomers, which can adopt helical conformations. The main results are (i) the INDO/S parametrization with rather small excitation manifolds is able to reproduce, at low computational costs, the experimental CD spectra of several helicenes as well as CD simulations performed at ab initio and time-dependent density functional theory level of approximation; (ii) in the series of homohelicenes, the rotatory strength of the lowest-energy band increases almost linearly with the size of the helix; (iii) as evidenced by the study of tetradodecyloxy helicene bisquinone, packing effects can change the sign of remarkable CD bands, which are used to assign the structure configuration.     

Construction and Analysis of Lattice Boltzmann Methods Applied to a 1D Convection-Diffusion Equation

To solve the 1D (linear) convection-diffusion equation, we construct and we analyze two LBM schemes built on the D1Q2 lattice. We obtain these LBM schemes by showing that the 1D convection-diffusion equation is the fluid limit of a discrete velocity kinetic system. Then, we show in the periodic case that these LBM schemes are equivalent to a finite difference type scheme named LFCCDF scheme. This allows us, firstly, to prove the convergence in L ^∞ of these schemes, and to obtain discrete maximum principles for any time step in the case of the 1D diffusion equation with different boundary conditions. Secondly, this allows us to obtain most of these results for the Du Fort-Frankel scheme for a particular choice of the first iterate. We also underline that these LBM schemes can be applied to the (linear) advection equation and we obtain a stability result in L ^∞ under a classical CFL condition. Moreover, by proposing a probabilistic interpretation of these LBM schemes, we also obtain Monte-Carlo algorithms which approach the 1D (linear) diffusion equation. At last, we present numerical applications justifying these results.     

A synthetic "tour de force": well-defined multivalent and multimodal dendritic structures for biomedical applications

Dendrimers have several unique properties that make them attractive scaffolds for use in biomedical applications. To date, multivalent and multimodal dendritic structures have been synthesized predominantly by statistical modification of peripheral groups. However, the potential application of such probes in patients demands well-defined and monodisperse materials that have unique structures. Current progress in the field of chemical biology, in particular chemoselective ligation methods, renders this challenge possible. In this Minireview, we outline the different available synthetic strategies, some applications that already make use of this new generation of multivalent and multimodal architectures, and the challenges for future developments.     

Dynamic response of gold nanoparticle chemiresistors to organic analytes in aqueous solution

We investigate the response dynamics of 1-hexanethiol-functionalized gold nanoparticle chemiresistors exposed to the analyte octane in aqueous solution. The dynamic response is studied as a function of the analyte-water flow velocity, the thickness of the gold nanoparticle film and the analyte concentration. A theoretical model for analyte limited mass-transport is used to model the analyte diffusion into the film, the partitioning of the analyte into the 1-hexanethiol capping layers and the subsequent swelling of the film. The degree of swelling is then used to calculate the increase of the electron tunnel resistance between adjacent nanoparticles which determines the resistance change of the film. In particular, the effect of the nonlinear relationship between resistance and swelling on the dynamic response is investigated at high analyte concentration. Good agreement between experiment and the theoretical model is achieved.     

Semi-synthesis of a protease-activatable collagen targeting probe

A protease-activatable collagen targeting probe (proCNA35) is synthesized by conjugation of a synthetic collagen fragment to the collagen binding protein CNA35 via a protease-cleavable linker. Cleavage of the linker by MMP1 releases the intramolecular inhibition of the collagen binding site and restores its collagen binding capacity.     

Solvent effect on the mean dimensions of model polyelectrolytes

The influence of the polarisation of the solvent on the mean dimensions of model polyelectrolytes is incorporated by solving numerically the Poisson equation for each conformation of the chain embedded in a continuous dielectric media. The mean squared end to end distance reveals the screening effect introduced by the charges induced within the dielectric. The highest departure from continuous dielectric models occurs at intermediate values of the Coulomb coupling strength.