Discrete-Time Multi-Scale Systems

We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the polydisc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.     

Deconvolution method for recovering the photon time-of-flight distribution from time-resolved measurements

A nonparametric deconvolution algorithm for recovering the photon time-of-flight distribution (TOFD) from time-resolved (TR) measurements is described. The algorithm combines wavelet denoising and a two-stage deconvolution method based on generalized singular value decomposition and Tikhonov regularization. The efficacy of the algorithm was tested on simulated and experimental TR data and the results show that it can recover the photon TOFD with high fidelity. Combined with the microscopic Beer-Lambert law, the algorithm enables accurate quantification of absorption changes from arbitrary time-of-flight windows, thereby optimizing the depth sensitivity provided by TR measurements.     

Reiterated Ergodic Algebras and Applications

We redefine the homogenization algebras without requiring the separability assumption. We show that this enables one to treat more complicated homogenization problems than those solved by the previous theory. In particular we exhibit an example of algebra which, contrary to the algebra of almost periodic functions, induces no homogenization algebra. We prove some general compactness results which are then applied to the resolution of some homogenization problems related to the generalized Reynolds type equations and to some nonlinear hyperbolic equations.     

Neumann problem for a quasilinear elliptic equation in a varying domain

We investigate the Neumann problem for a nonlinear elliptic operator of Leray–Lions type in ${\Omega }^{(s)}=\Omega \backslash F^{(s)}$, $s=1,2,\dots$, where Ω is a domain in ${\mathbf{R}}^n$$(n?3)$, $F^{(s)}$ is a closed set located in the neighborhood of a $(n?1)$-dimensional manifold Γ lying inside Ω. We study the asymptotic behavior of $u^{(s)}$ as $s\to \infty$, when the set $F^{(s)}$ tends to Γ. To cite this article: M. Sango, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Local strong solution for the incompressible Korteweg model

We consider a Navier–Stokes type system with a Korteweg stress tensor, coupled with a concentration equation without diffusion. We give a result concerning the local in time existence (and uniqueness) of strong solution for any data (and the global in time existence defined in a interval $(0,T)$ for $T<+\infty$ fixed if data are small enough), in the case of a bounded domain $\Omega ?{\mathbb{R}}^3$. To cite this article: M. Sy et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Controllability for some integrodifferential equations driven by vector measures

In this work, we consider the question of controllability of a class of integrodifferential equations on Hilbert space with measures as controls. We assume that the linear part has a resolvent operator in the sense given by R. Grimmer. We generalize the original work of N. Ahmed on vector measures, and we use it to develop necessary and sufficient conditions for weak and the exact controllability of the integrodifferential equation. Using the latter, we prove that exact controllability of the integrodifferential equation implies exact controllability of a perturbed integrodifferential equation. Controllability problem for the perturbed system is formulated fixed point problem in the space of vector measures. Our results cover impulsive controls as well as regular controls. Copyright © 2016 John Wiley & Sons, Ltd.     

SbCl3 as a Highly Efficient Catalyst for the Acetylation of Alcohols,Phenols, and Amines under Solvent‐Free Conditions

Antimony trichloride has been found to be an efficient and expedient catalyst for the acylation of alcohols, phenols, amines, and sugars with acetic anhydride in high yields and in a short reaction time under solvent‐free conditions at room temperature. Also, racemization of chiral alcohols and epimerization of sugars were not observed in any of the substrates.     

pKa calculations of aliphatic amines, diamines, and aminoamides via density functional theory with a Poisson-Boltzmann continuum solvent model

In order to make reliable predictions of the acid-base properties of macroligands with a large number of ionizable sites such as dendrimers, one needs to develop and validate computational methods that accurately estimate the acidity constants (pKa) of their chemical building blocks. In this article, we couple density functional theory (B3LYP) with a Poisson-Boltzmann continuum solvent model to calculate the aqueous pKa of aliphatic amines, diamines, and aminoamides, which are building blocks for several classes of dendrimers. No empirical correction terms were employed in the calculations except for the free energy of solvation of the proton (H+) adjusted to give the best match with experimental data. The use of solution-phase optimized geometries gives calculated pKa values in excellent agreement with experimental measurements. The mean absolute error is <0.5 pKa unit in all cases. Conversely, calculations for diamines and aminoamides based on gas-phase geometries lead to a mean absolute error >0.5 pKa unit compared to experimental measurements. We find that geometry optimization in solution is essential for making accurate pKa predictions for systems possessing intramolecular hydrogen bonds.     

Vertex-minor reductions can simulate edge contractions

We prove that local complementation and vertex deletion, operations from which vertex-minors are defined, can simulate edge contractions. As an application, we prove that the rank-width of a graph is linearly bounded in term of its tree-width.